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Two essays in financial economics

University of Florida Institutional Repository
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TWO ESSAYS IN FINANCIAL ECONOM ICS: FIRM RISK REFLECTED IN SECURITY PRICES By STANISLAVA M. NIKOLOVA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Stanislava M. Nikolova

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I would like to dedicate this dissertati on to my parents, Margarita and Marincho Nikolovi; and my brother, Roumen Nikolov.

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ACKNOWLEDGMENTS I would like to thank my supervisory committee members Mark Flannery, Jason Karceski, Nimal Nimalendran, Dave Brown, and Chunrong Ai. All of them have made the completion of this dissertation possible. I am grateful for their willingness to review my doctoral research and to provide me with constructive comments. I am especially thankful to Mark Flannery, my supervisory committee chair, who has been a major source of academic and personal encouragement. I thank him for his guidance, patience, and friendship through the painful process of writing this dissertation. His contagious enthusiasm for research, and willingness to share his knowledge and experience, stimulated me and kept me going. I also thank Jason Karceski for being an invaluable mentor throughout my graduate studies, gladly helping anytime I requested professional or research advice. I am grateful to all the people of the Finance Department: the professors who guided me through coursework and supported my research; and the fellow graduate students, too numerous to name but instrumental in my growth as a scholar. Finally, I want to thank my friends, without whom I would have finished this dissertation much sooner. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES...........................................................................................................ix ABSTRACT.........................................................................................................................x CHAPTER 1 INTRODUCTION........................................................................................................1 2 INDUSTRIAL-FIRM RISK REFLECTED IN SECURITY PRICES: PREDICTING CREDIT RISK WITH IMPLIED ASSET VOLATILITY ESTIMATES................................................................................................................5 2.1. The State of the Literature.....................................................................................9 2.1.1. Contingent Claim Valuation Models...........................................................9 2.1.2. Applications of Contingent Claim Valuation............................................11 2.2. Methodologies for Constructing Risk Measures from Market Prices.................15 2.2.1. Methodologies for Calculating Implied Asset Value and Volatility.........15 2.2.2. Calculating Credit Risk Measures from Implied Asset Value and Volatility....................................................................................................17 2.2.3. Methodology Assumptions........................................................................18 2.3. Data Sources........................................................................................................20 2.3.1. Bond Prices and Characteristics................................................................20 2.3.1.1. Tax adjustment................................................................................22 2.3.1.2. Call-option adjustment....................................................................24 2.3.1.3. Yield spread aggregation.................................................................25 2.3.2. Equity Prices and Characteristics..............................................................26 2.3.3. Accounting Data........................................................................................26 2.3.4. Default Data...............................................................................................28 2.4. Summary Statistics..............................................................................................28 2.5. Realized Asset Volatility Tests............................................................................32 2.5.1. Correlation between Implied Asset Volatility and Realized Asset Volatility....................................................................................................34 2.5.2. Is Implied Asset Volatility a Rational Forecast of Realized Asset Volatility?..................................................................................................35 v

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2.5.3. Is Implied Asset Volatility a Better Forecast Than Historical Asset Volatility?..................................................................................................38 2.6. Default and Default Probability Tests.................................................................39 2.6.1. Tests Based on the Occurrence of Default................................................40 2.6.2. Tests Based on Credit Ratings...................................................................43 2.6.2. Tests Based on Altmans (1968) Z............................................................49 2.7. Sensitivity of Estimates to Alternative Model Assumptions...............................54 2.7.1. Summary Statistics....................................................................................54 2.7.2. Realized Asset Volatility Tests.................................................................55 2.7.3. Default and Default Probability Tests.......................................................56 2.8. Summary and Conclusion....................................................................................58 3 BANK RISK REFLECTED IN SECURITY PRICES: EQUITY AND DEBT MARKET INDICATORS OF BANK CONDITION.................................................87 3.1. Introduction..........................................................................................................87 3.2. Extracting Information about Firm Risk from Security Prices............................94 3.2.1. Review of Contingent Claim Valuation Models.......................................94 3.2.2. Methodologies for Calculating Implied Asset Value and Volatility.........97 3.2.3. Distance-to-Default Measures.................................................................101 3.3. Data Sources......................................................................................................102 3.3.1. Bond Prices and Characteristics..............................................................103 3.3.1.1. Tax adjustment..............................................................................105 3.3.1.2. Call-option adjustment..................................................................107 3.3.1.3. Yield spread aggregation...............................................................108 3.3.2. Equity Prices and Characteristics............................................................109 3.3.3. Accounting Data......................................................................................109 3.4. Sample Selection and Summary Statistics.........................................................109 3.4. Relative Accuracy of Market Indicators of Risk...............................................113 3.5. Relative Forecasting Ability of Market Indicators of Risk...............................119 3.5.1. Forecasting Material Changes in Default Probability.............................119 3.5.2. Forecasting Changes in Asset Quality.....................................................122 3.6. Sensitivity of Market Indicators to Alternative Model Assumptions................125 3.7. Conclusions........................................................................................................128 4 CONCLUSION.........................................................................................................156 LIST OF REFERENCES.................................................................................................159 BIOGRAPHICAL SKETCH...........................................................................................166 vi

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LIST OF TABLES Table page 2-1. Summary statistics......................................................................................................61 2-2. Simple and rank correlations......................................................................................62 2-3. Simple and rank correlations of implied and historical asset volatility with realized asset volatility.............................................................................................63 2-4. Analysis of IAV and HAV forecasting properties......................................................64 2-5. Analysis of the relative informational content of IAV and HAV in forecasting RAV.........................................................................................................................65 2-6. Average DD statistics by default status......................................................................67 2-7. Logit analysis of defaults............................................................................................68 2-8. Median distance-to-default estimates by Moodys credit rating................................69 2-9. Median changes in distance-to-default estimates by Moodys credit rating change.......................................................................................................................70 2-10. Analysis of Moodys credit ratings..........................................................................71 2-11. Logit analysis of credit rating changes.....................................................................72 2-12. Average statistics by Z-score deciles........................................................................73 2-13. Analysis of Z-score...................................................................................................74 2-14. Analysis of Z-score changes.....................................................................................75 2-15. Sensitivity of summary statistics to alternative input assumptions..........................77 2-16. Analysis of IAV and HAV forecasting properties under alternative assumptions..............................................................................................................79 2-17. Logit analysis of defaults under alternative assumptions.........................................80 2-18. Analysis of Moodys credit ratings under alternative assumptions..........................81 vii

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2-19. Analysis of credit rating changes under alternative assumptions.............................83 3-1. Summary statistics....................................................................................................131 3-2. Simple and rank correlations....................................................................................132 3-3. Average market indicators of risk by Moodys credit rating....................................133 3-4. Average market indicators of risk by asset quality deciles......................................134 3-5. Average market indicators of risk by SCORE deciles.............................................135 3-6. Analysis of Moodys credit ratings..........................................................................136 3-7. Analysis of asset quality measures...........................................................................137 3-8. Analysis of financial health SCORE........................................................................139 3-9. Mean value tests of forecasting ability of market indicators....................................140 3-10. Logit analysis of material changes in firm condition.............................................141 3-11. Analysis of asset quality changes (LLAGL)..........................................................142 3-12. Analysis of asset quality changes (BADLOANS)..................................................144 3-13. Logit analysis of SCORE changes..........................................................................146 3-14. Sensitivity of summary statistics to alternative input assumptions........................148 3-15. Analysis of asset quality measures under alternative assumptions........................149 3-16. Analysis of asset quality changes...........................................................................150 3-17. Logit analysis of SCORE changes..........................................................................152 viii

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LIST OF FIGURES Figure page 2-1. Median implied asset volatility over 1975-2001........................................................84 2-2. Median implied asset volatility by assets-to-debt ratio quartile.................................85 2-3. Median distance to default over 1975-2001...............................................................86 3-1. Median implied asset volatility (IAV) through time for 1986-1999.......................153 3-2. Median implied asset volatility (IAV) by asset-to-debt ratio quartile.....................154 3-3. Median distance to default (DD) through time 1986-1999......................................155 ix

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TWO ESSAYS IN FINANCIAL ECONOMICS: FIRM RISK REFLECTED IN SECURITY PRICES By Stanislava M. Nikolova August 2004 Chair: Mark J. Flannery Major Department: Finance, Insurance, and Real Estate We examine the ability to extract risk information from the market prices of a firms securities. We use contingent claim models for firm valuation to construct risk measures from equity prices, debt prices, and a combination of both. We provide empirical evidence on the relative accuracy and forecasting ability of these measures for industrial and financial firms. We compare a number of methodologies for constructing implied asset volatility estimates for industrial firms. We document that while different methodologies produce different estimates, these differences are not crucial in explaining realized asset volatility, Moodys credit ratings, Altmans Z scores, or default occurrences. Within each test, some estimates outperform others, but no estimate is consistently best. We also show that, while the choice of using equity or debt prices to extract firm risk information appears to be inconsequential, the choice of model parameters is quite important. The manner in which we adjust yield spreads to account for embedded call options, and tax differences x

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between corporate and Treasury securities as well as assumptions about the maturity of debt and debt priority structure have a significant effect on the level and rank ordering of firm risk measures. Finally, we address the value of market information in the government oversight of U.S. bank holding companies. We construct risk measures obtained from equity prices alone, debt prices alone, and a combination of both. We observe that default risk measures constructed from debt prices generally outperform those constructed from equity prices in both contemporaneous and forecasting models. We further document that models using information from both equity and debt prices improves on the explanatory power of equity-only or debt-only models. Risk measures constructed from both equity and debt prices are more closely related to bank credit ratings, asset-portfolio quality indicators, and overall financial health. In addition, models using both equity and debt price information can better predict material changes in the firms default probability, and quarter-to-quarter changes in the firms asset-portfolio quality and overall condition. xi

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CHAPTER 1 INTRODUCTION The ability to accurately assess firm total asset risk has important applications in many areas of finance risk management, bank lending practices, and regulation of financial firms, among others. Thus, improving this ability can have important implications for both finance researchers and practitioners. Although considerable research effort has been put toward extracting firm risk information from either equity or debt prices, to the best of our knowledge, no previous study has assessed the relative informational quality of firm risk measures obtained from equity and debt prices; or the impact of alternative model assumptions on the accuracy of these measures. Financial theory suggests that in a world of complete and frictionless markets, both equity and debt prices fully reflect the available information about a firms condition. We can value firm equity as a call option written on the market value of the firms assets (Black and Scholes 1973), and we can value risky debt as a riskless bond with an embedded put (default) option (Merton 1974). Since both the equity-call and debt-put options are written on the same underlying the firms total assets they are functions of the same set of variables: the market value of firms assets, the volatility of the firms assets, the face value of debt, short-term interest rates, and the time to firm resolution (debt maturity). A firms credit risk should then be reflected in both equity and debt prices, if markets were perfect. However, both equity and debt markets are characterized by frictions. Which of these is characterized by fewer frictions, and which markets frictions have lower impact on firm risk measures? 1

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2 Debt markets are notorious for their lack of transparency and data availability. While some corporate bonds trade on NYSE and Amex, they account for no more than 2% of market volume (Nunn et al. 1986). In addition, data quotes on OTC trades tend to be diffused and based on matrix valuation rather than on actual trades. Warga and Welch (1993) document that there are large disparities between matrix prices and dealer quotes. Hancock and Kwast (2001) compare bond-price data from four sources and find that correlation between bond yields from the different sources are in the 70-80% range. Even if bond data were readily available, extracting firm risk information can be difficult. The typical approach is to use debt prices, and calculate yield spreads as the difference between a corporate yield and the yield on a Treasury security of the same maturity. This spread is assumed to be a measure of credit risk. However, corporate yields will differ from Treasury yields for a number of reasons other than credit risk (Delianedis and Geske 2001, Elton et al. 2001, Huang and Huang 2002). These include premiums for tax and liquidity differences between corporate and Treasury securities, as well as compensation for common bond-market factors. Yield spreads reflect not only default probability but also expected losses, which requires an adjustment for recovery rates. Adjustments are also needed for redemption and convertibility options, sinking fund provisions, and other common bond features. Finally, yield spreads reflect differences in duration/convexity, because cash flows of corporate and Treasury bonds are not perfectly matched. Despite all of these shortcomings, yield spreads are commonly used as a proxy for firm risk. In contrast to debt markets, equity markets are liquid and deep. Equity prices of high frequency and quality can be easily obtained. Nevertheless, these markets are also characterized by imperfections. Stock prices have been documented to overreact or

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3 underreact to news, and have been shown to appear too volatile than a basic dividend model would predict (Cochrane 1991, LeRoy and Porter 1981, Shiller 1981, West 1988). Also, while yield spreads are easily interpreted as a measure of firm risk, there is no analogous measure obtained from equity prices. Although some researchers have used equity abnormal returns as a measure of firm risk, these are not immediately interpreted as such: an increase in abnormal return might be the result of an increase in firm profitability and/or increase in firm risk. Since both equity and debt markets are characterized by frictions, and since both equity and debt prices impose challenges in extracting information about firm risk, whether one of these two information sources is better than the other is an empirical question. We evaluate the relative informational content and accuracy of firm risk measures obtained from equity or debt prices, and examine whether combining information from both markets can produce more accurate risk measures. We construct alternative estimates of asset volatility for a large set of U.S. firms, and tests their value as forecasting and risk-valuation variables. Chapter 2 focuses on industrial firms. We start by constructing asset volatility estimates for a set of 1,264 U.S. industrial firms. We then test the information content of these estimates by using them to predict defaults, credit-rating changes, and asset-return features. The result is specific information on the value of alternative methods for estimating a firms asset volatility. Chapter 3 applies general insights from the industrial-firm analysis to the specific case of assessing the condition of large financial firms. The value of market prices to assess bank risk has become an important issue among banks and their government supervisors. Banks also provide a valuable opportunity to expand our tests of asset volatility

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4 estimates: their extensive supervisory reports provide homogeneous and detailed financial information that can be used to help infer the properties of estimated asset volatilities. We start by constructing three implied asset volatility estimates for a set of 84 U.S. bank holding companies (BHCs) over the period 1986-1999. These asset volatilities are then combined with firm leverage to produce three versions of a single measure of default risk distance to default (DD). We then investigate the contemporaneous association among the three DD measures and other indicators of bank risk, and their ability to foresee changes in bank risk. Results of this analysis will have important implications for the regulation of large financial firms.

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CHAPTER 2 INDUSTRIAL-FIRM RISK REFLECTED IN SECURITY PRICES: PREDICTING CREDIT RISK WITH IMPLIED ASSET VOLATILITY ESTIMATES The ability to accurately assess firm total asset risk has important applications in many areas of finance claim pricing, risk management, and bank lending practices among others. Thus, improving this ability can have important implications for both finance researchers and practitioners. Although considerable research effort has been put toward extracting firm risk information from either equity or debt prices, to the best of our knowledge no previous study has assessed the relative informational quality of industrial-firm risk measures obtained from equity and debt prices, and the impact of alternative model assumptions on the accuracy of these measures. Since both equity and debt markets are characterized by frictions, and since both equity and debt prices impose challenges in extracting information about firm risk, whether one of these two information sources is better than the other is an empirical question. In this chapter, we evaluate the relative informational content and accuracy of firm risk measures obtained from equity or debt prices, and examine whether combining information from both price sources can produce more accurate risk measures. First, using information from equity and/or debt prices, we construct four asset volatility estimates for a set of 1,264 U.S. industrial firms over the period 1975-2001. Second, we test the information content of these asset volatility estimates by using them to predict defaults, credit ratings, Altmans (1968) Z scores, and asset-return features. The result is specific information on the value of alternative methods for estimating a firms total asset 5

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6 volatility. Finally, we investigate the effect of alternative-model assumptions on the quality of the firm risk measures. Four estimates of asset volatility are analyzed in this chapter: Asset volatility obtained by de-levering equity-return volatility: simple implied asset volatility (SIAV). Asset volatility implied by equity prices alone (EIAV). Asset volatility implied by debt prices alone (DIAV). Asset volatility implied by contemporaneous equity and debt prices (EDIAV). Our analysis indicates that implied asset volatility estimates can differ dramatically across methodologies. The low correlations of these estimates indicate that if they are to be used as measures of total firm risk, then risk rankings will depend significantly on the method used to calculate asset volatility. The correlations are even lower when asset volatilities are combined with leverage, to produce a measure of each firms distance to default (DD) the number of standard deviations required to push a firm into insolvency. These differences justify a closer look at the relative forecasting and risk-valuation ability of the implied asset volatility and corresponding DD estimates. Because implied asset volatility is the markets forecast of future volatility, the first set of tests examines the association among the four implied asset volatility (IAV) estimates and the subsequent realized volatility of total asset returns. We document that all of the IAV estimates are biased forecasts of realized volatility. Furthermore, they do not seem to incorporate all of the historical information available at the time they are calculated. Fit statistics indicate that SIAV and EIAV tend to outperform the others when it comes to forecasting realized volatility. Also, of the four IAV estimates, DIAV seems to add the most new information to historical asset volatility in forecasting realized

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7 volatility. This is contrary to the conventional assumption that debt prices are extremely noisy. The second set of tests examines if any of the four DD estimates successfully distinguishes firms that default from those that do not. We find that a decrease in any of the four DD estimates increases the probability that a firm will then default. We replicate the tests for the subsample of non-investment grade firms, in an attempt to achieve a more balanced sample. For non-investment grade firms, we find that only the DD estimates based on EDIAV and SIAV help forecast default. Judging by the fit statistics of the four models in both sets of tests, we conclude that the DD calculated from SIAV contains the most relevant information about an upcoming default. Because previous studies indicate that credit ratings can reliably proxy for default probability, our third test investigates the relation between a firms DD and its Moodys credit rating. Although all four DD measures are statistically significant, the one based on EIAV seems to be the most accurate, as indicated by its marginal contribution to the models fit. It is outperformed by DD_EDIAV when we limit ourselves to the subset of non-investment grade firms, and by DD_DIAV when we limit ourselves to the subset of investment-grade firms. We also examine the ability of changes in DD to predict credit-rating upgrades and downgrades. Although only some lags of the DD estimates are statistically significant in explaining Moodys upgrades, all of them successfully predict credit downgrades a decrease in DD increases the probability that a firm will be downgraded. The DD calculated from EIAV seems to be the most accurate predictor, as judged by the models fit statistics.

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8 Finally, we replicate the credit-rating tests above using another proxy for default probability Altmans (1968) Z score. We find that variations in DD successfully explain variations in Z but only for low-Z (high default probability) firms. This is consistent with Dichev (1998) who shows that Z is a better measure of default risk when the ex ante default probability is high. Of the four DD estimates, those calculated from EIAV and DIAV seem to add the most explanatory power to a base model that includes only control variables. We analyze the relationship between changes in DD and changes in Z separately for negative and positive changes, analogously to our separate analysis of rating downgrades and upgrades. Consistent with our rating-change results, we find that lagged changes in DD have more explanatory power for negative Z-score changes than for positive ones. The fit statistics of these models indicate that DD adds little-to-no new information to lagged Z changes, and that the most new information is added by the DD estimate calculated from EIAV. In summary, different methodologies produce different estimates of implied asset volatility. These differences are even larger when compounded by leverage differences to produce DD measures. However, the analysis in this chapter suggests that these differences are not crucial in explaining realized asset volatility, Moodys credit ratings, Altmans (1968) Z scores, or default occurrences. Within each test, some IAV and DD measures outperform others, but no estimate is consistently best. This implies that firm risk can be extracted from equity and debt prices equally accurately, thus suggesting that researchers and practitioners can use high-frequency and high-quality equity prices without losing much important information.

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9 While the choice between equity and debt prices as a source of firm risk information appears to be inconsequential, the choice of contingent-claim-model assumptions does not. The informational content of risk measures is significantly affected by tax and call-option adjustments, as well as time-to-firm-resolution and debt-priority-structure assumptions. This provides an important checklist of robustness tests for those conducting empirical research using contingent-claim pricing models. 2.1. The State of the Literature 2.1.1. Contingent Claim Valuation Models Black and Scholes (1973) were the first to recognize that their approach to valuing exchange-traded options could also be used to value firm equity. With limited liability the payoff to equityholders is equivalent to the payoff of a call option written on the firms assets with an exercise price equal to the face value of the firms debt. Consider a non-dividend paying firm with homogeneous zero-coupon debt that matures at time T. Assume that the market value of the firms assets follows a continuous lognormal diffusion process with constant variance. Then the current equity value of the firm is )()(21dNDedVNEfR (2-1) where VVfRDVd)5.0()ln(21 Vdd12 E is the current market value of the firms equity, V is the current market value of the firms assets, D is the face value of the firms debt, V is the instantaneous standard deviation of asset returns, is the time remaining to maturity, fR is the risk-free rate over )(xN is the cumulative standard normal distribution of x

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10 Merton (1974) uses the same insight to derive the value of a firms risky debt. He demonstrates that under limited liability, the payoff to debtholders is equivalent to the payoff to holders of a portfolio consisting of riskless debt with the same characteristics as the risky debt, and a short put option written on the firms assets with an exercise price equal to the face value of debt. Re-arranging the formula used by Merton (1974) allows us to express the credit-risk premium as the spread between the yield on risky debt, R, and the yield on risk-free debt with otherwise the same characteristics: /)(ln21dNdNeDVRRfRf (2-2) One of the basic assumptions underlying Mertons (1974) derivation is that the firm issues a single homogenous class of debt. In reality, the characteristics of debt are highly variable, which makes his model intuitively useful, but not precisely applicable to risky debt valuation. The single-class debt assumption is relaxed by Black and Cox (1976), who analyze the debt-valuation effect of having multiple classes of debtholders. Consider a firm financed by equity and two types of debt differentiated by their priority. Although the probability of default is the same for senior and subordinated debtholders, their expected losses differ; and that is reflected in the valuation of their claims. Assume that all of the firms debt matures on the same date. If at maturity the value of the firm is less than (the face value of senior debt) then senior debtholders receive the value of the firm, while subordinated debtholders (along with equityholders) receive nothing. If at maturity the value of the firm is greater than but less than the face value of all debt () then senior debtholders get paid in full, subordinated debtholders receive the residual firm value, and equityholders receive nothing. Note that the payoff to equityholders is the 1D 1D 21DD

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11 same, whether there is one or two classes of debtholders if the value of the firm at maturity is higher than the face value of all debt, they receive the residual after debt payments are made; and if the value of the firm at maturity is lower than the face value of all debt, they receive nothing. Thus, while knowing the precise breakdown of debt into priority classes is crucial for debt valuation, it does not affect the valuation of equity. Following Black and Cox (1976), the value of a firms subordinated debt is given by )()() ~ ()() ~ (22121112dNeDDdNeDdNdNVXffRR (2-3) where VVfRDVd)5.0()ln(~211 Vdd12 ~ ~ VVfRDDVd)5.0())(ln(2211 Vdd12 1D is the face value of the firms senior debt, 2D is the face value of the firms subordinated debt, 2X is the current value of subordinated debt. The Black-Cox model most frequently appears in the literature as the spread between the yield on subordinated debt () and the risk-free rate () of the same maturity: 2R fR /)()~()()~(ln22212211122dNDDDdNDDdNdNeDVRRfRf (2-3) 2.1.2. Applications of Contingent Claim Valuation The above contingent-claim approach to pricing firm debt has many applications in the literature on credit-risk analysis. Bohn (2000) surveys some of the main theoretical models of risky debt valuation that built on Merton (1974) and Black and Cox (1976). The empirical validity of these models has been rarely and poorly tested because of the unavailability and low quality of bond data. Jones, Mason, and Rosenfeld (1983) and

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12 Frank and Torous (1989) find that contingent-claim models yield theoretical credit spreads much lower than actual credit spreads. Sarig and Warga (1989) estimate the term structure of credit spreads, and show it to be consistent with contingent-claim model predictions. Wei and Guo (1997) test the models of Merton (1974) and Longstaff and Schwartz (1995), and find the Merton model to be empirically superior. It is important to note that in calculating theoretical credit spreads, all of these studies require an estimate of the variance of firm assets. One way to obtain such an estimate is by constructing a historical time series of firm asset values and calculating the variance. Asset value is typically the sum of market value of equity and book value of debt; or alternatively, the sum of market value of equity, market value of traded debt and the estimated market value of nontraded debt. Another way to estimate the variance of asset returns is by de-levering the historical variance of equity returns, as in a simple version of the boundary condition in Merton (1974): VEEV (2-4) where E is the historical standard deviation of equity returns, E is the market value of equity, and V is the sum of E and book value of debt. We call this the simple implied asset volatility (SIAV). It is important to note that any test of the contingent-claim models to debt valuation is a test of the joint hypothesis that the model and the estimate of V are both correct. Nevertheless, the relative accuracy of different V estimates has not been explored in any of the above studies. Contingent-claim valuation of equity has been used extensively in the literature on bank deposit insurance where the equity-call model is reversed to generate estimates of the market value of assets from observed stock prices. This approach, along with the

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13 observation in Merton (1977) that deposit insurance can be modeled as a put option, allows the calculation of fair deposit insurance premia. This insight is used by Marcus and Shaked (1984), Ronn and Verma (1986), Pennacchi (1987), Dale et al. (1991), and King and OBrien (1991) in the analysis of deposit insurance premia. The approach of these researchers is to solve a system of equations that consists of Eq. 2-1 and Mertons boundary condition )(1dVNEEV (2-4) for the market value and volatility of assets. Their proxy for E is the historical standard deviation of equity returns. We will refer to the volatility estimate produced by this approach as the equity-implied asset volatility (EIAV); and the asset value obtained along with it is V_EIAV. In addition to calculating the market value of assets for banks and bank holding companies, this methodology has also been used to calculate the market value of assets for savings and loan associations, by Burnett et al. (1991); and for insurance companies and investment banks, by Santomero and Chung (1992). Despite its wide use, the accuracy of the estimates it produces has rarely been questioned. We are aware of only one study that investigates whether the market value estimates obtained through this methodology are correct. Diba et al. (1995) use a contingent-claim model to calculate the equity values of failed banks and find that these greatly exceed the negative net-worth estimates of the FDIC. They conclude that the equity-call model produces poor estimates of the market value of assets. The accuracy of the asset volatility estimates, however, has not been previously examined. While the literature on deposit insurance uses the contingent-claim equity-pricing model, the literature on market discipline of bank and bank holding companies makes use

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14 of the contingent-claim debt-pricing model. Starting with Avery, Belton, and Goldberg (1988), yield spreads on bank subordinated notes and debentures have been examined for information about the banks risk profile. However, Gorton and Santomero (1990) recognize that subordinated yield spreads are a nonlinear function of risk, and insist that researchers focus on the variance of bank assets instead. They use the methodology of Black and Cox (1976) to estimate V from subordinated debt prices under the assumption that book value is a good proxy for the market value of assets. Their methodology insight has since been used by Hassan (1993) and Hassan et al. (1993) who apply contingent-claim valuation techniques to calculate implied asset volatilities; and by Flannery and Sorescu (1996), who use it to obtain theoretical default-risk spreads. We refer to the asset volatility estimate calculated from subordinated debt prices as the debt-implied asset volatility (DIAV); and the market value of assets obtained along with it is V_DIAV. The last methodology we analyze is closest in spirit to the one used by Schellhorn and Spellman (1996). They examine four banks over 1987-1988, and calculate two estimates of implied asset volatility for each bank. The first estimate is EIAV and is based on the methodology of Ronn and Verma (1986) described earlier. The second estimate solves Equations 2-1 and 2-3 simultaneously for the market value of assets and the standard deviation of asset returns. We refer to this volatility estimate as the equity-and-debt implied asset volatility (EDIAV); and the corresponding asset value estimate is V_EDIAV. Schellhorn and Spellman (1996) conclude that the two V estimates can differ substantially over the studied period, and that the estimates obtained from contemporaneous equity and debt prices are on average 40% higher than those obtained

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15 using historical information. The difference between the two estimates increases even more when the banks are perceived to be insolvent. This suggests that if asset volatility is to be used as a proxy for the total risk of a firm, then using historical equity variance can substantially underestimate firm risk. We expand the work of Schellhorn and Spellman (1996) in three ways. First, we use a larger and more-diverse sample. We obtain data on industrial firms for the period 1975-2001. Second, we compare a broader range of asset value and volatility estimates. We judge the EDIAV and corresponding V_EDIAV against estimates calculated using three more traditional methodologies (SIAV, EIAV, DIAV) and the corresponding asset value estimates. Third, we set up horse-race tests to determine the relative informational content and accuracy of the four asset volatility estimates. 2.2. Methodologies for Constructing Risk Measures from Market Prices This section summarizes the three methodologies traditionally used to estimate the market value and volatility of assets. It then proposes one that relies on contemporaneous equity and debt prices to obtain Vand V Finally, it explains the construction of default-risk measures from implied asset value and volatility estimates. 2.2.1. Methodologies for Calculating Implied Asset Value and Volatility The simple implied asset volatility (SIAV) is the most popular estimate of asset volatility found in the finance literature. This is likely due to the ease of computation since it uses a simplified version of the boundary condition VEEV (2-4) where all variables are as previously defined. This methodology assumes that the instantaneous standard deviation of equity returns at the end of quarter t is the standard

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16 deviation of equity returns over the quarter. It uses the sum of the market value of equity and book value of debt as a proxy for the market value of assets. This is equivalent to assuming that the firms debt is risk-free, which implies that we will overestimate its market value by the value of the put option embedded in risky debt. Thus, we expect this methodology to produce a market-value-of-assets estimate higher than those produced by the three simultaneous-equation methodologies that follow. The equity-implied asset volatility (EIAV) is calculated by solving the system )()(21dNDedVNEfR (2-1) )(1dVNEEV (2-4) for V and V. This is done using the Newton iterative method for systems of nonlinear equations. For the starting value of V, we use the sum of the market value of assets and book value of debt; and for the starting value of V we use SIAV. Adhering to previous studies, we assume that the instantaneous standard deviation of equity at the end of quarter t is the standard deviation of equity returns over the quarter. The debt-implied asset volatility (DIAV) is calculated by solving the system of nonlinear equations:1 /)()~()()~(ln22212211122dNDDDdNDDdNdNeDVRRfRf (2-3) )(1dVNEEV (2-4) for V and V using the Newton iterative method. Once again, for the starting value of we use the sum of the market value of assets and book value of debt; but for the V 1 We use the subordinated-debt valuation model, because we assume that publicly traded debt is likely to be last in a firms debt-priority structure. We discuss the reasonableness of this assumption later and explore the sensitivity of our results to alternative assumptions.

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17 starting value of V we use the theoretically more-accurate EIAV. As in the calculation of equity-implied asset volatilities, we assume that the historical standard deviation of equity over quarter t is a good approximation for the instantaneous standard deviation of equity returns at the end of the quarter. )1 ln The equity-and-debt implied asset volatility (EDIAV) is obtained by solving the system of nonlinear equations )((2dNDedVNEfR (2-1) /)()~()()~(22212211122dNDDDdNDDdNdNeDVRRfRf (2-3) for V and Vusing the Newton iterative method. We use the same starting values for V and Vas in the calculation of DIAV, and later ensure that the solutions are not sensitive to the starting values. Note that unlike the previous three methodologies, this one needs no historical information about the standard deviation of equity returns. 2.2.2. Calculating Credit-Risk Measures from Implied Asset Value and Volatility Three elements determine the probability that a firm will default the market value of its assets, the portion of liabilities due, and the volatility of asset returns. The first two determine the default point of the firm, which as explained earlier is at first set to 97% of total debt. The last element, asset volatility, captures business, industry, and market risks faced by the firm. If the implied asset volatility estimates calculated in our study are correct assessments of the firms future risk exposure, then along with the firms asset and liability values they should reflect default probability accurately. We combine asset volatility with the value of assets and liabilities, into a single measure of default risk, and refer to it as the distance-to-default (DD). This measure compares a firms net worth to the size of one standard deviation move in the asset value, and is calculated as

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18 TTRDVDDVVf25.0/ln Intuitively, a DD value of X tells us that a firm is X standard deviations of assets away from default. Thus, a low DD indicates that a firm has a high probability of default. 2.2.3. Methodology Assumptions The methodologies above are based on contingent-claim valuation, and as a result require that the standard assumptions of Black and Scholes (1976) and Black and Cox (1979) be met. Bliss (2000) lists a series of deviations from these assumptions. However, it is an empirical question whether these deviations make the estimates of asset value and volatility less meaningful. In addition to the standard assumptions, applying contingent-claim valuation techniques requires that we know the time left to equityholders exercising their option, and the default point of each firm. In obtaining estimates for these we initially adhere to previous studies, but later examine the sensitivity of our results to alternative assumptions. Our study aims to determine which of the simplifying assumptions made in calculating asset values and volatilities affect the informational content and accuracy of the estimates. Starting with Marcus and Shaked (1984) and Ronn and Verma (1986) the time to exercising the equity call option is typically assumed to be 1 year. Banking researchers claim that the 1-year expiration interval is justified because of the annual frequency of regulatory audits. If after an audit, the market value of assets is found to be less than the value of total liabilities, regulators can choose to close the bank. An alternative resolution-time assumption is used by Gorton and Santomero (1990), who set the time to expiration equal to the average maturity of subordinated debt, and find that the DIAV estimates calculated under this assumption are significantly higher than the ones

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19 calculated under the 1-year-to-maturity assumption. However, they offer no evidence as to which maturity assumption produces the better estimate of asset volatility. In the application of contingent-claim models to the valuation of industrial firms there is much less uniformity in the time-to-expiration assumption. Huang and Huang (2002) use the actual maturity of debt, Delianedis and Geske (2001) use the duration of debt, and Crosbie and Bohn (2002) use an interval of 1 year. Since the empirical properties of implied total asset volatility are not the focus of these studies, they offer little evidence on the sensitivity of their results to alternative time-to-expiration assumptions. To start with, we assume that the time to resolution equals 1 year. We later explore the effects of two alternative assumptions time to resolution equals to either the weighted average duration or the weighted average maturity of the firms bond issues. Although we often assume that firms default as soon as their asset value reaches the value of their liabilities, this is true only if the firms debt is due immediately. In reality, firms issue debt of various maturities and as a result their true default point is somewhere between the value of their short-term and long-term liabilities. Unfortunately, while previous studies recognize this (Crosbie and Bohn 2002), they offer little guidance on choosing each firms default point. The banking literature adheres to the assumptions made by Ronn and Verma (1986) who set the default point at 97% of the value of total debt. They originally experiment with default points in the range of 95-98% of debt and determine that rank orderings of asset values are significantly affected by the choice of default point. However, they do not examine the relative accuracy of the estimates obtained under alternative default-point assumptions.

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20 2.3. Data Sources To construct the above estimates of asset value and volatility, we combine a number of data sources for the period of December 1975 December 2001. Data on equity prices and characteristics is obtained from the Center for Research in Security Prices (CRSP). Data on bond prices and characteristics is obtained from the Warga-Lehman Brothers Fixed Income Database (WLBFID) and the Warga Fixed Investment Securities Database (FISD). Both sources are used since neither database alone covers the whole study period. Finally, balance sheet and income statement data comes from the Compustat Database. Combining these four data sources is nontrivial since (1) each database has its own unique identifier with only some of them overlapping across databases, and since (2) some of the identifiers are recycled. Therefore, the merging process that we use requires further explanation. We start with information from WLBFID and FISD, which use issuer CUSIP as one of their identifiers. We then match the issuer CUSIP against those obtained from CRSP making sure that the date on which the bond data is recorded falls within the date range for which the CUSIP is active in the CRSP database. Merging the WLBFID and FISD data with that from the CRSP database allows us to add one more identifier to our list PERMNOs. We use them to acquire Compustat data from the Merged CRSP/Compustat database. These matching procedures result in data on at least 1,264 unique industrial firms which give us 28,262 firm-quarter observations for 1975-2001. 2.3.1. Bond Prices and Characteristics The initial sample includes all firms from the WLBFID and FISD whose bonds are traded during the period of 1975-2001. The WLBFID reports monthly information on the major private and government debt issues traded in the United States until March 1997.

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21 We identify all U.S. corporate fixed-rate coupon-paying debentures that are not convertible, putable, secured, or backed my mortgages/assets. We collect data on their month-end yield, prepayment options, and amount outstanding.2 While most prices reflect live trader quotes, some are matrix prices estimated from price quotes on bonds with similar characteristics. Yields calculated from matrix prices are likely to ignore the firm-specific changes we are trying to capture, so we exclude them from our sample. The FISD contains comprehensive data on public U.S. corporate and agency bond issues with reasonable frequency since 1995. We use the same procedures for retaining observations as we do with the WLBFID in an attempt to make the two databases as comparable as possible we identify all fixed, non-convertible, non-putable, and non-secured debentures issued by U.S. corporations. The main difference between the two databases is the source and type of pricing information. The WLBFID reports bond trader quotes as made available by Lehman Brothers traders. The FISD reports actual transaction prices recorded electronically by Reuters/Telerate and Bridge/EJV who collectively account for 83% of all bond trader screens. In the spirit of making data from the two databases comparable, we calculate each issues month-end yield using the price closest to the end of the month. A cursory examination of the small number of debt issues that have both WLBFID and FISD data available indicates that yields across the two databases are extremely similar. Nevertheless, when combining the WLBFID with the 2 Data for December 1984 is substantially incomplete and produces no viable observations for the fourth quarter of that year. We use the November data to match it against balance sheet data for the last quarter of 1984.

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22 FISD sample, we choose actual trade prices over quotes only if the trade occurs in the last five days of the month. In order to compute a credit-risk spread, we need to subtract from each corporate yield the yield on a debt security that is risk-free but otherwise has the same characteristics as the corporate bond. The most common approach to calculating a credit-risk spread is to difference the yield on a corporate bond with that on a Treasury bond of the same remaining maturity. To do so we collect yields on Treasury bonds of different maturities from the Federal Reserve Boards H.15 releases. For each corporate debt issue in our sample we identify a Treasury security with approximately the same maturity as the remaining maturity on the corporate debenture. When there is no precise match, we interpolate to obtain a corresponding Treasury yield. The difference between a corporate yield and a corresponding Treasury yield is our first measure of the raw credit-risk spread. 2.3.1.1. Tax adjustment There is growing evidence that corporate yield spreads calculated as above cannot be entirely attributed to the risk of default. Huang and Huang (2002) and Delianedis and Geske (2001) demonstrate that at best less than half of the difference between corporate and Treasury bonds is due to default risk. Elton et al. (2001) suggest that this difference can be explained by the differential taxation of the income from corporate and Treasury bonds. Since interest payments on corporate bonds are taxed at the state and local level while interest payments on government bonds are not, corporate bonds have to offer a higher pre-tax return to yield the same after-tax return. Thus, the difference between the yield on a corporate and the yield on a Treasury bond must include a tax premium. Elton et al. (2001) illustrate that this tax premium accounts for a significantly larger portion of

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23 the difference than does a default risk premium. For example, they find that for 10-year A-rated bonds, taxes account for 36.1% of the yield spread over Treasuries compared to the 17.8% accounted for by expected losses. Cooper and Davydenko (2002) derive an explicit formula for the tax adjustment proposed by Elton et al. (2001). They calculate that the tax-induced yield spread over Treasuries is: MrftMtaxtrtyMexp11ln1 where t is the time to maturity for both the corporate and the Treasury bonds, M is the applicable tax rate, and is the Treasury yield.3 We use this formulation along with the estimated relevant tax rate of 4.875% from Elton et al. (2001) to calculate a hypothetical Treasury yield if Treasuries were to be taxed on the state and local level.4 The difference between a corporate yield and a corresponding taxable Treasury rate is a measure of the tax-adjusted raw credit-risk spread. rftMr Alternatively, we can difference corporate yields with the yield on the highest rated bonds under the assumption that these almost never default. We obtain Moodys average yield on AAA-rated bonds from the Federal Reserve Boards H.15 releases. It is important to note that differencing a corporate yield with the AAA yield might allow us to extract a more accurate estimate of the credit-risk premium by controlling for liquidity as well as tax differential between corporate and Treasury bonds. However, it is also the 3 This formulation of the yield spread due to taxes assumes that capital gains and losses are treated symmetrically and that the capital gain tax is the same as the income tax on coupons. 4 Corporate bonds are subject to state tax with maximum marginal rates generally between 5% and 10% depending on the state. This yields an average maximum state tax rate in the U.S. of 7.5%. Since in most states, state tax for financial institutions (the main holder of bonds) is paid on income subject to federal taxes, Elton et al. (2001) use the maximum federal tax rate of 35% and the maximum state tax rate of 7.5% to obtain an estimate for of 4.875%. An alternative estimate is produced by Severn and Stewart (1992) and equals to 5%.

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24 case that the AAA yield has a number of drawbacks it averages the yields on bonds of different maturity and different convertibility/callability options. Nevertheless, for the non-AAA-rated bonds in our sample we use the difference between their yield and the average AAA yield as an alternative tax adjustment for the raw credit-risk spread. We start by differencing the corporate yields with the hypothetical taxable Treasury yields. However, in the spirit of this study we later investigate whether using the average AAA yields significantly affects the accuracy and informational content of the implied asset volatility estimates. 2.3.1.2. Call-option adjustment The tax-adjusted yield spreads calculated above might still contain some non-credit related components. Perhaps the most important of these is the value of call options embedded in many corporate yield spreads. Since the value of a call option is always non-negative, the spread over Treasuries whether adjusted for taxes or not, will exceed the credit-risk spread unless we adjust for the options value. We follow the approach presented in Avery, Belton, and Goldberg (1988) and Flannery and Sorescu (1996) to estimate an option-adjusted credit spread. For each callable corporate bond in our sample, we use the maturity-corresponding taxable Treasury bond to calculate a hypothetical callable Treasury yield. That is, we calculate the required coupon rate on a Treasury bond with the same maturity and call-option parameters as the corporate bond but the same market price as the non-callable Treasury bond adjusted for taxes. The difference between the yield on the hypothetical callable and the actual non-callable Treasury bond is the value of the option to prepay. We subtract these option values from the tax-adjusted spreads calculated earlier to obtain option-adjusted credit spreads.

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25 The required yield on the hypothetical Treasury is computed following the method of Giliberto and Ling (1992). They use a binomial lattice based on a single factor model of the term structure to value the prepayment options of residential mortgages. Their methodology uses the whole term structure of interest rates to estimate the drift and volatility of the short-term interest rate process. These two parameters are then used to determine the interest rates at every node of the lattice, which are in turn used to calculate the value of the mortgage prepayment option. Following Flannery and Sorescu (1996) this methodology is adjusted to calculate the call option value of the Treasury bonds instead. In a small number of cases these credit spreads turn out to be negative. A cursory examination of these occurrences indicates that when the term structure of interest rates is relatively flat and interest rate volatility high, our option-adjustment methodology produces higher option values. When combined with an initially low yield (high-rated bonds) these high option values lead to negative credit spreads. Since the theoretical motivation used in this study does not allow for negative credit spreads and since negative credit spreads are heavily concentrated in highly rated bonds, we winsorize our set of credit spreads at zero. 2.3.1.3. Yield spread aggregation To obtain a firm yield spread, YS, we aggregate yield spreads on bonds issued by the same firm using three approaches. The first approach is to construct a weighted-average yield spread by averaging the spreads on same-firm bonds and weighing them by the bonds outstanding amount. The other approaches use the findings in Hancock and Kwast (2001) and Covitz et al. (2002) that due to higher liquidity larger and more recently issued debentures have more reliable prices. To minimize the liquidity

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26 component of yield spreads, for each firm we take the spread on its largest issue (based on amount outstanding) as our second measure of firm yield spread, and the spread on its most recent issue as our third measure. We investigate whether different aggregation approaches produce significantly different IAV estimates. 2.3.2. Equity Prices and Characteristics For all firms that have bond data available, we collect equity information from the daily CRSP Stock Files. We calculate the quarterly equity return volatility E as the annualized standard deviation of daily returns during the quarter. The market value of equity is the last stock price for each quarter multiplied by the number of shares outstanding. We exclude from our sample all stocks with a share price of less than $5 and for which E is computed from fewer than fifty equity-return observations in a quarter. These data filters attempt to reduce the effect of the bid-ask bounce on the estimate of equity-return volatility, while providing enough observations to make the quarterly volatility estimate meaningful. 2.3.3. Accounting Data Quarterly accounting data is obtained from the CRSP/COMPUSTAT Merged Database using PERMNOs. For each firm we collect information on the book value of total assets VB, and the book value of total liabilities, D, at the end of each calendar quarter during 1975-2001. We also obtain industry classification codes to construct 48industry indicator variables following Fama and French (1997). Our methodology requires information on the priority structure of total debt in addition to its amount. For industrial firms there is no information on the amount of

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27 senior versus subordinated debt, so we use the following approach for obtaining an estimate of the priority breakdown. Using the two bond databases described earlier, we aggregate the amount outstanding of each firms bonds at each quarter-end during 1975-2001. We use this as one estimate of the firms face value of subordinated debt and input it into Eq. 2-3. This simplification is based on the fact that firms tend to take out bank loans before they turn to the public debt markets, and is supported by the findings of Longhofer and Santos (2003) that most bank debt is senior. We investigate the sensitivity of our findings to two alternative assumptions about debt priority structure. The first one treats all debt as of a single priority class and as of homogeneous risk. That is, credit spreads calculated earlier are assumed to reflect the default probability on total debt and not only the default probability on bond issues outstanding. We use the credit spread, YS, and total debt as inputs into Eq. 2-2. The second alternative assumption allows for at least two priority and risk classes of debt. If YS is of a bond issue explicitly described as senior, then the spread is assumed to reflect the risk of the firms most senior debt. Along with the face value of the firms senior bonds outstanding it is inputted in Eq. 2-2. If YS is instead that of a non-senior bond issue, then it is assumed to reflect the risk of the firms most junior debt claims. This credit spread and the face value of subordinated bonds are then used as inputs in Eq. 2-3. This second alternative assumption is equivalent to assuming that senior bonds are the companys most senior debt compared to the base assumption that senior bonds might be subordinated to bank loans and private debt. If this generalization is incorrect and a firm has debt senior to the senior bond issues, then YS will overestimate the riskiness of the firms assets and produce IAV estimates higher than those produced by the base case.

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28 2.3.4. Default Data We use two proxies for the event of default the firms delisting date from the exchange that it trades on and the firms bankruptcy filing date. We obtain delisting dates from CRSP for the period 1975-2001 and retain those that are associated with bankruptcy, liquidation, and other financial difficulties (delisting codes greater than 400). We collect bankruptcy-filing dates from FISD for the period 1995-2001. Since an extremely small portion of the firms in our sample default and since there is a large overlap between the CRSP delisting dates and FISD bankruptcy-filing dates, we combine the two data sources.5 We construct an indicator variable DFLT that equals one for quarter t if a firm is either delisted or files for bankruptcy during the three years following that quarter. It equals zero otherwise. 2.4. Summary Statistics We use the methodologies described earlier to compute four estimates of implied asset value and volatility. The base input assumptions are: the time to debt resolution equals one year; the default point is at 97% of total debt; the issuers yield is the yield on the most recently issued bonds; the adjustment for taxes is based on Cooper and Davydenko (2002); and, subordinated debts face value is the face value of the firms bonds outstanding. For a small set of firm-quarter observations, the Newton iterative procedure had difficulties converging. We experimented with different starting values and different methods for solving a system of nonlinear equations (the Jacobi method and the Seidel method). We were successful in calculating all four implied asset value and volatility estimates for 27,723 out of the 28,557 original observations. 5 Estimating two separate logit models, one for delistings and one for bankruptcy filings, yields identical results.

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29 Table 2-1 presents summary statistics on the sample of 27,723 firm-quarters. The average market value of assets is in the range of $6.3-8.1 billion and is very similar across methodologies. The highest value is produced by the simple method of summing the market value of equity and the book value of debt. This is not a surprise since this methodology does not account for the riskiness of debt. When the value of the debt put option is subtracted, then the market value of assets is reduced as indicated by the estimates obtained from any of the system-of-equations methodologies. Unlike the estimates of asset value, the estimates of asset volatility are significantly different across methodologies. The average implied volatility is the lowest, 16.9%, when calculated by the simple method of de-levering equity volatility using the market value of equity and book value of debt. Once a system-of-equations methodology is used, the average estimate becomes higher it is 17.9% for EIAV, 22.9% for DIAV, and 31.9% for EDIAV. The magnitude of the EIAV and DIAV estimates is consistent with that documented in Cooper and Davydenko (2002) and Huang and Huang (2002) both of who rely on historical equity volatility in computing IAV. We investigate whether the IAV differences vary across quarters. Figure 2-1 plots median implied asset volatility for each quarter during 1975-2001, and makes four noteworthy points. First, the four IAV measures appear to follow a similar time pattern. The one notable exception is the last quarter of 1987 when median EIAV, DIAV, and SIAV dramatically increase, while EDIAV falls. This is likely due to the reliance of the first three estimates on historical equity volatility calculated over the three-month period that includes the October 1987 crash. On the other hand, EDIAV is not affected by the crash-induced historical equity volatility and as a result is a more forward-looking

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30 assessment of asset volatility. In fact, EDIAV increases in the second quarter of 1986 possibly in anticipation of the 1987 events. Third, the plot shows that the median SIAV is consistently the lowest estimate of IAV. This is an important observation given the wide use of the estimate in finance research. Finally, the plot shows that the four IAV estimates have significantly increased and the differences among them decreased since the latter part of 1998. We also explore whether our estimates of implied asset volatility are affected by firm leverage. At the end of each quarter, we use firm assets-to-debt ratio ranking to assign them to one of four quartiles. Figure 2-2 shows median implied asset volatilities from our four methodologies by assets-to-debt ratio quartile. It is apparent that the higher the amount of debt relative to assets, the lower the implied volatility. A possible explanation for this finding is that firm capital structure and asset volatility are simultaneously determined. Firms financed with relatively less debt might be willing to take on more risk since they have a significant equity cushion to absorb changes in asset value. Conversely, those that have relatively more debt in their capital structure might be more risk averse since small fluctuations of total asset value can push them into default. The distance-to-default (DD) measure can possibly avoid problems resulting from the endogenous relationship between implied volatility and leverage since it combines them into a single measure of default probability. Table 2-1 present summary statistics on DD calculated from the four estimates of asset volatility. The average DD is 5.08 if calculated from SIAV, 4.66 if calculated from EIAV, 2.17 if calculated from DIAV, and 2.23 if calculated from EDIAV.

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31 The time series behavior of the median of the four DD measures can be seen in Figure 2-3. While the DD estimates calculated from SIAV and EIAV are very volatile, the ones calculated from DIAV and EDIAV are relatively stable. For instance, during 1980-1997 the DD calculated from EDIAV has fluctuated only in the range of 1.50-2.50 while the median DD_EIAV has fluctuated in the range of 1.00-6.50. Once again, the medians of the four DD estimates seem to be converging towards the end of the sample period. Table 2-2 examines more closely the correlation among the four IAV estimates. The table indicates that market value of assets estimates are largely independent of the methodology used to compute them the simple and rank correlations among all of the four estimates are extremely close to 1. Three out of the four asset volatility estimates are also highly correlated. SIAV, EIAV, and DIAV have simple and rank correlations in the 90% range. Two of the three measures however have lower simple correlations with EDIAV 67.5% for SIAV and 62.4% for EIAV with the rank correlations only slightly higher. In contrast, EDIAV is highly correlated with DIAV as indicated by the simple (rank) correlation of 90.5% (88.3%). The simple and rank correlations among the four estimates of DD indicate a strong association between DD_SIAV and DD_EIAV on one hand, and DD_DIAV and DD_EDIAV on the other. Correlations between the first two are 91.3% (simple) and 92.3% (rank), and those between the second two are 94.7% (simple) and 90.9% (rank). In contrast, the DD calculated from DIAV has the lowest simple and rank correlation with the DD calculated from SIAV 19.1% and 21.7%. The correlation of DD_EDIAV with

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32 DD_SIAV and DD_EIAV is always less than 50%. Interestingly enough, the differences in DD measures do not simply reflect differences in IAV as indicated by the high correlation of DIAV with EIAV and SIAV, and relatively low correlations of DD_DIAV with DD_EIAV and DD_SIAV. The wide range of implied asset volatility and distance to default correlations reported in Table 2-2 suggests that different methodologies produce very different estimates. Although all of the simple and rank correlations are statistically different from zero, all of them are also statistically different from one. By using information from different sources the four methodologies discussed in this study produce total risk and default measures not only of different magnitude but also of different ranking. However, whether any of the estimates are superior to the others is an empirical question that requires a comparison of their informational content and accuracy. We conduct such comparisons in the two sections that follow. 2.5. Realized Asset Volatility Tests We start our comparison of the implied volatility measures by examining the relationship between them and realized asset volatility. We explore whether implied asset volatility is a rational forecast of realized asset volatility. This test is similar in spirit to tests used to examine the ability of equity-return volatility implied by equity option prices to predict realized volatility. These studies (Canina and Figlewski 1993, Chernov 2001, Day and Lewis 1992, Jorion 1995, Lamoureux and Lastrapes 1993, Poteshman 2000) yield different results depending on the time period, observation frequency, and data source used. However, their overall conclusion is that implied equity-return volatility is a biased forecast of realized volatility and that it does not use available information efficiently. It will be interesting to relate these findings on the informational content of

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33 implied equity volatility with our findings on the informational content of implied total asset volatility. Our difficulty in comparing implied to realized volatility stems from the fact that unlike the market value of equity which is easily and frequently observed, the market value of total assets can not be directly obtained and requires estimation. We construct a hypothetical monthly time series of the market value of assets as the sum of the market value of common equity, the last available book value of preferred equity, and an estimate of the last available market value of debt. We use two alternative estimates for the market value of debt. The first estimate uses the monthly price of each bond issue and the amount outstanding of all bond issues tracked in the two bond databases to calculate an estimate of each issuers total bond market value. It then substitutes the bonds market value for their face value in the amount of total debt available from quarterly balance sheet reports. That is, the first estimate is the sum of the market value of each firms publicly traded debt and the book value of its non-traded debt. The second estimate assumes that the yield on non-traded debt is the same as that on traded debt, and discounts the book value of total debt accordingly. We use the monthly series of the market value of assets to calculate continuously compounded total asset returns. We define realized asset volatility, RAVt, as the annualized standard deviation of these monthly returns over the two years following the end of quarter t. Historical asset volatility, HAVt, is the annualized standard deviation of monthly returns over the year prior to quarter t. RAV1and HAV1 use our first estimate of the market value of debt, and RAV2 and HAV2 use the second.

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34 2.5.1. Correlation between Implied Asset Volatility and Realized Asset Volatility Table 2-3 presents the simple and rank correlations of the implied asset volatility (IAV) and historical asset volatility (HAV) estimates with realized volatility. The table suggests that IAV is significantly correlated with RAV with simple and rank correlation coefficients in the range of 25.1-31.2% and 42.5-56.7% respectively.6 Among the four IAV estimates the DIAV has the highest simple correlation with RAV closely followed by SIAV and EIAV. The rank correlation of SIAV with RAV is the highest with the correlation of EIAV and DIAV with RAV coming in a close second and third. That is, none of the four implied volatilities appears to be a consistent winner with respect to its correlation with realized volatility. However, there is a consistent looser the correlation between EDIAV and RAV is always the lowest. It is interesting to note that the HAV estimate is very highly correlated with RAV. It has the highest simple and rank correlation coefficient among all the volatility forecast measures. Since a previous section of this study demonstrates that median implied asset volatilities vary with firm leverage, we investigate whether this variation occurs in the correlation between IAV and RAV as well. We calculate simple and rank correlations separately for each asset-to-debt ratio quartile and present these in Table 2-3. We find that as the amount of debt decreases (assets-to-debt ratio increases) simple correlations tend to increase. So do rank correlations of EDIAV and DIAV with RAV. On the other hand, rank correlations of EIAV and SIAV with RAV at first increase but then decrease as asset-to-debt ratio increases. 6 The correlations become smaller when the market value of debt is calculated under the assumption that all of a firms debt is of the same risk class. This implies that such a generalization introduces additional noise in the implied volatility estimates.

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35 2.5.2. Is Implied Asset Volatility a Rational Forecast of Realized Asset Volatility? Theoretically, the estimates of implied total asset volatility calculated earlier are the markets forecasts of future asset volatility. We can assess the accuracy of these forecasts by examining the relation between them and realized asset volatility. Note that realized volatility can be viewed as its expected value conditional on information available at quarter-end t plus a zero-mean random error that is orthogonal to this information. That is ntntntIRAVERAV,,,| where 0|, ntIE This formulation leads to the regression test for forecast rationality7: ntntntForecastVolatilityRAV,,10, (2-5) where Volatility Forecastt,n is one of the four implied asset volatility (IAV) estimates at the end of quarter t for firm n. If IAVt is the true expected value of realized asset volatility conditional on information available at t, then regressing realized asset volatilities on their expectations should produce estimates of 0 and 1 for 0 and 1 respectively. Deviation from these values will be evidence of bias and inefficient use of information in the markets forecasts. Note that the forecast error must be orthogonal to any rationally formed forecast for any information set available at t. Thus, estimating the above regression for each of our IAVt should produce 00 and 11 regardless of the quality of the information that IAVt is based on. However, a more inclusive information set will produce a forecast that explains a relatively larger portion of the variation in the realization. That is, an implied asset volatility estimate derived from a more appropriate model will produce a higher R2. 7 Theil (1966) is credited with introducing this test for forecast rationality. The test has be successfully used in economics research, see Brown and Maital (1981) for an example.

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36 The above tests might lead us to reject the null hypothesis that implied volatility is an unbiased forecast of realized volatility, if realized volatility is simply difficult to predict. That is, if the markets information set at quarter-end t contained very little useful information, then our results would be driven by estimation errors. To investigate whether realized asset volatility is at all predictable using information available at quarter-end t, we use yet another volatility forecast historical asset volatility, HAV. We calculate this from a time series of historical asset values under the assumption that past volatility trends will continue in the future. We then estimate the model above with HAV as the Volatility Forecast. Table 2-4 presents the results from the estimation of Eq. 2-5 for the whole sample of 21,570 firm-quarter observations. All of the intercepts are statistically different from zero which implies that both forward-looking and historical forecasts of asset volatility are positively biased. This bias is the smallest for the DIAV estimate (0.089) and the largest for the HAV estimate (0.137). The volatility forecasts do not appear to use information optimally as indicated by their coefficient estimates in all of the estimations these are significantly different from one. The relative magnitude of the coefficients suggests that DIAV and SIAV make the best use of available information with coefficients of 0.453 and 0.460. The lowest forecast efficiency is displayed by the EIAV estimate with a coefficient of 0.293. The whole-sample results indicate that there is some variation in the quality of information on which each of the forecasts is based. Out of the four IAVs, the SIAV, EIAV and DIAV seem to be the most informative RAV forecasts as indicated by their R2 of 9.6, 8.1, and 9.7% respectively. However, the R2

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37 produced by the HAV is even higher (10.3%) implying that this forecast is based on even better information. Our conjecture that assets-to-debt ratio might affect the forecasting abilities of IAV is supported by the results from estimating Eq. 2-5 for each of the four assets-to-debt quartiles. The first and fourth quartiles display relatively higher intercepts and lower coefficient estimates compared to the second and third quartiles. This suggests that biases in the IAV forecasts tend to be larger for firms with extremely low or extremely large amount of debt in their capital structures. The explanatory power of the models also varies across assets-to-debt ratio quartiles. The IAV measures produce an R2 that is extremely low in the first quartile in the range of 0.7-3.5% but increases as we move to higher quartiles. Nevertheless, explanatory power is always the highest for the model in which HAV is the independent variable. Its R2 starts at 8.2 and increases to 15.5%. It is interesting to note that the fourth assets-to-debt-ratio quartile is characterized by the highest explanatory power which implies that IAV estimates contain better information for low-debt firms. One possible explanation for this surprisingly high R2 is that the realized volatility of firms in that quartile is simply easier to predict since a larger proportion of their total asset volatility comes from equity volatility. Since equity markets are characterized by higher trading volume and more transparency than debt markets, equity volatility might be easier to estimate and forecast than debt volatility. However, the results in Table 2-4 suggest that information from equity prices alone is not enough to form a good asset volatility forecast. Except for the first quartile DIAV always outperforms EIAV it has the lower intercept implying lower bias, the higher coefficient implying higher informational efficiency, and the higher R2 implying better information.

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38 It is disappointing that EDIAV is a considerably worse forecast of RAV than any of the other IAV measures. This can be due to the fact that EDIAV is calculated from a single equity and debt value pair observed at the end of each quarter. This approach might produce measurement errors which can be reduced by using historical equity volatility calculated from equity prices over a whole quarter. As a result any of the IAV measures calculated from historical equity volatility might contain better information than EDIAV. 2.5.3. Is Implied Asset Volatility a Better Forecast Than Historical Asset Volatility? Having both implied asset volatility and realized asset volatility available allows us to examine their relative informational content by estimating a model that includes both: ntntntntHAVIAVRAV,,2,10, (2-6) If the information that is used to calculate one of the forecasts is a subset of the information used to calculate the other, then the coefficient on the more informative forecast will be statistically 1 and the coefficient on the redundant forecast will tend to 0. On the other hand, if the two forecasts are based on different subsets of information then both 1 and 2 will be significantly different from 0 with the larger coefficient corresponding to the more informative forecast. The difference between the R2 of Eq. 2-6 and that of Eq. 2-5 when the Volatility Forecast is HAV will indicate the relative contribution of implied asset volatility to historical data in forecasting future asset volatility. We estimate Eq. 2-6 for the whole sample of 21,570 firm-quarters and then separately for each of the asset-to-debt-ratio quartiles. The whole-sample results in Table 2-5 indicate that the coefficient estimates on both asset volatility forecasts are significantly different from zero. This implies that rather than being redundant, IAV and HAV are based on largely different information sets. Adding IAV to the regression of

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39 RAV on HAV significantly increases the R2. This suggests that implied asset volatility contributes a statistically and economically significant amount of information to a forecast based on historical asset values alone. The marginal contribution is the highest for the DIAV estimate. Interestingly enough, the coefficient estimate on HAV remains significant which suggests that markets do not fully impound historical asset-return volatility in their forecasts of future volatility. No matter the methodology used to extract implied asset volatility from equity and/or debt prices, these prices do not appear to reflect all of the information available. Day and Lewis (1992) and Lamoureux and Lastrapes (1993) reach the same conclusion when examining the relative informational content of implied and historical equity volatility. They document that information available at the time that market prices are set can be used to predict realized return variance better than the variance forecast embedded in stock option prices. The results by assets-to-debt ratio quartiles in Table 2-5 confirm that IAV adds a significant amount of information to HAV. The marginal information contribution does not appear to be systematically related to leverage. However, it is interesting to note that DIAV estimates display the largest marginal increase in R2 in all but the lowest assets-to-debt ratio quartile. Along with the results in Table 2-4, this suggests that for all but the highly levered firms DIAV is not only based on better information than any of the other IAV estimates but that a larger portion of that information is new and different from the information contained in historical asset-return volatility. 2.6. Default and Default Probability Tests To compare the relative default-forecasting accuracy of DD computed from the four asset value and volatility estimates, we design three tests. The first one is based on the occurrence of default and the other two on default probability. We use two proxies for

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40 default probability Altmans (1968) Z score and Moodys credit ratings. The two measures are likely to complement each other well because they are derived using different sets of information. The Z score is calculated from financial ratios that are publicly available, while credit ratings are believed to be based on proprietary models and inside information. 2.6.1. Tests Based on the Occurrence of Default The relative default-forecasting accuracy of the distance-to-default (DD) measures can be best examined through their ability to successfully distinguish between firms that default and those that do not. The analysis relates a firms default status over a three-year period to its DD prior to the beginning of that three-year period. We divide the data into eight subperiods: 1983-85, 1986-88, 1989-91, 1992-94, 1995-97, 1998-2000, and 2001-03. 8,9 The December 1982 estimate of the DD measure is used to explain whether or not the firm defaults in 1983, 1984, or 1985. A three-year period is chosen to balance the need for a short window to capture the DD-default relationship with the need for a long window to obtain sufficient number of defaults in each subperiod. We limit our sample to firms that have data available as of the beginning of at least one of the non-overlapping three-year periods defined earlier. This leaves us with 1,795 firm-quarter observations out of which only 35 are for defaulted firms.10 Being aware of 8 We exclude from our original sample observations prior to 1982 for two reasons. First, the Bankruptcy Reform Act of 1978 revised the administrative and, to some extent, the procedural, legal, and economic aspects of corporate bankruptcy filings in the United States. The Act went into effect on October 1st, 1979. Second, only one of the firms in our sample defaults before 1982. 9 We chose to split our sample into the above listed three-year periods because this particular split allowed us to retain the maximum number of default occurrences. Either of the other two possible splits (starting in 1982 or 1984) yields identical results. 10 Rather than having observations for 52 quarters as in our original sample of 23,857 firm-quarters, we now have observations for 4 quarters. This explains the large reduction in sample size from 23,857 firm-quarters to 1,795.

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41 the econometrics issues that such a lop-sided sample creates, we conduct the occurrence-of-default tests not only on the whole sample but also on the subsample of non-investment grade firms. This allows us to achieve a more balanced dataset 519 observations out of which 30 for distressed firms while biasing our results against detecting a relationship between DD and default occurrences. Table 2-6 provides summary statistics on the average distance-to-default estimates by financial distress status. It shows that independent of the asset volatility estimate used to calculate it, average DD is significantly lower for financially distressed firms. If we look at the subsample of non-investment grade firms, the differences in average DD persist but become smaller and less significant for DD_EIAV and DD_DIAV. We estimate a Logit model in which the dependent variable DFLTt equals 1 if the firm defaults in the three-year period following quarter t, and zero otherwise. The main independent variables are the four DDt calculated from the four implied asset volatility estimates. That is, )()1Pr(,2,1,ntntontControlsDDgDFLT (2-7) The control variables include period indicator variables intended to absorb the effect of macroeconomic changes on instances of default. It also includes an indicator variable, SMALLt that equals 1 if during quarter t a firm is in the bottom equity-value decile of all traded firms. Since for the purposes of our study we define default as a bankruptcy filing, or delisting due to bankruptcy or performance, our set of defaulted firms might include firms that are delisted for non-liquidation reasons (e.g., violation of price limits, not enough market makers, and infrequent trading). We believe that this is more likely to be a problem for relatively small firms and thus employ the variable SMALLt to control for the effects of miscategorizing firms into the set of defaulted ones.

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42 Table 2-7 presents the results from the estimation of Eq. 2-7. The whole-sample results indicate that all four DD measures are statistically significant in explaining the occurrence of financial distress. Their negative sign indicates that a decrease in the distance to default increases the probability that a firm will experience financial difficulties in the following three years. The fit of all four models as indicated by the max re-scaled pseudo R-square, 2 ~ R is in the range of 19.01-22.26%. The best fit is provided by the DD calculated from SIAV, which contributes 7.30% to 2 ~ R of a base logit model that includes period and size indicator variables only. The second best performance is displayed by DD_EDIAV with 2 ~ R of 20.88% and marginal contribution of 5.92% to a base models 2 ~ R The DD coefficient estimates, produced by fitting a logit model to the subsample of non-investment-grade firms, are still negative but of less statistical significance. The DD measures based on EIAV and DIAV are no longer statistically significant, the one based on EDIAV is significant at the 10% level, and the one based on SIAV at the 5% level. The change in statistical significance might be the result of the sample being smaller and more balanced. Alternatively, it might indicates that while methodology choice is not essential for the ability of DD to explaining default probability, it is important when predicting default probability conditional on non-investment grade rating. We examine 2 ~ R of the four models and not surprisingly the best fit is obtained when using SIAV closely followed by EDIAV. The marginal contribution of SIAV and EDIAV to 2 ~ R of a base logit model is 2.91% and 1.83% respectively. In summary, whether analyzing the whole sample or the subsample of non-investment grade firms, the DD estimates calculated from SIAV and EDIAV are better

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43 than the ones calculated from EIAV or DIAV at distinguishing between firms that default and those that do not. However, we should be cautious in interpreting these results as conclusive since they are based on a sample characterized by an extremely small percentage of defaults. 2.6.2. Tests Based on Credit Ratings Credit rating agencies, such as Moodys and Standard & Poor, assess the uncertainty surrounding a firms ability to service its debt and assign ratings designed to capture the results of these assessments. Credit ratings are revisited and revised often to ensure that they reflect the most recent information on the probability that a firm will default. Although the accuracy of credit ratings is difficult to judge, Altman (1989) shows that bond mortality rates are significantly different across credit ratings and that higher ratings imply higher bond mortality rates over a horizon of up to ten years. Based on these findings we interpret a Moodys credit rating as a proxy for the default probability of a firm and examine the relationship between credit ratings and DD. If implied asset volatility is a reliable estimate of firm risk, then the corresponding DD measure will be highly correlated with the firms credit rating. The stronger this relationship, the more accurate the asset volatility estimate. We allow for the DD estimates produced by the four IAV methodologies to differ for the subsamples of investment and non-investment grade firms. Table 2-8 breaks down the original sample of 20,298 observations by Moodys average credit rating and offers median DD statistics by rating category. A cursory examination suggests that credit rating rankings are generally consistent with average DD as ratings deteriorate, DD falls. This relationship is much more pronounced for non-investment grade firms and seems to be independent of the implied asset volatility that

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44 DD is based on. Table 2-9 investigates whether quarterly changes in firm DD over the period of 1975-2001 are consistent with subsequent quarterly changes in Moodys credit rating. The median DD_EDIAV and DD_DIAV changes seem consistent with the subsequent credit upgrades and downgrades. Moodys appear to downgrade a firm after its DD has fallen. This fall is larger if when downgraded the firm moves from investment into non-investment grade. Similarly, when a firms credit rating is adjusted upwards then its DD has just increased with the increase being larger for firms upgraded into investment grade. The average DD calculated from EIAV or SIAV do not follow this pattern. In fact, for the firms whose credit rating changes from investment into non-investment grade, the beginning-of-the-quarter DD is higher than that of the previous quarter. This counter-intuitive association between average DD and credit rating changes holds true for the firms downgraded from investment grade into non-investment grade when DD is based on SIAV. In order to control for the effect of other variables on firm credit rating, we estimate a multivariate regression model separately for investment and non-investment grade firms. That is, we estimate via OLS: 11 junknt k ntkControlsjunkkntDDjunkjunkjunkntRTGinvestntkntkControlsinvestkntDDinvestinvestinvestntRTG,,,,10,,,,,10, (2-8) The set of controls includes industry indicator variables and a measure of firm size. It is possible that credit rating agencies pay different attention to the financial health of small 11 Credit ratings are categorical variables which would suggest that the above model is better estimated via logit or probit model. We choose to use OLS for two reasons. First, although issue credit ratings are discrete, issuer credit ratings are not since they are the average issue ratings for that issuer. Second, the fact that issuer credit ratings are not discrete leaves us with more than 100 issuer rating categories and that creates convergence problems for an ordered logit model.

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45 versus large firms. We control for such differences by including the natural logarithm of the market value of assets corresponding to each volatility estimate in the logit estimations above. It might also be the case that the credit ratings of regulated firms contain different information compared to those of non-regulated firms. If government agencies intervene to correct problems as soon as they are detected, then all else equal the default risk of a regulated firm is less than that of a non-regulated one. We allow for this possibility by including an indicator variable REG that equals 1 if a firm operates in a regulated industry during the quarter in question, and equals 0 otherwise. Finally, the set of controls includes industry indicator variables that are designed to control for default-point variations among industry groupings. The results from estimating Eq. 2-8 via OLS are presented in Table 2-10. They indicate that DD measures calculated from any of the four IAV estimates are an accurate assessment of firm default risk as proxied by Moodys credit rating. The coefficient on DD is always negative and statistically significant which implies that higher distance to default is associated with a higher-number rating (lower credit rating is denoted by a higher number). In evaluating the relative accuracy of the four DD estimates we focus on the marginal contribution of each measure to the explanatory power of a regression that includes control variables only. The whole-sample results indicate that the increase in R2 is the highest (7%) when we add DD_EIAV to the set of independent variables. The second highest marginal contribution is provided by DD_SIAV (5.8%) and then by DD_EDIAV (3.6%). Assuming that Moodys credit rating is an accurate proxy of the probability that a firm defaults, then our results indicate that EIAV is the most precise

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46 forecast of future volatility. It is interesting to note that the accuracy ranking among the four estimation methodologies changes when we split our sample into investment and non-investment grade firms. The biggest surprise comes from the relative performance of EDIAV. This estimate produces a DD measure with the highest marginal contribution to R2 for the set of non-investment-grade firms 6.0%. For this set of firms relying on historical equity volatility appears to reduce the informational content of the IAV estimates as judged by the marginal contribution of any of the other three DD measures. In addition to investigating the accuracy of DD, we also investigate whether the information it contains is distinct from and timelier than that contained in credit ratings. We do so by employing a Granger-causality test. We examine whether credit rating upgrades and downgrades can be forecasted with information contained in lagged distance-to-default changes. We allow for a change in firm default probability to be reflected in its debt and equity valuation up to three quarters before it is reflected in a credit rating change. That is, we use up to three lags of DD in the models below. We also allow for the possibility that credit rating downgrades convey more information than credit rating upgrades. Hand et al. (1992) and Goh and Ederington (1993) investigate the informational content of credit ratings and conclude that downgrades contain negative information while upgrades contain little or no information as indicated by bond and stock price reactions. Thus, to test our conjecture we estimate two Logit models one for downgrades versus no changes, and another for upgrades versus no changes. That is, we estimate:

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47 ),,4431,3,4231,1(1,PrkntControlskntRTGjnjtdRTGjntDDinitdDDiog)nt(dRTG (2-9) where 1, ntdRTG if firm ns credit rating has been upgraded in quarter t from its rating in quarter t-1, and if the rating has remained the same. Similarly, we estimate: 0,ntdRTG kntControlskntRTGjnjtdRTGjntDDinitdDDiog)nt(dRTG),,4431,3,4231,1(0,Pr (2-10) where 0, ntdRTG if the rating has remained the same and if firm ns credit rating has been downgraded in quarter t from its rating in quarter t-1. In addition to the control variables described earlier, we include two more in the estimation of the above models. The literature on the informational content of credit ratings documents that highly rated firms are very rarely downgraded. This implies that a firms starting credit rating affects the probability of a subsequent downgrade/upgrade. Since the logit models include three lags of DD and rating changes, we choose to include the firms rating four quarters prior to t. We also include the contemporaneous DD estimate. 1,ntdRTG Table 2-11 presents the results from a logit analysis that examines the relation between credit rating upgrades/downgrades and DD changes. The relationship between changes in credit rating and changes in distance to default appears to be of the expected direction. The negative sign on the coefficient estimates indicates that the larger the decrease in distance to default, the larger the probability of a credit rating downgrade. All three lags of all four estimates of DD are statistically significant in explaining the

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48 probability of credit rating downgrades. This suggests that the DD estimates capture increases in default probability up to a year before these increases are reflected in an actual credit rating change. This information appears to be distinct from information contained in previous credit rating changes as indicated by the persistent statistical significance of some of the lagged rating change variables. In fact, it can be argued that the information contained in the DD estimates is better since adding DD into the model reduces the statistical significance of some of the lagged ratings. We compare the fit of the four models to that of a base model, which includes only control variables. We discover that the DD calculated from EIAV provides the highest marginal contribution to the R2 (1.6%) and is closely followed by the marginal contribution of the DD calculated from SIAV (1.3%). While changes in DD are highly significant in predicting credit rating downgrades, Table 2-11 shows that they lack forecasting power when it comes to rating upgrades. Only some of the lagged variables coefficients are statistically significant and significance levels are generally lower. While the explanatory power of the model is higher for upgrades than it is for downgrades, the marginal contribution of the lagged DD changes to the R2 is economically zero. On one hand this suggests that credit rating upgrades are easier to forecast than credit rating downgrades. On the other, it appears that lagged changes in DD do not aid in this forecasting process. This could be the result of credit rating upgrades containing little or no new information as documented in Hand et al. (1992) and Goh and Ederington (1993). Thus, the decrease in default probability that we use them to proxy for has been incorporated in the firms valuation earlier than the

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49 three quarter lags that we include. This is consistent with the fact that the most recent DD changes have the lowest statistical significance. To sum up, all four DD estimates are able to detect credit rating downgrades up to a year before they occur. The estimate based on EIAV seems to be better at explaining subsequent downgrades than are the estimates based on EDIAV, DIAV, and SIAV. Although some of the DD estimates lags are statistically significant in explaining credit rating upgrades, none of them improve our ability to distinguish between upgrades and no-changes as indicated by their marginal contribution to the R2 of a base regression. 2.6.2. Tests Based on Altmans (1968) Z Altmans (1968) Z-model provides an alternative proxy for default probability. This is probably the most popular model of bankruptcy prediction and has been extensively used in empirical research and in practice.12 The Z-model is obtained through multiple discriminant analysis of the financial ratios of industrial firms. It is given by: sTotalAssetSalesityBookValEqutyMktValEquisTotalAssetEBITsTotalAssetngsRetainedErsTotalAssetWrkCapitalZ6.03.34.12.1 The Z thus obtained is a measure of financial health and a higher Z implies a lower probability of default. If IAV is the markets rational expectation of future total asset volatility, then the DD it implies should reflect expected default probability. Since Z is a measure of the same expectation then a higher DD should be associated with a higher Z. Although Z has been documented to predict default occurrences quite accurately13, the evidence in Dichev (1998) suggests that Z is a better predictor of default when the ex 12 See Altman (1993) for an extensive review of empirical studies citing and using the Z-model. 13 See Altman (1993) and Begley, Ming, and Watts (1997) for tests of Zs predictive abilities.

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50 ante probability of default is high. He forms portfolios based on Z deciles and finds that the correlation between the number of distress delistings in each portfolio and the portfolios rank is high when Z is low (portfolio 1-5). In contrast, when Z is high (portfolios 6-10) the correlations are low and sometimes with a sign reversed from expected. To account for this asymmetry in the predictive abilities of the measure, we allow the relationship between Z and DD to differ across ex ante default probability. Following the approach in Dichev (1998) we use each firms Z-score at the end of each quarter and assign the firm to one of ten Z-decile portfolios. We start our analysis with simple univariate comparisons between Z-Scores and DD estimates. Each quarter we assign firms in our sample to one of ten Z-score deciles. Table 2-12 presents medians of the four DD estimates by Z-Score deciles and shows that higher deciles are typically associated with higher DDs. It is interesting to note that the two DD estimates that incorporate information from debt prices, DD_EDIAV and DD_DIAV, are more consistent over the low-Z deciles, while the ones that incorporate information from equity prices are more consistent over the high-Z deciles. We then estimate a model separately for low-Z (portfolios 1-5) and high-Z (portfolios 6-10) firms. That is, highntkntkControlshighkntDDhighihighhighntZlowntkntkControlslowkntDDlowilowlowntZ,,,,0,,,,,0, (2-11) Table 2-13 contains the results from this OLS estimation. All four DD estimates are highly statistically significant in explaining Z whether the model includes industry or firm fixed effects. The positive sign on the DD coefficient indicates that a larger distance to default is on average associated with a higher Z score. This implies that all four of the

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51 DD estimates contain accurate information about a firms default probability if Z is a good proxy of this probability. The relative accuracy of the four measures can be determined by their marginal contribution to the explanatory power of a base model that includes control variables only. In the regression that includes industry fixed effects, DD_DIAV produces the highest increase in R2 (2.74%). It is followed by DD_EIAV with 2.11%. This accuracy ranking is reversed when the regression includes firm fixed effects with DD_EIAV containing better information than DD_DIAV. For the subset of high-Z firms, the coefficient estimates of DD are less significant and/or of a sign opposite to the one expected. Also, these variables add little or no explanatory power when included among the explanatory variables. These results might indicate that DD is a poor estimate of a firms true distance to default, or perhaps Z is simply a poor measure of default risk. Although we cannot unambiguously distinguish between these two alternatives, the results in Dichev (1998) suggest that Z might be the flawed measure. He shows that Z score is a less accurate measure of default risk when the ex ante default risk is low. We also examine whether changes in default probability, as proxied by Z, can be predicted by changes in the four DD estimates. Since an increase in a firms distance to default implies that its financial condition is improving, then changes in DD should be associated with same-direction changes in Z. To examine whether this is the case, we estimate a model in which the dependent variable is dZt: the change in Z from quarter-end t-1 to quarter-end t. The main independent variable is the change in one of the four distance-to-default estimates, dDDt. The four DDt are calculated from the four implied asset value and volatility estimates in quarter t and the change dDDt is from quarter-end t

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52 1 to quarter-end t. We include up to three lags of dDDt to investigate whether financial markets detect changes in default probability before these are reflected in a firms accounting reports. We allow for our DD estimates to have different predictive power for positive and negative changes in Z. There is circumstantial evidence that when it comes to credit risk, investors tend to be surprised by negative information but not by positive information. Studies document that bank regulators and credit rating agencies downgrades are regarded as news while upgrades seem to have no new informational content. It has been maintained that the reason behind this asymmetry is managers willingness to share favorable and withhold unfavorable private information. Thus, the release of the latter is eventually forced by regulators and rating agencies. We extend this argument to quarterly reports. We contend that while managers might reveal good news as soon as it becomes available, they might wait to disclose bad news until their quarterly reports are due. We estimate a model separately for increases and decreases in Z to allow for a possible asymmetry in informational content: ntkntkControlskinitdDDintdZntkntkControlskinitdDDintdZ,,,31,0,,,,31,0, (2-12) All of the models in this subsection are estimated via ordinary least squares. The set of control variables includes the natural logarithm of the market value of assets, SIZEt, since previous research has established that smaller firms are more likely to default all else equal. It also includes an indicator variable, REGt, which equals 1 if the firm operates in a

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53 regulated industry during the quarter in question, and 0 otherwise.14 We include quarterly indicator variables designed to absorb the effect of macroeconomic changes on default probability. Finally, we include either industry or firm indicator variables in order to capture default-point differences across industries or firms respectively. In essence, this is identical to estimating a panel regression with industry or firm fixed effects.15 Table 2-14 presents the results from estimating Eq. 2-12. DD changes are statistically significant only for the subset of negative Z changes with industry fixed effects, and the subset of positive Z changes with firm fixed effects. When significant their coefficients are positive indicating that the larger the increase in DD, the larger the increase in Z. The marginal contribution of DD changes to the R2 of a regression including lagged Z changes and control variables only, indicates that the former add little to no new information the marginal contribution is always less than 0.2%. However, there is a DD estimate that stands out. An assessment of each of the four DD estimates statistical significance and marginal explanatory power suggest that the DD calculated from EIAV performs best. In summary, the results presented in this section indicate that when the ex ante probability of default is high all four DD estimates accurately reflect a firms default risk. It seems that the DD estimate calculated from EIAV is more accurate and timely than the other DDs. Furthermore, it appears to add the most new information to the firms lagged Z-score changes. 14 Regulated industries include railroads (SIC code 4011) through 1980, trucking (4210 and 4213) through 1980, airlines (4512) through 1978, telecommunications (4812 and 4813) through 1982, and gas and electric utilities (4900 and 4939). See Frank and Goyal (2003) for more. We estimate the regressions excluding regulated firms from the sample and the results remain unchanged. 15 Our sample contains more than one industries represented by a single firm. To ensure that the model is identified we do not include both industry and firm indicator variables in the same estimation.

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54 2.7. Sensitivity of Estimates to Alternative Model Assumptions The analysis above examines the properties of implied asset values, volatilities, and distance-to-default measures calculated under a set of base assumptions. In this section we assess the sensitivity of the estimates to changes in the assumptions. To do so, we repeat the realized asset volatility, and the default and default probability tests discussed earlier using alternative-assumption estimates of IAV and DD. We include a sample of our results below. 2.7.1. Summary Statistics Table 2-15 presents summary statistics under alternative assumptions. The sample statistics are largely unaffected when we use different default points, different issuer yields, or limit ourselves to non-callable bonds only. In contrast, employing alternative time-to-resolution, tax-adjustment, or debt-priority assumptions makes a significant difference. As the time to resolution increases from one year to the duration and then the maturity of debt, median EIAV considerably increases from 15.7% to 24.2% Median DIAV is almost unchanged when instead of one year we assume that the time to resolution equals the average duration of debt. However, if time to resolution is assumed to equal the average debt maturity, then average DIAV increases. It is interesting to note that increasing the time to resolution at first decreases but then slightly increases the EDIAV estimate. While under the one-year to resolution assumption the three system-of-equations IAV estimates are significantly different, increasing the time to resolution has the effect of making their magnitudes very similar and changing their relative ranking. In fact, if the time to resolution is assumed to equal the average maturity of debt then

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55 average EIAV is the highest, while under the one year to resolution assumption it is the lowest. Since DIAV and EDIAV are the only estimates calculated from credit spreads, they are the only estimates affected by employing an alternative tax adjustment. Table 2-15 shows that if we do not adjust for the differential taxation of corporate and Treasury securities altogether, both DIAV and EDIAV increase. This effect is expected since not adjusting for taxes overestimates the portion of yield spreads due to default risk, which in turn overestimates the implied volatility of total assets. On the other hand, when we adjust for taxes by differencing corporate yields with the average yield on Moodys AAA-rated bonds, the two IAV estimates significantly decrease. Finally, the sample summary statistics are most dramatically affected by changes in the debt priority assumption. Table 2-15 indicates that the DIAV and EDIAV estimates increase to unreasonable levels whenever we assume that bond yields are representative of the default risk of total debt. The increase is even more striking when we assume that senior bonds are senior to all remaining debt, and junior bonds are junior to all remaining debt. It is important to note that this latter result might be due to the loss observations. Under the second alternative debt-priority assumption the algorithm used to solve for the DIAV and EDIAV fails to converge for about 500 additional observations that tend to be characterized by low credit spreads. 2.7.2. Realized Asset Volatility Tests Table 2-16 presents the results from re-estimating Eq. 3-5. As suggested by the summary statistics in Table 2-15, alternative assumptions about each firms default point and credit spread do not considerable affect the informational content of the IAV estimates. Three alternative assumptions that significantly worsen the forecasting ability

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56 of the IAV estimates are that (1) time to resolution equals the weighted average maturity of traded debt, (2) differencing corporate yields with the average yield on Moodys AAA-rated bonds is a proper tax adjustment, and (3) senior (junior) bonds are the firms most senior (junior) debt. When we limit our sample to non-callable bonds we lose almost two-thirds of our observations. These seem to be observations that contain high-quality information, since the explanatory power for this subsample is quite lower than in our base case. Only two alternative assumptions produce IAV estimates which forecast RAV better than the base IAV estimates. Assuming that time to resolution equals the weighted average duration of each firms traded debt or assuming that all debt is of the same priority and homogeneous default risk produces the IAV estimates with the highest explanatory power. The former assumption also generates some of the highest coefficient estimates on IAV suggesting that these estimates use information most efficiently. 2.7.3. Default and Default Probability Tests The results from re-estimating the default forecasting model Eq. 2-7 are shown in Table 2-17. Increasing the time to resolution has the effect of decreasing the explanatory power of the DD estimates obtained through any of the system-of-equations IAV methodologies. Consistent with our realized asset volatility test, we find that alternative assumptions about default point or issuer yield do not significantly impact the explanatory power of the model. Employing no tax adjustment reduces the explanatory power of the two estimates whose calculation requires bond yields DIAV and EDIAV. Adjusting for taxes by using the average yield on Moodys AAA-rated bonds reduces explanatory power for the whole sample but produces some of the highest 2 ~ R for the subsample of non-investment grade firms. The sensitivity results in Table 2-17 indicate

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57 that some of the alternative assumptions employed affect the explanatory power of our model. However, DD_SIAV consistently produces the highest marginal contribution to 2 ~ R and is typically followed by DD_EDIAV. Assuming that all debt is senior and of homogeneous risk is the only assumption under which the distance to default obtained from EDIAV is relatively more informative than that produced by SIAV judging by 2 ~ R Table 2-18 presents the results from re-estimating the credit ratings model (Eq. 2-9). Most of the alternative assumptions preserve the performance ranking of the four DD measures. The equity DD measure, DD_EIAV, outperforms the others in the whole sample and the investment-grade subsample estimation. For the subsample of junk firms, the DD measures which combines information from equity and debt prices typically outperforms the other DD measures. Both DD_EIAV and DD_EDIAV have the highest explanatory power when constructed under the assumption that a firms default point equals 95% of its total debt. The results from re-estimating the downgrade/upgrade logit model (Eq. 2-10) can be seen in Table 2-19. As we already established, the market measures are statistically significant but improve the fit of forecasting models only marginally. Table 2-19 points out that this relatively poor forecasting ability is not significantly worsened or improved by alternative model assumptions. The DD measures that rely on debt price information, DD_DIAV and DD_EDIAV, produce the best fit when credit spreads are calculated using the average yield on Moodys AAA-rated bonds rather than the yield on Treasury securities.

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58 2.8. Summary and Conclusion The results reported in this study have important implications for financial theory and practice. Researchers and practitioners have employed a variety of methods to obtain estimates of asset volatility for the purpose of valuing corporate debt and derivative products written on it, measuring total firm risk, or pricing deposit insurance. However, despite the variety in available methods, we know very little about the empirical properties of the implied asset volatility estimates they produce. We address this gap in the literature in two steps. First, we examine whether the source of information debt versus equity prices, and historical versus implied equity volatility impacts the informational content and accuracy of implied asset volatility. Second, we explore whether assumptions about the model parameters time to resolution, default point, debt priority structure, and tax and call option adjustments appear to be important. To address the first issue we construct four estimates of implied asset volatility. We obtain the simplest one by de-levering historical equity volatility using the market value of equity and the book value of debt. To construct the other three we use contingent-claim pricing models to simultaneously solve for the market value and volatility of assets. The first estimate reflects information from equity prices and historical equity volatility, and the second one reflects information from debt prices and historical equity volatility. The last estimate incorporates information from contemporaneous equity and debt prices without relying on past equity volatility information. We assess the relative performance of the four implied asset volatility estimates by using them to forecast realized asset-return volatility, defaults, credit ratings, and Z scores. We document that the implied asset volatility calculated from debt prices best explains variations in realized asset volatility. This is contrary to the commonly held

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59 belief that debt markets are characterized by many frictions and as a result debt prices are too noisy to be useful. In addition to directly examining the relation between implied and realized volatility of asset returns, we perform a number of indirect tests that draw on the intuition that, all else equal, firms with highly volatile assets have a higher default probability. For the purpose of these tests we use firm leverage and asset volatility to construct a default risk measure, distance to default, that represents the number of asset-value standard deviations required to push a firm into default. We find that this default risk measure can successfully forecast defaults, and is highly correlated with a firms credit rating and Z score. However, none of our four implied-asset-volatility methodologies produces a default risk measure that consistently outperforms the others. When we examine whether the distance-to-default measures are able to forecast changes in credit ratings and Z scores, we find that their predictive power is limited to negative changes in the dependent variables. This is consistent with the findings of previous studies that market participants rarely regard decreases in default probability as news. In determining which of the four methodologies analyzed in this study produces the most informative and accurate estimate of total firm risk, we examine the marginal contribution of each methodologys default risk measure to the explanatory power of a base regression. We find that although there is no consistent winner, the measure calculated from equity prices and historical equity volatility has slightly better forecasting abilities than do measures constructed through other methodologies. The second contribution of this study is that it documents the impact of alternative model assumptions on estimates of implied asset volatility. While the choice of using equity or debt prices to extract firm risk information appears to be inconsequential, we

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60 find that the choice of model parameters is quite important. We show that the manner in which we adjust yield spreads to account for embedded call options, and tax differences between corporate and Treasury securities has a significant effect on the level and rank ordering of firm risk measures. In addition, assumptions about the maturity of debt and debt priority structure seem to affect the forecasting ability of both implied-volatility and distance-to-default estimates. In contrast, using alternative assumptions about each firms default point and alternative approaches to aggregating issue yields into issuer yields appear immaterial. This finding underscores the importance of robustness checks whenever equity and debt valuation is based on contingent-claim pricing models. It also provides researcher and practitioners with some guidance as to the model parameters most likely to influence results.

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61 Table 2-1. Summary statistics. Summary statistics are for the sample of 27,723 firm-quarter observations over 1975-2001. SIAV is the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. Implied asset volatilities are reported in percent per year. V_SIAV, V_EIAV, V_DIAV, and V_EDIAV are the corresponding estimates of the market value of assets in billion dollars. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. VariableMinimumMaximumMedianMeanStdDevV_SIAV0.03404.072.908.1420.52V_EIAV0.02383.082.777.7619.37V_DIAV0.02395.202.216.3116.93V_EDIAV0.02383.082.777.7519.37SIAV0.6154.614.816.910.6EIAV0.7208.015.717.911.6DIAV1.1141.220.222.912.8EDIAV1.9172.429.531.915.3DD_SIAV0.0520.344.835.082.12DD_EIAV-1.3818.244.364.662.20DD_DIAV-0.7019.261.902.171.40DD_EDIAV-0.3432.562.022.231.26

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Table 2-2. Simple and rank correlations. Correlations are for the sample of 27,723 firm-quarter observations over 1975-2001. SIAV is the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. V_SIAV, V_EIAV, V_DIAV, and V_EDIAV are the corresponding estimates of the market value of assets. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. All correlations are significantly different from 0 at the 1 percent level. Simple Correlations V_SIAVV_EIAVV_DIAVV_EDIAVV_SIAVV_EIAVV_DIAVV_EDIAVV_SIAV1.0001.000V_EIAV1.0001.0001.0001.000V_DIAV0.9850.9821.0000.9900.9891.000V_EDIAV1.0001.0000.9821.0001.0001.0000.9891.000SIAVEIAVDIAVEDIAVSIAVEIAVDIAVEDIAVSIAV1.0001.000EIAV0.9871.0000.9961.000DIAV0.9070.8711.0000.9370.9231.000EDIAV0.6750.6240.9051.0000.6930.6640.8831.000DD_SIAVDD_EIAVDD_DIAVDD_EDIAVDD_SIAVDD_EIAVDD_DIAVDD_EDIAVDD_SIAV1.0001.000DD_EIAV0.9131.0000.9231.000DD_DIAV0.1910.3151.0000.2170.3311.000DD_EDIAV0.3480.4260.9471.0000.4170.4730.9091.000Rank Correlations 62

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Table 2-3. Simple and rank correlations of implied and historical asset volatility with realized asset volatility. Correlations are for the sample of 21,570 firm-quarter observations over 1975-2001. SIAV is the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. HAV1 and HAV2 are two estimates of annualized historical asset volatility calculated over the year prior to the end of each quarter. RAV1 and RAV2 are two estimates of annualized realized asset volatility over the year following each quarter-end. HAV1 and RAV1 assume that the market value of debt is the sum of the market value of traded debt and the book value of non-traded debt. HAV2 and RAV2 assume that the yield to maturity on non-traded debt is the same as the yield to maturity on traded debt. All correlations are significantly different from 0 and 1 at the 1 percent level. Simple CorrelationsRank EDIAVEIAVDIAVSIAVHAV1HAV2EDIAVEIAVDIAVSIAVHAV1HAV2Whole Sample, N=21,570RAV10.2510.2850.3120.3100.3210.3200.4250.5330.5140.5670.5630.490RAV20.2060.2720.2740.2670.3160.3340.3280.4890.4300.4630.5120.499Assets-to-Debt Ratio, Quartile 1, N=5,428RAV10.0840.1780.1700.1890.2870.3030.2490.4050.3860.4220.5050.425RAV20.0760.1800.1650.1600.2870.3240.1910.3740.3300.3100.4580.470Assets-to-Debt Ratio, Quartile 2, N=5,380RAV10.2070.2890.3040.3330.3440.3080.2620.5200.4500.5370.5620.501RAV20.1810.2840.2850.3130.3300.3110.2200.4920.4040.4710.5280.517Assets-to-Debt Ratio, Quartile 3, N=5,410RAV10.2410.2660.3060.3030.3690.3750.3500.4550.4530.4780.4740.455RAV20.2270.2710.2970.2970.3580.3740.3000.4550.4150.4490.4520.463Assets-to-Debt Ratio, Quartile 4, N=5,352RAV10.3370.3320.3910.3660.3940.3860.4050.4310.4590.4460.4220.411RAV20.3200.3510.3830.3730.4060.4040.3580.4350.4230.4290.4190.420Correlations 63

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64 Table 2-4. Analysis of IAV and HAV forecasting properties. We estimate via OLS ntntntForecastVoaltilityRAV,,10, .Volatility forecast is one of the five: SIAV, EIAV, DIAV, EDIAV, or HAV. SIAV is the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. HAV is an estimate of annualized historical asset volatility calculated over the year prior to the end of each quarter. RAV is an estimate of annualized realized asset volatility over the two years following each quarter-end. Standard errors are reported in parenthesis. All coefficient estimates are statistically significant at the 1 percent level. Sample Used in EstimationEDIAVEIAVDIAVSIAVHAVWhole Sample, N=21,570Intercept0.1080.1220.0890.1130.137(0.002)(0.018)(0.003)(0.024)(0.014)Slope0.3430.2930.4530.4600.273(0.009)(0.006)(0.015)(0.014)(0.003)R20.0630.0810.0970.0960.103Assets-to-Debt Ratio, Quartile 1, N=5,428Intercept0.1330.1260.0990.1060.134(0.009)(0.003)(0.010)(0.005)(0.012)Slope0.2020.2330.4270.6490.186(0.002)(0.008)(0.004)(0.024)(0.016)R20.0070.0310.0290.0350.082Assets-to-Debt Ratio, Quartile 2, N=5,380Intercept0.0910.1090.0630.0790.107(0.010)(0.005)(0.013)(0.015)(0.004)Slope0.3790.3020.5570.6850.385(0.001)(0.024)(0.003)(0.004)(0.014)R20.0430.0830.0920.1110.118Assets-to-Debt Ratio, Quartile 3, N=5,410Intercept0.0980.1280.0800.1030.114(0.005)(0.003)(0.013)(0.028)(0.015)Slope0.3980.2800.5050.5140.448(0.002)(0.014)(0.003)(0.015)(0.003)R20.0580.0710.0940.0920.136Assets-to-Debt Ratio, Quartile 4, N=5,352Intercept0.1230.1440.1070.1300.131(0.009)(0.005)(0.014)(0.005)(0.015)Slope0.3090.2640.3910.3730.426(0.005)(0.024)(0.006)(0.021)(0.016)R20.1130.1100.1530.1340.155IAV Methodology

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65 Table 2-5. Analysis of the relative informational content of IAV and HAV in forecasting RAV. We estimate via OLS ntntntntHAVIAVRAV,,2,10, .The independent variable IAV is SIAV, EIAV, DIAV, or EDIAV. SIAV is the simple implied asset volatility obtained by de-levering historical equity volatility. EIAV is the equity-implied asset volatility obtained from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility obtained from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility obtained from contemporaneous equity and debt prices. HAV is an estimate of historical asset volatility calculated over the year prior to the end of each quarter. RAV is an estimate of realized asset volatility over the 2 years following each quarter-end. Standard errors are reported in parenthesis. All coefficient estimates are statistically significant at the 1 percent level. R2 (IAV) is the marginal contribution of the corresponding IAV to the models R2 when compared to a base model including HAV only. Sample Used in EstimationEDIAVEIAVDIAVSIAVWhole Sample, N=21,570Intercept0.0790.0990.0690.091(0.002)(0.034)(0.004)(0.003)IAV0.2790.2180.3620.357(0.007)(0.005)(0.012)(0.014)HAV0.2450.2230.2220.218(0.002)(0.046)(0.003)(0.015)R20.1430.1440.1610.157R2 ( IAV)0.0410.0410.0580.054Assets-to-Debt Ratio, Quartile 1, N=5,428Intercept0.1000.1020.0730.082(0.002)(0.004)(0.031)(0.016)IAV0.2090.1930.3880.576(0.007)(0.026)(0.008)(0.004)HAV0.1860.1750.1800.177(0.006)(0.003)(0.004)(0.014)R20.0890.1030.1060.110R2 ( IAV)0.0070.0210.0240.028Assets-to-Debt Ratio, Quartile 2, N=5,380Intercept0.0600.0830.0480.063(0.002)(0.014)(0.017)(0.017)IAV0.2630.1920.3840.475(0.009)(0.005)(0.008)(0.005)HAV0.3530.3060.3030.279(0.005)(0.022)(0.006)(0.022)R20.1380.1460.1560.162R2 ( IAV)0.0200.0280.0380.044IAV Methodology

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66 Table 2-5. Continued Sample Used in EstimationEDIAVEIAVDIAVSIAVAssets-to-Debt Ratio, Quartile 3, N=5,410Intercept0.0620.0920.0590.079(0.002)(0.004)(0.032)(0.016)IAV0.2530.1450.3170.295(0.010)(0.014)(0.008)(0.004)HAV0.3980.3790.3580.354(0.006)(0.005)(0.005)(0.024)R20.1580.1520.1670.160R2 ( IAV)0.0220.0160.0310.024Assets-to-Debt Ratio, Quartile 4, N = 5,352Intercept0.0850.1150.0840.107(0.006)(0.021)(0.044)(0.017)IAV0.2060.1300.2630.214(0.033)(0.004)(0.008)(0.004)HAV0.3400.3280.2910.297(0.004)(0.022)(0.005)(0.012)R20.1990.1740.2080.185R2 ( IAV)0.0440.0190.0530.029IAV Methodology

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67 Table 2-6. Average DD statistics by default status. A firm is considered Defaulted if it is delisted due to liquidation or performance, or files for bankruptcy in the three years following the fourth quarter of 1982, 1985, 1988, 1991, 1994, 1997, and 2000. SIAV is the simple asset volatility, EIAV is the equity-implied asset volatility, DIAV is the debt-implied asset volatility, and EDIAV is the equity-an-debt-implied asset volatility. DD is the distance to default measure calculated from the corresponding asset values and volatilities, and represents the number of standard deviations required to push a firm into default. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Default StatusNInvestment and Non-investment Grade ObservationsAll1,7953.292.891.301.39Non-defaulting1,7603.322.911.321.40Defaulting352.061.650.720.89Difference1.25***1.26***0.59***0.51***Non-investment Grade ObservationsAll5192.451.920.861.01Non-defaulting4892.481.940.871.02Defaulting301.901.520.680.83Difference0.58***0.42**0.19*0.19***Average DD Calculated fromSIAVEIAVDIAVEDIAV

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Table 2-7. Logit analysis of defaults. We estimate ntntntontControlsDDDFLT,,2,1, .These are the results from a logistic regression on the sample of all 1,795 observations and the subsample of 519 non-investment-grade observations. The dependent variable DFLT equals 1 if the firm is delisted due to liquidation or performance, or files for bankruptcy in the three years following the fourth quarter of 1982, 1985, 1988, 1991, 1994, 1997, and 2000; it equals 0 otherwise. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. P3-P8 are period indicator variables. R2 is max-rescaled pseudo R2, which is an indicator of fit for logit models. R2 is the marginal contribution of each DD to R2. It is measured as the difference between R2 of a model including DD, and that of a base model excluding it. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Investm SIAVEIAVDIAVEDIAVSIAVEIAVDIAVEDIAVIntercept-3.350***-4.424***-4.590***-3.318***-3.028***-3.917***-3.817***-3.365***(0.867)(0.789)(0.760)(0.887)(0.904)(0.777)(0.773)(0.855)DD-1.001***-0.599***-0.932***-1.923***-0.659**-0.209-0.451-0.870*(0.240)(0.180)(0.253)(0.478)(0.306)(0.176)(0.290)(0.463)P32.143***1.973**1.516*1.578*1.4351.1550.9781.040(0.816)(0.813)(0.808)(0.808)(0.874)(0.859)(0.852)(0.851)P42.300***1.776**1.2811.3841.4200.9650.7630.786(0.842)(0.846)(0.843)(0.848)(0.913)(0.888)(0.900)(0.906)P62.053**1.811**1.394*1.507*1.560*1.2471.0741.154(0.832)(0.826)(0.827)(0.825)(0.859)(0.841)(0.835)(0.834)P72.920***3.056***2.900***2.833***2.595***2.519***2.463***2.512***(0.837)(0.834)(0.834)(0.833)(0.881)(0.875)(0.872)(0.872)P82.949***3.291***3.597***3.249***2.579***2.852***2.912***2.830***(0.830)(0.819)(0.809)(0.819)(0.852)(0.837)(0.831)(0.833)SMALL1.464***1.299**1.394**1.055*1.273**1.167*1.078*0.961(0.562)(0.609)(0.603)(0.621)(0.616)(0.639)(0.650)(0.668)R20.2230.1960.1900.2090.1560.1340.1380.145R2 (DD)0.0730.0460.0400.0590.0290.0070.0110.018ent and Non-investment Grade ObservationsNon-investment Grade Observations 68

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69 Table 2-8. Median distance-to-default estimates by Moodys credit rating. Median statistics are on the sample of 20,298 firm-quarters for the period 1975-2001. SIAV is the simple asset volatility, EIAV is the equity-implied asset volatility, DIAV is the debt-implied asset volatility, and EDIAV is the equity-an-debt-implied asset volatility. DD is the distance to default measure calculated from the corresponding asset values and volatilities. Prob of Default comes from Moodys Investors Service (2000) and is the average one-year default rate over 1983-1999. For B3 and below average rates are calculated over 1998-1999, the only two cohort years available so far for the Caa subcategories. Moody's Credit RatingNProb of Default,1983-1999 (%)DD_EDIAVDD_EIAVDD_DIAVDD_SIAVInvestment GradeAaa1,0700.002.113.712.164.02Aa13580.001.483.631.563.89Aa22,1640.001.593.461.663.81Aa31,1510.101.533.181.583.53A12,0830.001.493.261.543.59A24,5320.001.543.041.523.48A32,1760.001.493.101.483.47Baa11,4960.001.483.091.443.44Baa22,2830.101.412.881.343.32Baa31,3600.301.382.731.303.14Non-Investment GradeBa16960.601.302.371.212.81Ba29140.501.212.131.162.57Ba31,0902.501.152.101.092.44B12,9053.501.011.620.912.18B28826.900.991.670.912.10B34798.040.951.530.881.87Caa11710.780.740.950.541.64Caa24215.790.701.270.462.04Caa3128.870.711.150.581.68Ca2N/A-0.260.14-0.932.96

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Table 2-9. Median changes in distance-to-default estimates by Moodys credit rating change. Median statistics are on the sample of 20,298 firm-quarters for the period 1975-2001. SIAV is the simple asset volatility, EIAV is the equity-implied asset volatility, DIAV is the debt-implied asset volatility, and EDIAV is the equity-an-debt-implied asset volatility. dDD is the quarterly change in the distance-to-default measure calculated from the corresponding asset values and volatilities. it Rating ChangeNdDD_EDIAVdDD_EIAVdDD_DIAVdDD Cred_SIAVDowngrade Crossing the Investment Grade Boundary107-0.04830.0123-0.07860.1546Downgrade Without Crossing the Investment Grade Boundary1,009-0.0048-0.0256-0.0027-0.0265No Change18,2280.00360.01820.00380.0130Upgrade Without Crossing the Investment Grade Boundary8550.00710.04340.01040.0541Upgrade Crossing the Investment Grade Boundary990.05090.07460.08890.0680 70

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71 Table 2-10. Analysis of Moodys credit ratings. We estimate via OLS for the sample of 25,701 firm-quarters for the period 1975-2001. Moodys rating of Aaa to Caa is coded as 1 to 19 respectively, so that as ratings deteriorate, the dependent variable increases. The dependent variable is not discrete since firm rating is the average rating of its debt issues which does not have to be the same. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. SIZE is the log of the market value of assets. REG is an indicator variable that equals 1 if the firm operates in a regulated industry during that quarter and 0 otherwise. R2 is the contribution of DD to the R2 of a model including control variables only. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. ntkntkControlskntDDntRTG,,,,10, EDIAVEIAVDIAVSIAVInvestment and Non-Investment Grade FirmsIntercept21.36***21.23***21.30***21.60***(0.25)(0.24)(0.25)(0.24)DD-0.72***-0.65***-0.65***-0.60***(0.01)(0.01)(0.01)(0.01)SIZE-1.64***-1.56***-1.65***-1.56***(0.01)(0.01)(0.01)(0.01)REG-1.34***-1.06***-1.32***-0.92***(0.21)(0.20)(0.21)(0.21)R20.6110.6450.6100.633R2 (DD)0.0360.0700.0350.058Investment Grade FirmsIntercept13.65***14.08***13.62***14.18***(0.23)(0.23)(0.23)(0.23)DD-0.37***-0.33***-0.35***-0.31***(0.01)(0.01)(0.01)(0.01)SIZE-0.85***-0.87***-0.85***-0.85***(0.01)(0.01)(0.01)(0.01)REG-0.90***-0.74***-0.90***-0.62***(0.17)(0.17)(0.17)(0.17)R20.4030.4200.4050.413R2 (DD)0.0320.0490.0340.042Non-Investment Grade FirmsIntercept16.48***16.38***16.26***16.42***(0.26)(0.26)(0.27)(0.27)DD-0.75***-0.24***-0.43***-0.19***(0.03)(0.01)(0.02)(0.01)SIZE-0.41***-0.45***-0.45***-0.45***(0.01)(0.01)(0.01)(0.01)REG0.20-1.09***-0.40-1.32***(0.30)(0.29)(0.30)(0.29)R20.3660.3510.3420.337R2 (DD)0.0600.0450.0360.031

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72 Table 2-11. Logit analysis of credit rating changes. We estimate for the sample of 20,298 firm-quarters during the period 1975-2001. Moodys rating change, dRTG, equals -1 if a firm is downgraded, 0 if the credit rating remains the same, and 1 if the firm is upgraded. When credit rating change is the dependent variable, we further distinguish between upgrades/downgrades that cross the investment grade threshold (dRTG=2/dRTG=-2) and those that do not (dRTG=1/dRTG=-1). The model estimates the probability of the lower rating change values. dDD_SIAV, dDD_EIAV, dDD_DIAV, and dDD_EDIAV are quarterly changes in the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. SIZE is the log of the market value of assets. Lags of variables are so indicated. Indicator variables are not presented for ease of exposition. The models fit is indicated by the max rescaled pseudo R2. R2 is the contribution of all lags of DD and dDD to R2 of a model including all but these variables. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. ntkntControlskntRTGjnitdRTGjntDDinitdDDiontdRTG,,,4431,3,4231,1, VariableSIAVEIAVDIAVEDIAVSIAVEIAVDIAVEDIAVIntercept-5.77***-5.72***-5.82***-5.84***9.29***9.91***9.75***9.71***(1.11)(1.11)(1.11)(1.11)(0.61)(0.62)(0.61)(0.61)dDD_lag1-0.25***-0.30***-0.25***-0.33***0.02-0.06-0.07-0.06(0.04)(0.04)(0.06)(0.08)(0.05)(0.05)(0.06)(0.07)dDD_lag2-0.44***-0.48***-0.29***-0.41***0.06-0.05-0.13**-0.12(0.05)(0.05)(0.07)(0.09)(0.05)(0.05)(0.07)(0.09)dDD_lag3-0.34***-0.34***-0.39***-0.45***0.02-0.12**-0.19***-0.18**(0.05)(0.05)(0.07)(0.09)(0.05)(0.05)(0.07)(0.09)DD_lag4-0.28***-0.29***-0.47***-0.50***0.04-0.11***-0.13**-0.12(0.04)(0.04)(0.06)(0.08)(0.04)(0.04)(0.06)(0.08)SIZE0.18***0.15***0.16***0.17***-0.62***-0.62***-0.61***-0.61***(0.03)(0.03)(0.03)(0.03)(0.04)(0.04)(0.04)(0.04)dRTG_lag1-0.07-0.04-0.07-0.080.050.060.060.06(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)dRTG_lag2-0.25***-0.23***-0.24***-0.25***0.050.060.070.06(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)dRTG_lag3-0.23***-0.22***-0.22**-0.23***-0.10-0.08-0.08-0.08(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)(0.08)RTG_lag4-0.01-0.02-0.02*-0.01-0.27***-0.29***-0.28***-0.28***(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)(0.01)R20.0960.0990.0920.0900.1550.1560.1560.155R2 (dDD and DD)0.0130.0160.0090.0070.0000.0010.0010.001Credit Rating DowngradesCredit Rating Upgrades

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73 Table 2-12. Average statistics by Z-score deciles. Z-score is a measure of default probability proposed by Altman (1969) where a higher Z implies lower default probability. SIAV is the simple implied asset volatility, EIAV is the equity-implied asset volatility, DIAV is the debt-implied asset volatility, and EDIAV is the equity-an-debt-implied asset volatility. DD is the distance to default measure calculated from the corresponding asset values and volatilities. Z-Score DecileNDD_EDIAVDD_EIAVDD_DIAVDD_SIAVAll23,6001.402.791.363.1412,4091.112.370.852.9322,3541.283.291.033.7232,3641.312.631.113.1942,3581.362.481.223.0252,3441.452.591.373.0462,3731.482.731.443.1072,3691.492.811.493.1282,3521.502.891.553.1792,3661.462.981.563.18102,3111.383.061.543.17

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Table 2-13. Analysis of Z-score. We estimate via OLS for the sample of 23,600 firm-quarter observations for 1975-2001. The dependent variable is Z-Score as calculated in Altman (1969) and is a measure of default probability based on accounting reports. A higher Z-Score implies lower probability of default. SIZE is the log of market value of assets. REG is an indicator variable that equals one if the firm operates in an industry regulated during the quarter in question. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities and values respectively. Control variables (industry and year-quarter indicator variables) are not presented for ease of exposition. R2 (DD) is the contribution of DD to the R2 of a model including all but these variables. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Industry Fixed EffectsFirm Fixed Effects ntkntkControlskntDDintZ,,,,0, EDIAVEIAVDIAVSIAVEDIAVEIAVDIAVSIAVLow Z-Score FirmsDD0.090***0.053***0.082***0.039***0.029***0.042***0.032***0.022***(0.005)(0.003)(0.004)(0.003)(0.004)(0.003)(0.003)(0.003)SIZE0.011***0.012***0.012***0.015***0.090***0.081***0.089***0.085***(0.003)(0.003)(0.003)(0.003)(0.009)(0.009)(0.009)(0.009)REG-0.003-0.006-0.001-0.013-0.084*-0.082*-0.077-0.094*(0.032)(0.032)(0.032)(0.032)(0.049)(0.049)(0.049)(0.049)R20.2400.2410.2470.2310.7090.7140.7100.709R2 (DD)0.0210.0210.0270.0110.0020.0070.0030.002High Z-Score FirmsDD-0.111***0.019**0.024**-0.058***-0.036***0.049***0.014*0.012*(0.014)(0.009)(0.011)(0.008)(0.010)(0.007)(0.008)(0.006)SIZE0.147***0.123***0.123***0.142***0.611***0.613***0.611***0.613***(0.007)(0.007)(0.007)(0.006)(0.017)(0.017)(0.017)(0.017)REG0.2750.1940.1760.204-0.354*-0.345*-0.337*-0.347*(0.210)(0.210)(0.210)(0.210)(0.190)(0.190)(0.190)(0.190)R20.2180.2140.2140.2170.7300.7310.7290.729R2 (DD)0.0040.0000.0000.0030.0000.0010.0000.000 74

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Table 2-14. Analysis of Z-score changes. We estimate via OLS on the sample of 19,800 firm-quarter observations for 1975-2001. The dependent variable is Altmans (1969) Z-Score. A higher Z-Score implies a lower probability of default. SIZE_lag is the one quarter lag of the log of market value of assets. REG is an indicator variable that equals one if the firm operates in an industry regulated during the quarter in question. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities and values respectively. Control variables (industry and year-quarter indicator variables) are not presented for ease of exposition. R2 (DD) is the contribution of all lags of dDD to the R2 of a model including all but these variables. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Industry Fixed Effects ntkntkControlskinitdDDintdZ,,,31,0, SIAVEIAVDIAVEDIAVSIAVEIAVDIAVEDIAVNegative Z Score ChangesdDD_lag10.010***0.013***0.008**0.008*0.0000.0030.0010.001(0.003)(0.003)(0.004)(0.005)(0.003)(0.002)(0.003)(0.002)dDD_lag20.008**0.011***0.007*0.009*0.0020.0040.0020.000(0.003)(0.004)(0.004)(0.005)(0.003)(0.003)(0.003)(0.002)dDD_lag30.0040.006*0.0030.0040.0010.0030.0010.002(0.003)(0.003)(0.004)(0.004)(0.003)(0.002)(0.002)(0.002)dZ_lag1-0.186***-0.188***-0.186***-0.186***-0.338***-0.340***-0.338***-0.338***(0.009)(0.009)(0.009)(0.009)(0.010)(0.010)(0.010)(0.010)dZ_lag2-0.122***-0.124***-0.122***-0.122***-0.213***-0.215***-0.213***-0.213***(0.009)(0.009)(0.009)(0.009)(0.011)(0.011)(0.011)(0.011)dZ_lag3-0.122***-0.123***-0.122***-0.122***-0.145***-0.147***-0.145***-0.145***(0.009)(0.009)(0.009)(0.009)(0.010)(0.010)(0.010)(0.010)SIZE0.007***0.007***0.007***0.007***-0.044***-0.044***-0.044***-0.044***(0.002)(0.002)(0.002)(0.002)(0.009)(0.009)(0.009)(0.009)REG0.0380.0380.0400.0400.0590.0590.0580.059(0.032)(0.032)(0.032)(0.032)(0.044)(0.044)(0.044)(0.044)R20.17480.17540.17430.17420.33550.33570.33550.3356R2 (dDD)0.00100.00170.00060.00040.00010.00030.00010.0001Firm Fixed Effects 75

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Table 2-14. Continued SIAVEIAVDIAVEDIAVSIAVEIAVDIAVEDIAVPositive Z Score ChangesdDD_lag1-0.0010.0000.0010.0010.0070.010**0.0050.008*(0.003)(0.003)(0.003)(0.004)(0.008)(0.005)(0.006)(0.005)dDD_lag20.0010.0030.0010.0010.0010.009*0.0020.006(0.003)(0.003)(0.003)(0.004)(0.009)(0.006)(0.007)(0.005)dDD_lag30.0030.004-0.001-0.0010.0010.011**0.0020.008*(0.003)(0.003)(0.003)(0.004)(0.008)(0.005)(0.006)(0.005)dZ_lag1-0.047***-0.048***-0.048***-0.048***-0.272***-0.273***-0.272***-0.272***(0.009)(0.009)(0.009)(0.009)(0.011)(0.011)(0.011)(0.011)dZ_lag20.0070.0070.0070.008-0.142***-0.143***-0.142***-0.142***(0.009)(0.009)(0.009)(0.009)(0.011)(0.011)(0.011)(0.011)dZ_lag30.0060.0060.0070.007-0.143***-0.144***-0.143***-0.143***(0.008)(0.008)(0.008)(0.008)(0.011)(0.011)(0.011)(0.011)SIZE-0.011***-0.011***-0.011***-0.011***0.041***0.042***0.041***0.042***(0.002)(0.002)(0.002)(0.002)(0.014)(0.014)(0.014)(0.014)REG-0.010-0.010-0.009-0.0090.1250.1150.1260.117(0.029)(0.029)(0.029)(0.029)(0.149)(0.149)(0.149)(0.149)R20.11070.11070.11050.11050.22810.22870.22810.2285R2 (dDD)0.00020.00020.00000.00000.00010.00060.00010.0004Industry Fixed EffectsFirm Fixed Effects 76

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Table 2-15. Sensitivity of summary statistics to alternative input assumptions. SIAV is the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. Implied asset volatilities are reported in percent per year. V_SIAV, V_EIAV, V_DIAV, and V_EDIAV are the corresponding estimates of the market value of assets in billion dollars. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. Time to Firm ResolutionDefault Po MedianMeanMedianMeanMedianMeanMedianMeanMedianMeanMedianMeanV_SIAV2.928.352.918.312.908.162.908.152.918.292.918.28V_EIAV2.216.551.795.572.747.692.777.762.828.012.828.00V_DIAV2.206.661.886.032.206.282.216.312.236.462.236.45V_EDIAV2.226.591.815.632.747.692.777.762.828.002.827.99SIAV14.716.714.816.814.816.914.816.914.816.914.816.9EIAV20.023.424.228.215.918.115.717.915.517.715.517.7DIAV21.122.525.226.020.223.020.222.920.323.120.323.1EDIAV22.823.825.926.629.331.729.531.930.032.430.132.4DD_SIAV3.183.573.273.864.835.094.835.094.835.084.835.08DD_EIAV1.681.791.201.294.054.324.174.464.364.664.364.66DD_DIAV1.291.690.991.451.812.071.862.131.882.161.892.15DD_EDIAV1.311.551.001.271.972.151.992.192.002.222.002.21N28,23628,11327,75027,75427,73527,717Weighted Average Debt DurationWeighted Average Debt Maturity95% of Total Debt99% of Total DebtintIssuer YieldWeighted Averge Issue YieldsLargest Issue's Yield 77

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Table 2-15. Continued MedianMeanMedianMeanMedianMeanMedianMeanMedianMeanV_SIAV2.918.325.3212.092.888.231.714.175.7613.75V_EIAV2.838.065.1811.642.757.831.523.895.6413.30V_DIAV2.186.354.8311.262.035.881.072.754.3410.86V_EDIAV2.828.045.1811.642.737.781.513.885.6313.29SIAV14.816.914.816.214.817.025.127.113.915.3EIAV15.517.715.416.815.818.027.630.714.315.8DIAV20.923.616.718.123.827.043.343.118.921.2EDIAV31.533.820.321.838.640.849.549.628.930.7DD_SIAV4.815.065.225.544.825.063.383.665.295.56DD_EIAV4.364.664.785.094.154.422.762.994.905.20DD_DIAV1.821.974.224.201.131.471.021.432.122.38DD_EDIAV1.942.054.614.021.411.651.081.332.222.46N27,7407,42527,80227,41210,031Senior (Junior) Bonds Senior (Junior) to Remaining DebtDebt PriorityCredit Spreads Calculated from Non-Callable Bonds OnlyNoneMoody's AAA-Rated YieldTax AdjustmentAll Debt Assumed Senior 78

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79 Table 2-16. Analysis of IAV and HAV forecasting properties under alternative assumptions. We estimate ntntntForecastVoaltilityRAV,,10, Volatility forecast is one of the five: SIAV, EIAV, DIAV, EDIAV, or HAV. SIAV is the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. HAV is an estimate of annualized historical asset volatility calculated over the year prior to the end of each quarter. RAV is an estimate of annualized realized asset volatility over the two years following each quarter-end. Standard errors are reported in parenthesis. All coefficient estimates are statistically significant at the 1 percent level. EDIAVEIAVDIAVSIAVHAVEDIAVEIAVDIAVSIAVHAVTime to ResolutionIntercept0.0950.1140.0750.1030.1220.1060.1160.0900.1040.112(0.002)(0.002)(0.002)(0.002)(0.001)(0.003)(0.002)(0.003)(0.002)(0.001)Slope0.3820.3050.4980.4960.3310.2980.2440.3690.4900.391(0.010)(0.006)(0.010)(0.010)(0.005)(0.009)(0.006)(0.009)(0.010)(0.006)R20.0620.0830.0950.1000.1320.0440.0660.0640.0980.157Default PointIntercept0.1090.1060.0970.1040.1230.1080.1070.0960.1040.124(0.002)(0.002)(0.002)(0.002)(0.001)(0.002)(0.002)(0.002)(0.002)(0.001)Slope0.2420.4470.3950.4910.3290.2430.4500.3960.4900.328(0.007)(0.009)(0.008)(0.010)(0.005)(0.007)(0.009)(0.008)(0.010)(0.005)R20.0520.0960.0930.0970.1310.0520.0960.0930.0970.130Issuer YieldIntercept0.1100.1070.0970.1040.1230.1090.1070.0970.1040.123(0.002)(0.002)(0.002)(0.002)(0.001)(0.002)(0.002)(0.002)(0.002)(0.001)Slope0.2390.4490.3930.4910.3280.2400.4490.3950.4910.328(0.007)(0.009)(0.008)(0.010)(0.005)(0.007)(0.009)(0.008)(0.010)(0.005)R20.0510.0960.0920.0970.1300.0510.0960.0920.0970.130Tax AdjustmentIntercept0.1090.1070.0970.1040.1230.1240.1020.1000.1010.088(0.002)(0.002)(0.002)(0.002)(0.001)(0.004)(0.004)(0.004)(0.004)(0.003)Slope0.2310.4490.3820.4910.3290.2310.4260.4150.4530.501(0.007)(0.009)(0.008)(0.010)(0.005)(0.017)(0.020)(0.022)(0.022)(0.012)R20.0490.0960.0900.0970.1310.0280.0640.0540.0630.208Debt PriorityIntercept0.0940.1070.0890.1040.1230.1070.1070.0990.1010.123(0.003)(0.002)(0.002)(0.002)(0.001)(0.003)(0.002)(0.003)(0.002)(0.001)Slope0.2300.4530.3700.4950.3320.1580.2610.2020.3180.333(0.006)(0.009)(0.007)(0.010)(0.006)(0.006)(0.006)(0.006)(0.007)(0.006)R20.0610.1000.1030.1020.1330.0320.0670.0450.0730.134Intercept0.1070.0920.0940.0910.092(0.004)(0.003)(0.003)(0.003)(0.002)Slope0.2000.4770.3490.5040.451(0.011)(0.017)(0.014)(0.018)(0.010)R20.0360.0800.0670.0780.177Average Yield on Moody's AAA-rated BondsNon-callable Bonds OnlyAverage Duration of Traded DebtAverage Maturity of Traded Debt95% of Total Debt99% of Total DebtAll Debt Assumed SeniorSenior Bonds Assumed Senior to all other DebtWeighted Average Issue YieldLargest Isssue YieldNone

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80 Table 2-17. Logit analysis of defaults under alternative assumptions. We estimate the logistic regression ntntntontControlsDDDFLT,,2,1, on the sample of all 1,795 observations and the subsample of 519 non-investment-grade observations. The dependent variable DFLT equals 1 if the firm is delisted due to liquidation or performance, or files for bankruptcy in the three years following the fourth quarter of 1982, 1985, 1988, 1991, 1994, 1997, and 2000; it equals 0 otherwise. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. R2 is max-rescaled pseudo R2, which is an indicator of fit for logit models. R2 is the marginal contribution of each DD to R2, which is the difference between R2 of a model including DD, and that of a base model excluding it. DD_SIAVDD_EIAVDD_DIAVDD_EDIAVDD_SIAVDD_EIAVDD_DIAVDD_EDIAVTime to Resolution: Weighted Average Duration of Traded DebtR20.2270.1680.1560.1560.1580.1430.1310.134R2 (DD)0.0790.0200.0080.0080.0340.0180.0060.009Time to Resolution: Weighted Average Maturity of Traded DebtR20.2080.1510.1390.1370.1360.1280.1120.113R2 (DD)0.0770.0200.0070.0060.0330.0240.0080.009Deafult Point: 95% of Total DebtR20.2120.1970.1890.2040.1490.1340.1370.143R2 (DD)0.0620.0470.0390.0540.0220.0070.0100.016Deafult Point: 99% of Total DebtR20.2350.1920.1850.2030.1650.1340.1390.148R2 (DD)0.0850.0430.0360.0540.0380.0070.0120.021Issuer Yield: Weighted Average Issue YieldsR20.2230.1960.1910.2110.1560.1340.1380.146R2 (DD)0.0730.0460.0420.0610.0290.0070.0110.019Issuer Yield: Largest Issue YieldR20.2230.1960.1900.2090.1560.1340.1390.146R2 (DD)0.0730.0460.0410.0600.0290.0070.0120.019Tax Adjustment: NoneR20.2220.1960.1820.1930.1560.1340.1380.145R2 (DD)0.0730.0470.0320.0430.0290.0070.0110.019Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.4890.4780.5110.5140.5900.5760.5980.586R2 (DD)0.0110.0010.0340.0370.0390.0250.0460.034Debt Priority: All Debt Assumed SeniorR20.2300.1960.1980.2330.1640.1410.1560.178R2 (DD)0.0750.0410.0430.0780.0320.0080.0240.046Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remaining DebtR20.2440.2410.1970.2150.1800.1740.1500.160R2 (DD)0.0870.0840.0400.0570.0430.0370.0130.023Non-callable Bonds OnlyR20.3440.3350.4250.4110.3920.4140.4020.361R2 (DD)0.0100.0000.0900.0770.0560.0780.0660.025Investment and Non-investment Grade ObservationsNon-investment Grade Observations

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81 Table 2-18. Analysis of Moodys credit ratings under alternative assumptions. We estimate via OLS for the sample of 25,701 observations over 1975-2001. Moodys rating of Aaa to Caa is coded as 1 to 19 respectively, so that as ratings deteriorate, the dependent variable increases. The dependent variable is not discrete since firm rating is the average rating of its debt issues which does not have to be the same. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. R2 is the contribution of DD to the R2 of a model including control variables only. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. ntkntkControlskntDDntRTG,,,,10, DD_SIAVDD_EIAVDD_DIAVDD_EDIAVTime to Resolution: Weighted Average Duration of Traded DebtR20.5900.6360.6150.627R2 (DD)0.0000.0470.0260.038Time to Resolution: Weighted Average Maturity of Traded DebtR20.6070.6430.6220.629R2 (DD)0.0000.0350.0150.022Deafult Point: 95% of Total DebtR20.6380.6620.6180.629R2 (DD)0.0600.0850.0400.052Deafult Point: 99% of Total DebtR20.6360.6550.6140.623R2 (DD)0.0600.0790.0380.047Issuer Yield: Weighted Average Issue YieldsR20.6330.6450.6160.616R2 (DD)0.0590.0700.0410.041Issuer Yield: Largest Issue YieldR20.6330.6450.6090.611R2 (DD)0.0590.0700.0350.037Tax Adjustment: NoneR20.6340.6440.6010.604R2 (DD)0.0600.0700.0270.030Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.4530.4760.4860.440R2 (DD)0.0630.0860.0960.050Debt Priority: All Debt Assumed SeniorR20.6360.6590.6220.630R2 (DD)0.0560.0790.0420.050Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remaining DebtR20.6280.6370.6210.624R2 (DD)0.0160.0250.0100.012Non-callable Bonds OnlyR20.4880.4980.4990.497R2 (DD)0.0730.0830.0830.082All Observations

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82 Table 2-18. Continued DD_SIAVDD_EIAVDD_DIAVDD_EDIAVDD_SIAVDD_EIAVDD_DIAVDD_EDIAVTime to Resolution: Weighted Average Duration of Traded DebtR20.3760.4080.4000.4060.3180.3580.3420.363R2 (DD)0.0000.0320.0240.0300.0000.0400.0240.045Time to Resolution: Weighted Average Maturity of Traded DebtR20.3910.4150.4060.4090.3370.3690.3520.364R2 (DD)0.0000.0250.0160.0180.0000.0320.0150.027Deafult Point: 95% of Total DebtR20.4180.4370.4130.4180.3400.3670.3480.383R2 (DD)0.0440.0630.0390.0440.0320.0600.0400.075Deafult Point: 99% of Total DebtR20.4170.4300.4090.4130.3390.3620.3460.376R2 (DD)0.0440.0580.0360.0410.0310.0540.0390.069Issuer Yield: Weighted Average Issue YieldsR20.4130.4200.4130.4100.3370.3510.3390.362R2 (DD)0.0430.0500.0430.0390.0310.0450.0330.056Issuer Yield: Largest Issue YieldR20.4130.4200.4030.4020.3370.3510.3350.355R2 (DD)0.0420.0500.0330.0310.0310.0450.0290.049Tax Adjustment: NoneR20.4120.4180.3890.3890.3380.3510.3440.365R2 (DD)0.0430.0490.0200.0200.0320.0450.0380.059Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.4020.4250.4100.3850.5330.5310.5410.546R2 (DD)0.0390.0620.0470.0220.0070.0060.0160.020Debt Priority: All Debt Assumed SeniorR20.4120.4290.4150.4190.3440.3680.3500.386R2 (DD)0.0410.0580.0440.0480.0310.0550.0370.073Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remaining DebtR20.4310.4410.4300.4360.3150.3200.3120.311R2 (DD)0.0190.0290.0180.0240.0040.0090.0010.000Non-callable Bonds OnlyR20.4420.4510.4640.4580.5060.5030.4940.498R2 (DD)0.0340.0440.0570.0500.0230.0200.0110.015Investment-Grade FirmsNon-Investment-Grade Firms

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83 Table 2-19. Analysis of credit rating changes under alternative assumptions. We estimate the logit model for the period 1975-2001. Moodys rating change, dRTG, equals -1 if a firm is downgraded, 1 if it is upgraded, and 0 if its rating remains the same. When rating change is the dependent variable, we further distinguish upgrades and downgrades that cross the investment grade threshold from those that do not. The model estimates the probability of the lower rating change values. dDD_SIAV, dDD_EIAV, dDD_DIAV, and dDD_EDIAV are quarterly changes in the distance-to-default measures calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. Lags of variables are so indicated. The models fit is measured by the max re-scaled pseudo R2. R2 is the contribution of all lags of DD and dDD to the R2 of a model including all but these variables. ntkntControlskntRTGjnitdRTGjntDDinitdDDiontdRTG,,,4431,3,4231,1, DD_SIAVDD_EIAVDD_DIAVDD_EDIAVDD_SIAVDD_EIAVDD_DIAVDD_EDIAVTime to Resolution: Weighted Average Duration of Traded DebtR20.09190.09340.08540.08990.15720.15910.15870.1607R2 (DD)0.01360.01510.00710.01160.00040.00230.00190.0038Time to Resolution: Weighted Average Maturity of Traded DebtR20.09160.09530.08660.09100.15890.15890.15900.1595R2 (DD)0.01340.01710.00840.01280.00030.00030.00050.0009Deafult Point: 95% of Total DebtR20.09340.09880.09160.08880.15520.15610.15560.1552R2 (DD)0.01040.01580.00860.00580.00060.00140.00100.0005Deafult Point: 99% of Total DebtR20.09910.09970.09390.09200.15510.15640.15620.1555R2 (DD)0.01530.01590.01010.00820.00020.00150.00130.0006Issuer Yield: Weighted Average Issue YieldsR20.09640.09950.09610.09480.15540.15650.15590.1557R2 (DD)0.01300.01610.01270.01140.00040.00150.00090.0007Issuer Yield: Largest Issue YieldR20.09590.09900.09280.09060.15530.15640.15580.1554R2 (DD)0.01290.01590.00980.00760.00040.00150.00090.0005Tax Adjustment: NoneR20.09530.09820.09240.08920.15510.15620.15590.1554R2 (DD)0.01280.01570.00980.00660.00030.00140.00100.0006Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.08740.09860.10970.10640.15630.15390.15230.1542R2 (DD)0.00100.01220.02330.02000.00550.00310.00160.0034Debt Priority: All Debt Assumed SeniorR20.09560.09830.09260.09090.15440.15550.15720.1561R2 (DD)0.01290.01550.00980.00820.00080.00190.00360.0025Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remaining DebtR20.09350.11320.08570.09160.16280.16420.16390.1646R2 (DD)0.01650.03620.00870.01460.00060.00200.00170.0024Non-callable Bonds OnlyR20.13870.15610.12620.12020.17320.16430.15990.1619R2 (DD)0.03230.04960.01980.01370.00980.0009-0.0035-0.0015Credit Rating DowngradesCredit Rating Upgrades

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84 00.10.20.30.40.50.6197503197512197609197706197803197812197909198006198103198112198209198306198403198412198509198606198703198712198809198906199003199012199109199206199303199312199409199506199603199612199709199806199903199912200009200106QuarterIAV SIAV EIAV DIAV EDIAV Figure 2-1. Median implied asset volatility over 1975-2001

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85 1234 SIAVEIAVDIAVEDIAV 00.050.10.150.20.250.30.350.40.450.5IAVAsset/Debt Ratio Quartiles Figure 2-2. Median implied asset volatility by assets-to-debt ratio quartile

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86 012345678197503197603197703197803197903198003198103198203198303198403198503198603198703198803198903199003199103199203199303199403199503199603199703199803199903200003200103QuarterDD DD_SIAV DD_EIAV DD_DIAV DD_EDIAV Figure 2-3. Median distance to default over 1975-2001

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CHAPTER 3 BANK RISK REFLECTED IN SECURITY PRICES: EQUITY AND DEBT MARKET INDICATORS OF BANK CONDITION 3.1. Introduction The banking industry is one of the most heavily regulated industries in the U.S. There are two commonly cited reasons for this extensive oversight. Banks play an important role in the economy, which creates the concern that bank failures might have a ripple effect and de-stabilize the financial system. In addition, bank claimholders are thought to be unable or unwilling to curb a banks appetite for risk. These widely held beliefs have resulted in a complex set of government regulations that attempt to limit the risk-taking activities of banking firms. It was not until recently that bank supervisors warmed up to the idea that market discipline can aid them in this task: The real pre-safety-net discipline was from the market, and we need to adopt policies that promote private counterparty supervision as the first line of defense for a safe and sound banking system. (Greenspan, 2001) Regulators have started to view market discipline as a desirable and necessary supplement to government oversight. Market discipline was proposed as one of the three pillars discussed in the Basel II proposal, and the Gramm-Leach-Bliley legislation required the study of mandatory subordinated debt proposals as a tool of improving market discipline. In order to determine whether market discipline can deliver the benefits ascribed to it, researchers have examined whether the information in bank-issued securities is 87

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88 accurate and timely, and whether it can improve supervisory assessments.1 The general consensus is that bank risk is reflected in the valuation of all the securities that a bank issues. Most studies focus on the information in uninsured liabilities. They document a positive contemporaneous association between bank subordinated debt yields or large deposit rates, and indicators of risk (Evanoff and Wall 2002, Hall et al. 2002, Jagtiani and Lemieux 2000, Jagtiani and Lemieux 2001, Jagtiani et al. 2002, Krishnan et al. 2003, Morgan and Stiroh 2001, Sironi 2002). Although there are fewer studies that investigate the informational content of equity prices, they reach the same conclusion market prices reflect a banks current condition (Gropp et al. 2002, Krainer and Lopez 2002). Event studies provide further evidence that the prices of publicly traded debt and equity respond to relevant news in a rational manner (Allen et al. 2001, Berger and Davies 1998, Harvey et al. 2003, Jordan et al. 2000). Even if market information is timely and accurate, there is also the question of whether it can add value to supervisory information. Numerous studies document that equity-market and debt-market indicators can aid regulators in their monitoring of banks by marginally increasing the explanatory power of regulatory-rating forecasting models. Berger et al. (2000) find that supervisory assessments are less accurate than equity market indicators in reflecting the banks condition except when the supervisory assessment is based on recent inspections. Gunther et al. (2001) show that equity data in the form of expected default frequency adds value to BOPEC forecasting models. Elmer and Fissel (2001) and Curry et al. (2001) find that simple equity-market indicators (price, return, and dividend information) add explanatory power to CAMEL forecasting models 1 See Flannery (1998) for an overview of the literature on the market discipline of financial firms.

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89 based on accounting information. Evanoff and Wall (2001) show that yield spreads are slightly better than capital ratios in predicting bank condition. Krainer and Lopez (2003) find that equity and debt-market indicators are in alignment with subsequent BOPEC ratings and that including these in BOPEC off-site monitoring model helps identify additional risky firms. These studies suggest that regulators can benefit from explicitly or implicitly including market information into supervisory models. However, they do not address the question of which market information to include. Previous research has argued that using debt prices is better suited for the purpose of oversight, since the incentives of debt holders are more closely aligned with those of regulators in that neither group likes an increase in asset risk.2 However, this advantage of debt market prices is balanced out by a number of disadvantages. Debt prices are notoriously difficult to collect. While some corporate bonds trade on NYSE and Amex, they account for no more than 2% of market volume (Nunn et al. 1986). The accuracy of bond data is also problematic. Data quotes on OTC trades tend to be diffuse, and based on matrix valuation rather than on actual trades, and Warga and Welch (1993) document that there are large disparities between matrix prices and dealer quotes. Hancock and Kwast (2001) compare bond-price data from four sources, and find that the correlation among bond yields from the different sources are only about 70-80%. Finally, Saunders et al. (2002) document that the 2 Gorton and Santomero (1990) are the first to point out that this statement is not necessarily true. The payoff to subordinated debt-holders is a nonlinear function of risk. Thus, at low leverage levels, subordinated debtholders have incentives similar to those of equityholders. However, the authors document that none of the banks in their sample have low enough leverage for this to occur. Furthermore, this describes an extreme situation that supervisors are likely to have already detected.

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90 corporate bond market is characterized by a small number of bidders, slow trade execution, and large spreads between the best and second-best price bids. Even if bond data were readily available and accurate, extracting risk information from debt spreads is complicated. The typical approach is to use debt prices, and calculate yield spreads as the difference between a corporate yield and the yield on a Treasury security of the same maturity. This spread is assumed to be a measure of credit risk. However, corporate yields will differ from Treasury yields for a number of reasons other than credit risk (Delianedis and Geske 2001, Elton et al. 2001, Longstaff 2002). They include premiums for tax, liquidity, and expected recovery differences between corporate and Treasury bonds, as well as compensation for common bond-market factors. Yield spreads also reflect redemption and convertibility options, sinking fund provisions, and other common bond features. The complexity of bond spreads raises new questions about their interpretation. In contrast to debt markets, equity markets are liquid and deep, and equity prices of high frequency and quality can be easily obtained. Offsetting this data advantage is the difficulty in extracting firm risk information from equity prices. Increases in stock values do not always correspond to a safer bank, and by extension to a lower expected claim on the federal safety net. Under some circumstances, an insured institutions equity value can rise simply because its portfolio risk has risen, which leaves the banks failure probability higher than before. This calls for using equity-market indicators other than prices or returns to extract information about firm risk. One such way is proposed by KMV (Crosbie and Bohn 2002, Gropp et al. 2002), who use equity prices and historical

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91 equity volatility to calculate estimates of implied asset volatility. These are then combined with firm leverage to construct equity-based measures of default risk. Since both debt and equity prices can impose challenges in inferring a banks condition, perhaps the best way to overcome these challenges is to combine the information from these two sources. Saunders (2001) points out that contingent-claim models of firm valuation imply that in perfect markets both equity and debt prices will reflect the same information about firm market value and portfolio risk. To the extent that debt (or equity) prices contain noise, or fail to conform to the Black-Scholes assumptions used to back out risk parameters, using both securities (where they are available) might provide more accurate information. Gropp, Vesala and Vulpes (GVV) (2002) and Krainer and Lopez (KL) (2003) document the advantage of this approach by showing that a model using both equity-market and debt-market indicators to forecast bank risk outperforms a model using either set of indicators alone. We address the general question of whether market information can aid regulators in their assessment of bank risk. More specifically, we evaluate the relative informational content and accuracy of firm risk measures obtained from equity or debt prices, and examine whether combining information from both markets can produce a more accurate risk assessment. We extend the analysis of KL and GVV in a number of ways. First, we argue that the equity and debt market indicators that these papers analyze are not necessarily comparable. KL compare debt credit spreads to equity abnormal returns but the link between changes in equity prices and changes in bank risk is not an obvious one. Positive abnormal returns can result from an increase in the market value of assets which reduces bank default probability, or from an increase in asset volatility which increases

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92 default probability. GVV compare debt credit spreads to a distance-to-default measure extracted from equity prices using a structural credit risk model. Although theoretically appealing, structural models have attracted a lot of criticism for their limitations in explaining observed prices. Thus, the forecasting ability of the equity distance-to-default measure might be affected by its construction. To avoid such issues, we construct the exact same risk measure a distance-to-default measure first from equity prices and then from debt prices. We believe that this allows for a fairer comparison of the accuracy and informational content of equity and debt prices. Second, we conduct a larger set of tests in assessing the relative usefulness of equity and debt market indicators. The analysis in KL and GVV focuses on the forecasting ability of market indicators. However, even if market information cannot systematically improve supervisory assessments of a banks future condition, contemporaneous affirmation of supervisory information can still provide substantial value. It may enable supervisors to act sooner when they perceive a problem, or it may cause appropriate forbearance if it suggests that the supervisory view is too bearish. We recognize this and as our second extension conduct both contemporaneous and forecasting tests on the accuracy of market indicators. Third, our data covers the period 1986-1999 which is a longer time series than in either KL or GVV. This also allows us to document the changes in market participants behavior after the passage of the Federal Deposit Insurance Corporation Improvement Act (FDICIA) of 1991. We start this study by constructing three implied asset volatility estimates for a set of 84 U.S. bank holding companies (BHCs) over the period 1986-1999. We model equity as a call option written on the market value of the firms assets (Black and Scholes 1973),

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93 and risky debt as riskless debt short a put (default) option (Merton 1974). Since both the equity-call and debt-put options are written on the same underlying, the firms total assets, they are functions of the same set of variables: the market value of firms assets, the volatility of the firms assets, the face value of debt, interest rates, and the time to firm resolution (debt maturity). We use this framework to extract implied asset volatility from equity prices alone, debt prices alone, and equity and debt prices together. These asset volatilities are then combined with firm leverage to produce three versions of a single measure of default risk distance to default (DD). We then investigate the contemporaneous association between the three DD measures and other indicators of bank risk (1) credit ratings, (2) asset portfolio quality, and (3) a composite financial-health score calculated from accounting-report variables. We find that all three DD measures are significantly related to the three risk proxies. This relationship is stronger for the measure constructed from debt prices than it is for the one constructed from equity prices, suggesting that the debtholders are relatively more informed about BHC risk. However, in the post-FDICIA period, the DD measure that combines information from equity and debt prices outperforms the other market indicators. It is more closely related to bank risk than is equity volatility, credit spread, or any of the other DD estimates. Next, we compare the forecasting abilities of the three DD estimates. Since prices are inherently forward-looking, risk measures derived from them might detect changes in a banks condition before these changes are observed in the banks balance sheet or have resulted in a revised credit rating. We examine whether changes in the above proxies of bank risk can be forecasted using our three DD estimates. We document that these

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94 estimates can predict which banks will be downgraded from investment grade to junk as much as three quarters prior to the downgrade. Once again, the DD measure constructed from debt performs better than the one constructed from equity prices. We also document that all five measures can foresee quarter-to-quarter changes in asset-portfolio quality and overall firm condition up to a year before these changes materialize in the firms accounting reports. Finally, all of the forecasting tests confirm the contemporaneous tests result that combining information from equity and debt prices is superior to using either set of information alone. All of the combination models have better fit than their equity or debt counterparts. Some of the above risk measures are constructed using contingent-claim models of firm valuation which require a set of theoretical assumptions. The final goal of this study is to investigate whether deviations from these assumptions are empirically important. We initially produce asset value and volatility estimates under a set of base assumptions and later explore the sensitivity of these estimates to alternative model assumptions. We document that while the estimates magnitude and explanatory power changes, varying the model assumptions does not significantly affects our main findings. 3.2. Extracting Information about Firm Risk from Security Prices 3.2.1. Review of Contingent Claim Valuation Models Black and Scholes (1973) were the first to recognize that their approach to valuing exchange-traded options could also be used to value firm equity. With limited liability, the payoff to equityholders is equivalent to the payoff of a call option written on the firms assets with an exercise price equal to the face value of the firms debt. Consider a non-dividend-paying firm with homogeneous zero-coupon debt that matures at time

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95 Assume that the market value of the firms assets follows a continuous lognormal diffusion process with constant variance. Then the current equity value of the firm is )()(21dNDedVNEfR (3-1) where VVfRDVd)5.0()ln(21 Vdd12 E is the current market value of the firms equity, V is the current market value of the firms assets, D is the face value of the firms debt, V is the instantaneous standard deviation of asset returns, is the time remaining to maturity, fR is the risk-free rate over )(xN is the cumulative standard normal distribution of x Merton (1974) uses the same insight to derive the value of a firms risky debt. He demonstrates that under limited liability, the payoff to debtholders is equivalent to the payoff to holders of a portfolio that consists of riskless debt with the same characteristics as the risky debt, and a short put option written on the firms asset with an exercise price equal to the face value of debt. Re-arranging the formula in Merton (1974) allows us to express the credit-risk premium as the spread between the yield on risky debt, R, and the yield on risk-free debt with otherwise the same characteristics: /)(ln21dNdNeDVRRfRf (3-2) One of the basic assumptions underlying Mertons (1974) derivation is that the firm issues a single homogenous class of debt. In reality, the characteristics of debt are highly variable, which makes his model intuitively useful, but not precisely applicable to risky debt valuation. The single-class debt assumption is relaxed by Black and Cox (1976) who analyze the debt-valuation effect of having multiple classes of debtholders. Consider a firm

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96 financed by equity and two types of debt differentiated by their priority. Although the probability of default is the same for senior and subordinated debtholders, their expected losses differ; and that is reflected in the valuation of their claims. Assume that all of the firms debt matures on the same date. If at maturity the value of the firm is less than (the face value of senior debt), then senior debtholders receive the value of the firm, while subordinated debtholders (along with equityholders) receive nothing. If at maturity the value of the firm is greater than but less than the face value of all debt ( 1D2D 1D 1D ) then senior debtholders get paid in full, subordinated debtholders receive the residual firm value, and equityholders receive nothing. Note that the payoff to equityholders is the same, whether there is one or two classes of debtholders if the value of the firm at maturity is higher than the face value of all debt, they receive the residual after debt payments are made; and if the value of the firm at maturity is lower than the face value of all debt they receive nothing. Thus, while knowing the precise breakdown of debt into priority classes is crucial for debt valuation, it does not affect the valuation of equity. Following Black and Cox (1976), the value of a firms subordinated debt is given by )()()~()()~(22121112dNeDDdNeDdNdNVXffRR (3-3) where VVfRDVd)5.0()ln(~211 Vdd12 ~ ~ VVfRDDVd)5.0())(ln(2211 Vdd12 1D is the face value of the firms senior debt, 2D is the face value of the firms subordinated debt,

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97 2X is the current value of subordinated debt. The Black-Cox model most frequently appears in the literature as the spread between the yield on subordinated debt (R2) and the risk-free rate (Rf) of the same maturity: /)()~()()~(ln22212211122dNDDDdNDDdNdNeDVRRfRf (3-3) 3.2.2. Methodologies for Calculating Implied Asset Value and Volatility The above contingent-claim models of firm valuation suggest that information about a firms asset value and volatility is embedded in both equity and debt prices. This section summarizes the two methodologies traditionally used to extract this information. It then describes a new one that relies on contemporaneous equity and debt prices to obtain V and V The equity-implied asset volatility (EIAV) is calculated by solving the system: )()(21dNDedVNEfR (3-1) )(1dVNEEV (3-4) for and V. For the starting value of V, we use the sum of the market value of assets and book value of debt, and for the starting value of V V we use de-levered historical equity volatility.3 Adhering to previous studies we assume that the instantaneous standard deviation of equity at the end of quarter t is the standard deviation of equity returns over the quarter. Marcus and Shaked (1984), Ronn and Verma (1986), Pennacchi (1987), Dale et al. (1991), and King and OBrien (1991) apply this methodology to the analysis of deposit insurance premiums. It has also been used to calculate the market value of assets for savings and loan associations (Burnett et al. 1991), and insurance companies and 3 We ensure that the asset value and volatility estimates produced by all three methodologies are not sensitive to the starting values used.

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98 investment banks (Santomero and Chung 1992). We are aware of only one study that investigates whether the market value estimates obtained through this methodology are correct. Diba et al. (1995) use a contingent-claim model to calculate the equity values of failed banks and find that these values greatly exceed the negative net worth estimates of the FDIC. They conclude that the equity-call model produces poor estimates of market values. The accuracy of the asset volatility estimates, however, has not been previously examined. The debt-implied asset volatility (DIAV) is calculated by solving the system of nonlinear equations4 /)()~()()~(ln22212211122dNDDDdNDDdNdNeDVRRfRf (3-3) )(1dVNEEV (3-4) for and V. Once again, for the starting value of V we use the sum of the market value of equity and book value of debt, but for the starting value of we use the theoretically more accurate EIAV. As in the calculation of the equity-implied asset volatilities, we assume that the historical standard deviation of equity over quarter t is a good approximation for the instantaneous standard deviation of equity returns at the end of the quarter. This methodology is proposed in Gorton and Santomero (1990) and has since been used in Hassan (1993) and Hassan et al. (1993) to calculate implied asset volatilities, and in Flannery and Sorescu (1996) to obtain theoretical credit risk spreads. V V 4 For the purpose of this study we use the subordinated debt valuation model under the assumption that a BHCs publicly issued bonds are subordinated to at least deposits. This assumption is quite reasonable. One of the statutes in the Omnibus Budget Reconciliation Act of 1993 established a national depositor preference in distributing the assets of a failed institution. That is, a failed banks depositors have priority over nondepositors claims. Such statutes were already in force in twenty-eight states.

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99 The equity-and-debt implied asset volatility (EDIAV) is obtained by solving the system of nonlinear equations )()(21dNDedVNEfR (3-1) /)()~()()~(ln22212211122dNDDDdNDDdNdNeDVRRfRf (3-3) for and V. We use the same starting values for V and V V as in the calculation of DIAV. Note that unlike the previous three methodologies, this one needs no historical information about the standard deviation of equity. To the best of our knowledge this methodology has been used only in Schellhorn and Spellman (1996). They examine the difference between EIAV and EDIAV for four banks over 1987-1988. The authors conclude that the two volatility estimates can differ substantially over the studied period and that the estimates obtained from contemporaneous equity and debt prices are on average 40% higher than those obtained using equity prices and historical equity volatility. These three methodologies are based on contingent-claim valuation and as a result require that the theoretical assumptions of Black and Scholes (1976) and Black and Cox (1979) be met. Bliss (2000) points out that this is unlikely to be the case. However, it is an empirical question whether deviations from these assumptions make the estimates of asset value and volatility obtained under them less meaningful. In addition to the theoretical assumptions, applying contingent-claim valuation techniques requires that we know the time left to equityholders exercising their option, and the default point of each firm. In obtaining estimates for these we initially adhere to previous studies but later examine the sensitivity of our results to alternative assumptions. It is the goal of this study to determine whether the simplifying assumptions typically made in calculating

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100 asset values and volatilities affect the informational content and accuracy of these estimates. Starting with Marcus and Shaked (1984) and Ronn and Verma (1986) the time to exercising the equity call option is typically assumed to be one year. Banking researchers claim that the one-year expiration interval is justified because of the annual frequency of regulatory audits. If an audit indicates that the market value of assets is found to be less than the value of total liabilities, regulators can choose to close the bank. An alternative resolution-time assumption is employed by Gorton and Santomero (1990) who set the time to expiration equal to the average maturity of subordinated debt and find that the DIAV estimates calculated under this assumption are significantly higher than the ones calculated under the one-year-to-maturity assumption. However, they offer no evidence as to which maturity assumption produces the better estimate of asset volatility, which is a question we address in the current study. In the application of contingent-claim models to the valuation of industrial firms there is much less uniformity in the time-to-expiration assumption. Huang and Huang (2002) use the actual maturity of debt, Delianedis and Geske (2001) use the duration of debt, and Crosbie and Bohn (2002) use an interval of one year. Since the empirical properties of implied asset volatility are not the focus of these studies, they offer little evidence on the sensitivity of their results to alternative time-to-expiration assumptions. The study at hand fills this gap in the literature. To start with, we assume that the time to resolution equals one year. We later explore the effects of two alternative assumptions time to resolution equals to either the weighted average duration or the weighted average maturity of the firms bond issues.

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101 Although it is often assumed that firms default as soon as their asset value reaches the value of their liabilities, this is true only if the firms debt is due immediately. In reality, firms issue debt of various maturities and as a result their true default point is somewhere between the value of their short-term and long-term liabilities. Unfortunately, while previous studies recognize this (Crosbie and Bohn 2002), they offer little guidance on choosing each firms default point. The banking literature adheres to the assumptions made by Ronn and Verma (1986) who set the default point at 97% of the value of total debt. They originally experiment with default points in the range of 95-98% of debt and determine that rank orderings of asset values are significantly affected by the choice of default point (p.881). They do not examine the relative accuracy of the estimates obtained under alternative default-point assumptions which is an issue that we address. In summary, we employ the following base assumptions when calculating the three implied asset volatility estimates. The time to debt resolution equals one year; the default point is at 100% of total debt; the issuers yield is the yield on the most recently issued bonds (Hancock and Kwast 2001); and, the adjustment for taxes is based on Cooper and Davydenko (2002). In the following sections we present detailed results obtained under this initial set of assumptions and in Section 3.4 investigate the sensitivity of our findings to alternative assumptions. 3.2.3. Distance-to-Default Measures Three elements determine the probability that a firm will default the market value of its assets, the market value of its liabilities, and the probability distribution of its asset returns. The difference between the first two determines the default of the firm. The last element captures the business, industry, and market risks faced by the firm and is measured by asset volatility. If the implied asset volatility estimates calculated in this

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102 study offer a correct assessment of the firms risk exposure, then along with asset and liability values they should reflect default probability accurately. We combine asset volatility with the value of assets and liabilities into a single measure of default risk and refer to it as distance to default (DD). This measure compares a firms net worth to the size of one standard deviation move in asset value and is calculated as: TTRDVDDVVf25.0/ln Intuitively, a DD value of X tells us that a firm is X standard deviations of asset returns away from default. Thus, a low DD indicates that a firm is close to its default point and has a high probability of default. The opposite is true for firms characterized by high DD values. We calculate a DD measure based on each of the three asset volatility and value estimates discussed above: EIAV (uses equity values and historical equity volatility), DIAV (uses debt values and historical equity volatility), and EDIAV (uses debt and equity values). In the tests that follow we assess the relative accuracy and forecasting abilities of these three measures and compare their performance to that of more traditional risk measures equity volatility and credit spreads. 3.3. Data Sources This study combines a number of data sources for the period of January 1986 December 1999. Data on equity prices and characteristics is obtained from the Center for Research in Security Prices (CRSP). Data on bond prices and characteristics is obtained from the Warga-Lehman Brothers Fixed Income Database (WLBFID) and the Warga Fixed Investment Securities Database (FISD). Both sources are used since neither

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103 database alone covers the whole study period. Finally, accounting data comes from the Y-9 reports filed by bank holding companies. Combining equity-characteristic, debt-characteristic, and accounting data from these four sources is nontrivial since (1) each database has its own unique identifier with only some of them overlapping across databases, and since (2) some of the identifiers are recycled. Therefore, the merging process that we use requires further explanation. We start with information from WLBFID and FISD, which use issuer CUSIP as one of their identifiers. We then match the issuer CUSIP against those obtained from CRSP making sure that the date on which the bond data is recorded falls within the date range for which the CUSIP is active in the CRSP database. Merging the WLBFID and FISD data with that from the CRSP database allows us to add one more identifier to our list PERMNOs. We use them to acquire Compustat data from the Merged CRSP/Compustat database. Finally, the Y-9 reports filed by bank holding companies (BHC) do not report any generally used identifiers. In addition to the BHC name, the reports contain entity numbers assigned by the Federal Reserve. We manually link PERMNOs to entity numbers by first matching by BHC name and then confirming the match by comparing balance sheet data from the Y-9 Report to the data available from the Merged CRSP/Compustat. If the name is similar and total assets/total liabilities numbers are also comparable, then we consider this a match. 3.3.1. Bond Prices and Characteristics The initial sample includes all firms from the WLBFID and FISD whose bonds are traded during the period of 1986-1999. The WLBFID reports monthly information on the major private and government debt issues traded in the United States until March 1997. We identify all U.S. BHC-issued fixed-rate coupon-paying debentures that are not

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104 convertible, putable, secured, or backed by mortgages/assets. We collect data on their month-end yield, prepayment options, and amount outstanding. While most prices reflect live trader quotes, some are matrix prices estimated from price quotes on bonds with similar characteristics. Yields calculated from matrix prices are likely to ignore the firm-specific changes we are trying to capture, so we exclude them from our sample. The FISD contains comprehensive data on public U.S. corporate and agency bond issues with reasonable frequency since 1995. We use the same procedures for retaining observations as we do with the WLBFID in an attempt to make the two databases as comparable as possible we identify all fixed, non-convertible, non-putable, and non-secured debentures issued by U.S. BHCs. The main difference between the two databases is the source and type of the pricing information. The WLBFID reports bond trader quotes as made available by Lehman Brothers traders. The FISD reports actual transaction prices recorded electronically by Reuters/Telerate and Bridge/EJV who collectively account for 83% of all bond trader screens. In the spirit of making the data from the two databases comparable, we calculate each issues month-end yield using the price closest to the end of the month. A cursory examination of the small number of debt issues that have both WLBFID and FISD data available indicates that yields across the two databases are extremely similar. Nevertheless, when combining the WLBFID with the FISD sample, we choose actual trade prices over quotes only if the trade occurs in the last five days of the month. In order to compute a credit spread, we need to subtract from each corporate yield the yield on a debt security that is risk-free but otherwise has the same characteristics as the corporate bond. The most common approach to calculating a credit spread is to

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105 difference the yield on a corporate bond with that on a Treasury bond of the same remaining maturity. To do so we collect yields on Treasury bonds of different maturities from the Federal Reserve Boards H.15 releases. For each corporate debt issue in our sample we identify a Treasury security with approximately the same maturity as the remaining maturity on the corporate debenture. When there is no precise match, we interpolate to obtain a corresponding Treasury yield. The difference between a corporate yield and a corresponding Treasury yield is a measure of the raw credit spread. These spreads are further adjusted for tax and call-option premiums, and are then aggregated to obtain an issuer credit spread. 3.3.1.1. Tax adjustment There is growing evidence that corporate yield spreads calculated as above cannot be entirely attributed to the risk of default. Huang and Huang (2002) and Delianedis and Geske (2001) demonstrate that at best less than half of the difference between corporate and Treasury bonds is due to default risk. Elton et al. (2001) suggest that this difference can be explained by the differential taxation of the income from corporate and Treasury bonds. Since interest payments on corporate bonds are taxed at the state and local level while interest payments on government bonds are not, corporate bonds have to offer a higher pre-tax return to yield the same after-tax return. Thus, the difference between the yield on a corporate and the yield on a Treasury bond must include a tax premium. Elton et al. (2001) illustrate that this tax premium accounts for a significantly larger portion of the difference than does a default risk premium. For example, they find that for 10-year A-rated bonds, taxes account for 36.1% of the yield spread over Treasuries compared to the 17.8% accounted for by expected losses. Cooper and Davydenko (2002) derive an

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106 explicit formula for the tax adjustment proposed by Elton et al. (2001). They calculate that the tax-induced yield spread over Treasuries is: MrftMtaxtrtyMexp11ln1 where tis the time to maturity for both the corporate and the Treasury bonds, M is the applicable tax rate, and is the Treasury yield.5 We use this formulation along with the estimated relevant tax rate of 4.875% from Elton et al. (2001) to calculate a hypothetical Treasury yield if Treasuries were to be taxed on the state and local level.6 The difference between a corporate yield and a corresponding taxable Treasury rate is a measure of the tax-adjusted raw credit-risk spread. rftMr Alternatively, we can difference corporate yields with the yield on the highest rated bonds under the assumption that these almost never default. We obtain Moodys average yield on AAA-rated bonds from the Federal Reserve Boards H.15 releases. It is important to note that differencing a corporate yield with the AAA yield might allow us to extract a more accurate estimate of the credit-risk premium by controlling for liquidity as well as tax differential between corporate and Treasury bonds. However, it is also the case that the AAA yield has a number of drawbacks it averages the yields on bonds of different maturity and different convertibility/callability options. Nevertheless, for the non-AAA-rated bonds in our sample we use the difference between their yield and the average AAA yield as an alternative tax adjustment for the raw credit-risk spread. We 5 This formulation of the yield spread due to taxes assumes that capital gains and losses are treated symmetrically and that the capital gain tax is the same as the income tax on coupons. 6 Corporate bonds are subject to state tax with maximum marginal rates generally between 5% and 10% depending on the state. This yields an average maximum state tax rate in the U.S. of 7.5%. Since in most states, state tax for financial institutions (the main holder of bonds) is paid on income subject to federal taxes, Elton et al. (2001) use the maximum federal tax rate of 35% and the maximum state tax rate of 7.5% to obtain an estimate for of 4.875%. An alternative estimate is produced by Severn and Stewart (1992) and equals to 5%.

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107 start by differencing the corporate yields with the hypothetical taxable Treasury yields. However, in the spirit of this study we later investigate whether using the average AAA yields significantly affects the accuracy and informational content of the implied asset volatility estimates. 3.3.1.2. Call-option adjustment The tax-adjusted yield spreads calculated above might still contain some non-credit related components. Perhaps the most important of these is the value of call options embedded in many corporate yield spreads. Since the value of a call option is always non-negative, the spread over Treasuries whether adjusted for taxes or not, will exceed the credit-risk spread unless we adjust for the options value. We follow the approach presented in Avery, Belton, and Goldberg (1988) and Flannery and Sorescu (1996) to estimate an option-adjusted credit spread. For each callable corporate bond in our sample, we use the maturity-corresponding taxable Treasury bond to calculate a hypothetical callable Treasury yield. That is, we calculate the required coupon rate on a Treasury bond with the same maturity and call-option parameters as the corporate bond but the same market price as the non-callable Treasury bond adjusted for taxes. The difference between the yield on the hypothetical callable and the actual non-callable Treasury bond is the value of the option to prepay. We subtract these option values from the tax-adjusted spreads calculated earlier to obtain option-adjusted credit spreads. The required yield on the hypothetical Treasury is computed following the method of Giliberto and Ling (1992). They use a binomial lattice based on a single factor model of the term structure to value the prepayment options of residential mortgages. Their methodology uses the whole term structure of interest rates to estimate the drift and volatility of the short-term interest rate process. These two parameters are then used to

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108 determine the interest rates at every node of the lattice, which are in turn used to calculate the value of the mortgage prepayment option. Following Flannery and Sorescu (1996) this methodology is adjusted to calculate the call option value of the Treasury bonds instead. In a small number of cases these credit spreads turn out to be negative. A cursory examination of these occurrences indicates when the term structure of interest rates is relatively flat and interest rate volatility high, our option-adjustment methodology produces higher option values. When combined with an initially low yield (high-rated bonds) these high option values lead to negative credit spreads. Since the theoretical motivation used in this study does not allow for negative credit spread values and since negative credit spreads are heavily concentrated in high-rated bonds, we winsorize our set of credit spreads at zero.7 3.3.1.3. Yield spread aggregation To obtain a firm yield spread, YS, we aggregate yield spreads on bonds issued by the same firm using three approaches. The first approach is to construct a weighted-average yield spread by averaging the spreads on same-firm bonds and weighing them by the bonds outstanding amount. The other approaches use the findings in Hancock and Kwast (2001) and Covitz et al. (2002) that due to higher liquidity larger and more recently issued debentures have more reliable prices. To minimize the liquidity component of yield spreads, for each firm we take the spread on its largest issue (based on amount outstanding) as our second measure of firm yield spread, and the spread on its 7 We intend to investigate the resulting statistical bias by repeating all test after having excluded negative yield spreads altogether.

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109 most recent issue as our third measure. We investigate whether different aggregation approaches produce significantly different IAV estimates. 3.3.2. Equity Prices and Characteristics For all firms that have bond data available, we collect equity information from the daily CRSP Stock Files. We calculate the quarterly equity return volatility, E as the annualized standard deviation of daily returns during the quarter. The market value of equity, MVE, is the last stock price for each quarter multiplied by the number of shares outstanding. We exclude from our sample all stocks with a share price of less than $5 and for which E is computed from fewer than fifty equity-return observations in a quarter. These data filters attempt to reduce the effect of the bid-ask bounce on the estimate of equity-return volatility, and attempt to provide enough observations to make the quarterly volatility estimate meaningful. 3.3.3. Accounting Data Quarterly accounting data for the bank holding companies is obtained from the Consolidated Financial Statements (Y-9 reports) filed with the Federal Reserve Board. These statements consolidate the balance sheets of the parent corporation with those of its subsidiaries. For each BHC in our sample we collect information on the book value of total assets VB, the book value of subordinated notes and debentures, D2, loan quality, profitability, and capitalization at the end of each calendar quarter during 1986-1999. 3.4. Sample Selection and Summary Statistics Merging data from the above sources produces a sample of 98 unique BHCs which give us 2,110 firm-quarter observations for 1986-1999. We require each BHC to have

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110 filed at least four quarters of supervisory data in order to be able to conduct our forecasting analysis. We then employ the methodologies and the input assumptions described earlier to compute our three estimates of implied asset value and volatility using the Newton iterative method for solving systems of nonlinear equations.8 Our final sample contains 2,060 observations for 84 different BHCs. Table 3-1 presents summary statistics on the 2,060 firm-quarters. The BHCs in our sample are quite large which is not surprising given that they have both publicly traded debt and equity. The average market value of assets is in the range of $40-42 billion and is very similar across methodologies. The estimates of implied asset volatility show relatively more variation the average is 3.02% for EIAV, 3.16% for DIAV, and 4.55% for EDIAV. The magnitude of EDIAV is consistent with that reported in Schellhorn and Spellman (1996) who find EDIAV to be on average 40% higher than EIAV. We investigate whether the implied asset volatility estimates vary across quarters. Figure 3-1 plots median implied asset volatility for each quarter during 1986-1999, and makes three noteworthy points. First, the three IAV measures appear to follow a similar time pattern. The one notable exception is the last quarter of 1987 when median EIAV and DIAV dramatically increase, while EDIAV falls. This is likely due to the reliance of the first two estimates on historical equity volatilities calculated over the three-month period that includes the October 1987 crash. EDIAV on the other hand is not affected by the crash-induced historical equity volatility and as a result is a more forward-looking assessment of asset volatility. In fact, EDIAV increases in the second quarter of 1987 8 For a small set of observations, the Newton procedure had difficulties converging. We experimented with different starting values and different methods for solving a system of nonlinear equations (the Jacobi method and the Seidel method). We were successful in calculating all three asset value and volatility estimates for the majority of the original observations.

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111 possibly in anticipation of the crisis to come. Finally, the plot shows a general upward trend in the three IAV estimates suggesting that the risk of BHC assetss has been increasing over time. We also explore whether our estimates of implied asset volatility are affected by BHC capitalization. At the end of each quarter in 1986-1999, we use each firms book value of assets to debt ratio ranking to assign it to one of four quartiles. Figure 3-2 shows median implied asset volatilities from our four methodologies by assets-to-debt ratio quartile. It is apparent that the higher the amount of debt relative to assets, the lower the implied volatility. A possible explanation for this finding is that a firms capital structure and asset volatility are simultaneously determined. BHCs that are relatively better capitalized might be willing to take on more risk since they have a significant equity cushion to absorb changes in total asset value. This is consistent with the findings of Shrieves and Dahl (1992) and Calomiris and Wilson (1998) that increases in bank risk are positively related to increases in bank capital. The distance-to-default measures (DD) can possibly avoid problems resulting from the endogenous relationship between implied volatility and leverage since it combines them into a single measure of credit risk. Table 3-1 presents summary statistics on DD calculated from the three estimates of implied asset volatility. The average DD is 3.91 if calculated from EIAV, 2.32 if calculated from DIAV, and 2.43 if calculated from EDIAV. Figure 3-3 shows the time series behavior of the three DD estimates. While the estimate calculated from EIAV is very volatile, those calculated from DIAV and EDIAV are very stable. For instance, during 1986-1999 the median DD_EDIAV and DD_DIAV

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112 have remained in the range of 1.5-2.5 while the median DD_EIAV has fluctuated in the much wider range of 1.5-5.5. Table 3-2 examines more closely the differences among the three implied asset value, volatility, and distance-to-default estimates. Panel A indicates that the estimate of market value of assets is largely independent of the methodology used to compute it simple and rank correlations among all of the three estimates are essentially 1. Panel B shows that this is not the case for the three implied asset volatility estimates. Two of them are still very similar EIAV and DIAV have simple and rank correlations in the 90% range while the third one appears to be quite different. The simple (rank) correlation of EDIAV with EIAV and DIAV is 70% (66%) and 80% (73%) respectively. Panel C presents the correlations among the three DD estimates and points to a strong association between DD_DIAV and DD_EDIAV, and low association between these two and DD_EIAV. Interestingly enough, these do not simply reflect differences in implied asset volatility. Comparing the results in Panel B with those in Panel C suggests that high correlation between any two implied volatility estimates does not necessarily translate into high correlation between the corresponding distances to default. The wide range of correlation among the distance-to-default measures reported in Table 3-2, Panel C suggests that different methodologies produce very different estimates. Although all of the simple and rank correlations are statistically different from zero, all of them are also statistically different from one. By using information from different sources these three methodologies produce risk measures not only of different magnitude but also of different ranking. In the two sections that follow we investigate

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113 whether these differences translate into differences in informational content and accuracy. 3.4. Relative Accuracy of Market Indicators of Risk Our comparison of market indicators of risk starts with an assessment of their relative accuracy. If market participants are able to correctly evaluate a BHCs condition and promptly reflect it in the BHCs security prices, then risk measures constructed from these prices will be significantly related to other indicators of bank risk. That is, if a banks risk increases, so will its default probability, which implies a lower distance to default, higher equity volatility, and higher yield spread. To measure a BHCs risk we employ three proxies. The first one, RTG, is the average Moodys rating of each banks subordinated notes and debentures (SNDs) weighted by its amount outstanding. RTG is designed to capture the risk assessment of rating agencies. The Moodys rating of each SND issue is coded as a discrete number varying from 1 (Aaa) to 20 (Ca). Since most BHCs in our sample have more than one SND issue outstanding, their rating turns out to be non-discrete variable between 1 and 20 where a higher RTG indicates a riskier bank.9 The second proxy is a set of balance sheet variables that previous studies have found to reflect the financial health of banks. These include profitability, asset quality, and capitalization measures, which are summarized in Table 3-1. Our third proxy, SCORE, is a composite score of the firms condition based on five indicators: CAP (Capital Adequacy), LLAGL (Asset Quality), EFFIC (Management), ROA (Earnings), and LIQ (Liquidity). For every year in our sample, we consider each banks percentile ranking for all five indicators. We divide the 9 I also used Moodys ratings without notches and the results were even stronger.

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114 ranking distributions into quartiles and assign a score varying from 1 (best) to 4 (worst) to each bank based on its ranking. We obtain our composite score by summing up the scores for each indicator yielding a variable between 5 and 20 where a lower composite score indicates a healthier firm. We start our analysis with several univariate examinations of whether the five market measures of risk are generally consistent with the above three indicators of BHCs financial health. Table 3-3 provides summary statistics on the average market indicator estimates by Moodys credit rating. It shows that the market indicators derived from debt prices (DD_DIAV and YS), or from equity and debt prices (DD_EDIAV) agree with credit ratings. The average DDs decrease and average YS increases as rating deteriorates. Except for the highest rating categories, equity market indicators are also consistent in that average DD_EIAV decreases and average EV increases as we move from Aaa-rated to Caa-rated firms. We also examine whether our five market indicator estimates are consistent with BHC asset quality. Each year we assign firms in our sample to one of ten asset quality deciles. We use two proxies for asset quality (1) loan loss allowances as a proportion of total loans (LLAGL), and (2) the sum of past-due loans, non-accruing loans, and other real estate owned as a proportion of total loans (BADLOANS). Table 3-4 presents averages of the three DD estimates by asset quality deciles and shows that higher deciles are typically associated with lower DDs. The relationship between average market indicator estimates and asset quality deciles appears to be non-monotonic, but a closer look at the data suggests that this is due to the effect of outliers.

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115 Finally, we use the same approach to explore the relationship between a BHCs overall financial condition and the five market indicators. As above, each year we assign firms to one of ten SCORE deciles. Table 3-5 presents averages of the three DD estimates, EV, and YS by SCORE decile. It documents that BHCs in relatively worse condition typically have lower DDs, higher equity volatility, and higher credit spreads. It is interesting to note that the market measures are typically more consistent over the higher SCORE deciles, which suggests that they might be more accurate for firms in a weaker financial state. We test the contemporaneous accuracy of the five market indicators of BHC risk three DD measures, equity volatility (EV), and credit spread (YS) by estimating the model below with two-way fixed effects: ititititSizeFHMktInd 210 (3-6) For each firm i at the end of quarter t, is one of the five market indicators: DD_EIAV, DD_DIAV, DD_EDIAV, EV, or YS; is one of the three financial health proxies described earlier; andSize is the natural logarithm of the market value of assets. The model also includes cross-sectional and time-series fixed effects. Previous studies have found that the passage of FDICIA has limited the implicit and explicit government guarantees and has thus affected the informational content of market measures of risk. To account for this regime shift in late 1991, we estimate the above model for separately for the pre-FDICIA (June 1986 September 1991) and post-FDICIA (December 1991 December 1999) periods. itMktIndit itFH Table 3-6 contains the results from the multivariate analysis using Moodys ratings as the main independent variable. In all five models the BHC Moodys rating, RTG, is

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116 statistically significant in explaining each of the five market indicators of risk. This implies that investors are both willing and able to accurately assess BHCs underlying risk, and that they promptly price it in these firms debt and equity securities. In comparing the informational content of equity and debt prices, we examine the fit statistics for Model 1 versus Model 2, and Model 4 versus Model 5. We find that debt-price-only indicators (DD_DIAV and YS) always outperforms equity-price-only indicators (DD_EIAV and EV) suggesting that debtholders are on average more accurate in their assessment of BHC risk. We also document that using more complex market indicators (distance-to-default measures) over simpler ones (credit spreads or equity volatilities) increases the explanatory power of debt-market indicators and reduces that of equity-market indicators. Finally, we show that using both equity and debt prices in constructing a market risk measure is superior to using either set of prices alone. In the post-FDICIA period DD_EDIAV the distance to default measure calculated from contemporaneous equity and debt prices without reliance on historical volatility is most closely related to BHC credit rating. The R2 of the model in which DD_EDIAV is the dependent variable is at least 2.5 percentage points higher than those of any of the other models. Table 3-7 shows the results from a multivariate analysis that uses a set of asset quality measures to explain BHC market indicators of risk. These are consistent with the results presented in Table 3-6. BHCs with less low-quality assets (past-due loans, non-accruing loans, and other real estate owned) have higher DD measures, lower EV, and lower YS. The interactions of these variables with firm leverage (equity-to-debt ratio) are expected to capture the non-linear effect of asset quality and leverage. Their positive

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117 coefficients in the DD models and negative coefficients in the EV and YS models suggest that asset quality is more relevant for banks with higher leverage. Profitability (ROA) is typically not statistically significant but whenever significant it enters with a positive sign in the DD models and negative sign in the EV and YS models. This implies that BHCs with higher return-on-assets ratio are perceived as having lower credit risk. The explanatory power in these regressions follows a pattern similar to that in Table 3-6. First, debt-only market indicators (DD_DIAV and YS) outperform equity-only market indicators (DD_EIAV and EV). Second, in the post-FDICIA period of 1991-1999, the DD_EDIAV model has the best fit (R2 of at least 2.2 percentage points higher than that of any of the other models), thus suggesting that the DD measure calculated from contemporaneous equity and debt prices is more closely related to accounting measures of asset quality than are other market indicators of risk. It is interesting to note that while the equity-derived DD is related to OREOGL and the debt-derived DD is related to NALGL, the equity-and-debt DD is significantly related to both OREOGL and NALGL. This supports the idea the using equity and debt market indicators performs better because it combined risk information from two sources. Finally, Table 3-8 presents the results in which the main explanatory variable is the composite score of the BHC financial health. The negative coefficient on SCORE in the DD models implies that weaker firms (as indicated by a higher SCORE) are characterized by lower DD measures. It is interesting to note the change in sign and statistical significance of SIZE across the two subperiods in the fixed-effects estimation. During pre-FDICIA period firm size is either not significant or has a negative coefficient in the EV and YS models, thus suggesting that larger firms have lower credit risk. This is

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118 consistent with the existence of implicit or explicit government guarantees for banks considered too big to fail. In the post-FDICIA period, larger banks are associated with lower DD measures, higher EV, and higher YS. One possible explanation for this finding is that larger banks are more flexible and better able to handle adverse shocks. Another explanation is that investors have come to believe regulators claims that too big to fail guarantees are over. Bank managers, on the other hand, might know that political pressures in the face of a big bank failure can make it difficult for regulators to keep their word. Our findings on the relative accuracy of the five market indicators in the post-FDICIA period are consistent with those presented in Table 3-6 and Table 3-7. First, debt-price indicators outperform equity-price indicators. Second, using more complex risk indicators improves the model fit for debt-price indicators and worsens that for equity-market indicators. Finally, judging by the explanatory power of the five models, DD_EDIAV is the most accurate measure as indicated by the highest R2 of that model which is at least 1.9 percentage points higher than that of any of the other models. In summary, the above tests suggest that all five market indicators of BHC risk are closely related to credit agency assessments, asset portfolio quality, and overall firm condition as indicated by accounting variables. This confirms the findings of previous studies10 that both equity and debt prices of BHC-issued securities accurately and promptly reflect information about the firms financial condition. Comparison of the explanatory power of the five models reveals three noteworthy points. First, market indicators based on debt prices alone outperform market indicators based on equity prices 10 See Flannery (1998) for a review of these studies.

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119 alone. Second, the use of structural credit risk models to construct market indicators tends to improve the informational content of debt measures and worsen that of equity measures. Finally, as indicated by the models fit, the distance-to-default measure calculated from both equity and debt prices displays the closest association with the three proxies of BHC true risk. This suggests that combining information from equity and debt prices can improve the quality of market measures of risk. 3.5. Relative Forecasting Ability of Market Indicators of Risk In this section we empirically examine the forecasting ability of market indicators of BHC risk. Since market prices are investors expectations of future outcomes, risk indicators constructed from them might reflect not only current but also future bank condition. To test this conjecture we examine (1) whether market indicators of BHC risk can predict material changes in the firms default probability, and (2) whether changes in the indicators can foresee quarter-to-quarter changes in the firms asset portfolio quality and composite financial health score. 3.5.1. Forecasting Material Changes in Default Probability We first examine the ability of market indicators to predict significant changes in the BHCs default probability. The clearest manifestation of such a change would be a default, but large U.S. BHCs almost never fail only three firms in our sample do. In the absence of BHC failures, we consider a downgrade from investment to non-investment grade by Moodys as a signal of a material weakening of the BHCs financial condition (an approach similar to that in Gropp et al. 2002). We start our analysis with simple mean-comparison tests to determine whether market risk indicators can distinguish the financially weak banks in our sample. Table 3-9 presents the results. As hypothesized, BHCs that eventually experience a material

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120 negative change in their financial condition have lower DD measures, higher EV, and higher YS. All five of our market indicators have predictive power up to two quarters prior to the event. Three quarters prior only the measures derived from debt prices can distinguish between BHCs that will be significantly downgraded from those that are not. As a second step in testing whether our market indicators of risk can predict material changes in BHC default probability, we estimate a standard logit model of the form: ktiktiktitiSizeRTGMktIndgChange ,3,2,10,1Pr (3-7) where otherwisegradeinvestmentnontoinvestmentfromdowngradedisbankifChangeti01, The cumulative logistic distribution is denoted by )( g is one of the five market indicators DD_EIAV, DD_DIAV, DD_EDIAV, EV, or YS for firm i, k quarters prior to quarter t. is firm i's Moodys rating k quarters prior to quarter t.11 is the natural logarithm of firm i's market value of assets k quarters prior to quarter t. We explicitly control for size for at least two reasons. Large BHCs might attract more government oversight and this might have the effect of preventing small problems escalating into more serious ones. It might also be the case that credit rating agencies pay different attention to the financial health of small versus large firms. ktiMktInd, ktiRTG, ktiSize, 11In an alternative model specification we substitute the continuous variable RTG with indicator variables for each of the major rating categories. The results are basically the same with DD_EDIAV having higher explanatory power one and two quarters prior to the event.

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121 The results from the logit analysis are presented in Table 3-10. Consistent with the mean difference tests, we find that all five market indicators are statistically significant in explaining the probability of experiencing a material negative change one and two quarters prior to the change occurring. Only, DD_DIAV, DD_EDIAV, and YS have predictive power three quarters prior.12 This is in contrast to the findings of Gropp et al. (2002) that equity-market indicators are the first to respond to European financial institutions weakening condition. In order to compare the informational content of equity-market indicators to that of debt-market indicators of risk, we estimate two models which include both sets of indicators as explanatory variables. The last two columns of Table 3-10 show that in these specifications equity indicators are not statistically significant. This suggests that when it comes to predicting downgrades from investment to junk, the information available from equity prices is a subset of the information available from debt prices. That is, equityholders do not know more than debtholders when it comes to material negative changes in BHC default probability. Finally, information from both equity and debt prices is neither better nor worse than debt-price information in predicting significant credit downgrades. The fit of the models which include equity-price and debt-price information is the same as that of the models including debt-price information alone. This is the direct result of equity prices containing redundant information about material changes in default probability. 12 Four quarters prior, DD_DIAV and DD_EDIAV are marginally significant (at the 10 percent level) in explaining the probability of a material negative change in BHC condition.

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122 3.5.2. Forecasting Changes in Asset Quality After confirming that our five market indicators can foresee material changes in BHC financial conditions, we investigate whether their forecasting power extends to changes of any (low and high) magnitude. In this section we explore whether changes in any of the five market indicators can explain future changes in BHC asset quality beyond what can be explained by historical asset quality information. As in Section 3.4, we use two proxies for asset quality (1) loan loss allowances as a proportion of total loans (LLAGL), and (2) past-due loans, non-accruing loans, and other real estate owned as a proportion of total loans (BADLOANS). To test our hypothesis we estimate the following model: tititikktiktikktiktiSIZEAQdAQMktInddMktInddAQ,1,54,431,,34,231,,10, (3-8) where for each BHC i in quarter t AQi,t is one of the two asset quality proxies at the end of quarter t and dAQi,t, is the change from quarter t-1 to t; MktIndi,t is one of the five market indicators of risk at the end of quarter t and dMktIndi,t is the change from quarter t-1 to t; SIZEi,t is the natural logarithm of the market value of assets at time t. Tables 3-11 and 3-12 present the results from an OLS estimation of Eq. 3-8 in which AQ is proxied by LLAGL and BADLOANS respectively. It is interesting to note that our findings depend on the asset quality proxy used. Table 3-11 shows that in the pre-FDICIA period none of the five market indicators can explain subsequent changes in LLAGL. The results are dramatically different for the post-FDICIA period. All five of our market indicators foresee changes in LLAGL up to four quarters prior to the changes occurring, and all of them contribute significantly to the models fit. A comparison of the explanatory power of equity versus debt indicators (columns 1 and 2) reveals that debt

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123 indicators marginal contribution to the models R2 is twice that of equity indicators. This suggests that the information available from debt prices is a more accurate forecaster of future LLAGL changes than is the information available from equity prices. Had we evaluated the explanatory power of equity volatility against that of credit spreads, we would have reached the opposite conclusion which underscores the importance of analyzing comparable equity and debt indicators. Consistent with the contemporaneous tests results, we document that using information from both equity and debt prices is better than using information from either set of prices alone. DD_EDIAV produces a better fit than DD_EIAV or DD_DIAV. Including both DD_EIAV and DD_DIAV in the set of explanatory variables increases the explanatory power of the model even further. The latter specification allows us to assess the relative informational content of equity-price and debt-price indicators. Since both DD_EIAV and DD_DIAV retain their statistical significance and estimates magnitude, we conclude that the credit risk information contained in equity prices has little or no overlap with the information contained in debt prices when it comes to forecasting LLAGL changes. Table 3-12 presents the results from an OLS estimation of Eq. 3-8 in which we use BADLOANS as a proxy of BHC asset quality. In contrast to our findings for LLAGL above, we document that market indicators can foresee changes in BADLOANS even before FDICIA is passed. Equity indicators have lower statistical significance and lower explanatory power, mostly concentrated in the first three lags. On the other hand, all four lags of the debt indicators are strongly significant. The estimation results for the post

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124 FDICIA period are similar to those in Table 3-11 where BHC asset quality is proxied by LLAGL. Finally, we examine whether changes in a firms overall financial condition can be forecasted using market indicators from up to four lags. This requires the estimation of a logit model analogous to Eq. 3-8: )(1Pr,54,431,,34,231,,10,titikktiktikktiktiSIZESCOREdSCOREMktInddMktIndgCHG (3-9) where increasesSCOREifchangenotdoesSCOREifdecreasesSCOREifCHGti101, and other variables are as defined earlier. Recall that SCORE increases when the BHCs financial condition weakens. The results are presented in Table 3-13. In the pre-FDICIA period, market indicators either do not foresee changes in a BHCs SCORE or do so only in the quarter prior to the change occurring. In the post-FDICIA period, market indicators seem to react much sooner. Both DD_DIAV and DD_EDIAV are statistically significant one, two, and three quarters before SCORE changes. This causes the explanatory power of the models to more than double from the early to the latter part of the sample period. As in the previous tests, debt-price indicators seem to outperform equity price indicators. All three lagged changes of DD_DIAV are strongly significant, while only two lagged changes of DD_EIAV are significant at the 10% level. Furthermore, debt indicators produce a better model fit as judged by a pseudo R2 of at least 2-3 percentage points higher than that of

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125 equity indicators. Finally, combining risk information from equity and debt prices is only marginally better than using debt prices alone as judged by the relevant models fit. It appears that equity indicators lose most of their statistical significance while debt indicators continue to be significant at the 1% level. This suggests that changes in equity indicators contain little risk information beyond what is already contained in debt indicator changes. That is, when it comes to forecasting changes in BHC overall condition relative to its peers, the default risk information in equity prices is a subset of that in debt prices. 3.6. Sensitivity of Market Indicators to Alternative Model Assumptions In this study we use contingent-claim models for firm valuation in order to construct some of the market indicators of firm risk. The application of such models requires that a set of simplifying assumptions be made. So far in the analysis we examine distance-to-default (DD) measures calculated under the following base assumptions. The time to debt resolution equals one year; the default point is at 100% of total debt; the issuers yield is the yield on the most recently issued bonds (Hancock and Kwast 2001); and, the adjustment for taxes is based on Cooper and Davydenko (2002). In this section we investigate the sensitivity of our findings to alternative assumptions. Table 3-14 presents summary statistics for the new estimates of implied asset value, implied asset volatility, and distance-to-default (DD). Increasing the time to expiration from one year to the weighted average duration or maturity of the firms outstanding debt issues decreases asset value, increases asset volatility, and decreases DD. Reducing the firms default point has a similar effect. An assumption that appears to have little or no effect on our estimates is that the issuer credit spread can be represented by the credit spread on the firms most recently issued bonds. If we instead use the weighted average

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126 issue credit spreads or the credit spread on the firms largest issues, then the median asset value, volatility, and DD estimates remain the same. Not adjusting credit spreads for taxes causes our estimates of DD to decrease slightly. If we calculate credit spreads by using the average yield on Moodys AAA-rated bonds instead of Treasury securities tends to increase the average DD estimates that use debt prices. Finally, excluding all callable issues from our bond data sample leaves summary statistics effectively unchanged. Having established that some of the model assumptions affect the magnitude of the DD estimates, we then explore whether they affect the estimates informational content as well. We re-estimate the contemporaneous and forecasting models described earlier in the paper using each set of new market indicators. We document that the statistical significance of the DD measures stays essentially the same while the models fit shows slight variation. Tables 3-15 presents the results from estimating Eq. 3-6 where financial health is proxied by a set of accounting measures of BHC asset quality. Judging by the models fit, the only assumption that dramatically affects the explanatory power of the three DD measures is the default point assumption. In the post-FDICIA period, reducing the default point to 97% or 95% of total debt increases the R2 of all three DD models. Furthermore, it also underscores the outperformance of the DD measure which combines information from equity and debt prices. Table 3-15 points out that the R2 of the DD_EDIAV model is at least 15 percentage points higher than that of the other models. An estimation of Eq. 3-6 in which financial health is proxied by credit rating (RTG) or overall condition (SCORE) confirms the results in Table 3-15. Once again, the R2 of the DD_EDIAV model is at least 9 percentage points (when RTG is the explanatory variable)

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127 and 8 percentage points (when SCORE is the explanatory variable) higher than that of the other models.13 Alternative time-to-expiration and issuer-yield assumptions do not significantly alter the models fit. It is interesting to note that employing no adjustment for taxes produces the best model fit. Using the Cooper and Davydenko (2002) adjustment or the yield on Moodys AAA-rated bonds reduces the association between DD estimates and proxies of the BHC financial health. Finally, alternative model assumptions tend to preserve the ranking of the DD estimates and leave the main findings of this study unchanged. In the post-FDICIA period DD measures constructed from debt prices are more closely related to BHC credit rating, asset quality, and overall condition than are DD measures constructed from equity prices. However, both measures are further outperformed by the equity-and-debt DD. Re-estimating the forecasting models (Equations 3-7, 3-8, and 3-9) under alternative model assumptions produces results similar to those above. Once again, the assumption that most significantly affects our DD estimates is the BHC default point. When we reduce it to 95% of total debt, we obtain the DD estimates with the highest explanatory power. Table 3-16 indicates that the R2 of a model forecasting changes in BADLOANS increases by 5 percentage points if we assume that BHC default point is at 95% of total debt. Table 3-17 shows that such an assumption improves the fit of a model forecasting changes in SCORE as well pseudo R2 increases by 3 to 5 percentage points. Employing alternative model assumptions preserves our main findings that the forecasting ability of debt indicators is slightly better than that of equity indicators, and 13 Results are available from the author upon request.

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128 that combining information from equity and debt prices produces an even better forecast of changes in BHC risk. 3.7. Conclusions The literature on market discipline of banks and BHCs offers voluminous evidence that market prices reflect information about firm condition in an accurate and timely manner, and that this information can be different from that available to regulators. This evidence has been used as justification for supplementing government oversight with information from the equity and debt markets. However, research to date has offered little guidance as to which set of market information to use and how to use it. This paper addresses both questions. First, we compare information from equity prices with that from debt prices to determine which set produces risk estimates that more accurately reflect a banks true condition. We construct the same credit risk indicators (distance-to-default (DD) measures) from equity prices as we do from debt prices and then assess their relative performance in contemporaneous and forecasting models. We document that the contemporaneous association between the debt implied DD and BHC credit rating, asset-portfolio quality, and overall financial condition than is higher than it is between these and equity implied DD. In addition, debt-price indicators have slightly higher explanatory power than equity-price indicators when it comes to forecasting significant credit downgrades, changes in accounting proxies of risk, and changes in the BHC overall standing relative to its peers. When both equity and debt DD measures are used to forecast changes in BHC credit risk, the explanatory power is concentrated in the debt measures. This finding is in contrast to the commonly held belief that debt prices are too

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129 noisy for the information in them to be useful. It appears that despite the noise, debt prices are a better overall source of BHC risk information than are equity prices. We further propose that combining information from both equity and debt prices might be superior to using either source alone. Judging by the explanatory power of the contemporaneous models, the DD measure calculated from contemporaneous equity and debt prices is the one most closely related to indicators of BHC credit risk in the post-FDICIA period. It produces an R2 that is at least 2 percentage points higher than that produced by any of the other market indicator. The forecasting regressions also confirm the benefits of combining information from equity and debt prices. Combination models improve on the explanatory power of equity-only or debt-only models and the magnitude of the improvement depends on how similar the information in equity and debt prices is. Both equity and debt markets are characterized by frictions and as a result both equity and debt prices reflect a BHCs true credit risk with noise. Statistical theory tells us that combining two forecasts that are not perfectly correlated can produce a better estimate. Our findings are consistent with this explanation. A final dimension of the analysis evaluates how market information is to aid regulators in the assessment of a BHCs financial condition. Is it to be used as contemporaneous affirmation, or as a forecasting tool? The contemporaneous analysis suggests that risk measures constructed from equity and/or debt prices are related to indicators of BHC risk. This implies that market information can be used by regulators to confirm a BHCs current condition. In that sense, it can also be used as a tripwire for supervisory actions, which might help reduce regulatory forbearance (Evanoff and Wall 2000). The DD measure using information from both equity and debt prices provide the

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130 most accurate affirmation of BHC credit risk in the post-FIDICIA period as indicated by the models fit. Our forecasting analysis indicates that market indicators can also be used to predict material changes in the firms default probability and quarter-to-quarter changes in the firms asset-portfolio quality and overall condition. Once again, models that combine information from equity and debt prices produce the best fit.

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131 Table 3-1. Summary statistics. Summary statistics are for the sample of 2,060 firm-quarter observations over 1986-1999. VariableDefinitionMinMaxMedianMeanStdDevV_EIAVEquity-implied asset value calculated from equity prices and historical equity volatility0.97391.4123.7142.2553.93V_DIAVDebt-implied asset value calculated from debt prices and historical equity volatility0.92398.3022.9540.8152.09V_EDIAVEquity-and-debt-implied asset value calculated from contemporaneous equity and debt prices0.97391.0123.7142.2553.91EIAVEquity-implied asset volatility calculated from equity prices and historical equity volatility0.4820.552.663.021.86DIAVDebt-implied asset volatility calculated from debt prices and historical equity volatility0.6419.652.843.161.79EDIAVEquity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices0.4919.484.364.552.19DD_EIAVDistance to default calculated from equity-implied asset value and volatility0.1413.313.853.911.42DD_DIAVDistance to default calculated from debt-implied asset value and volatility0.785.582.252.320.63DD_EDIAVDistance to default calculated from equity-and-debt-implied asset value and volatility0.815.822.332.430.74EVequity volatility over the quarter.8.23122.5629.1132.7314.58YScredit spread of the firms most recently issued subordinated debt0.0018.820.681.111.44LEVMarket value of equity / Book value of debt0.011.190.100.110.09ROANet income / Total assets-0.0270.0280.0050.0050.005LLAGLLoan and lease allowance / Total loans0.0070.1280.0210.0250.014NALGLNon-performing loans / Total loans0.0000.1040.0120.0180.018PDL90GLTotal loans past due more than 90 days / Total loans0.0000.0380.0030.0030.003OREOGLOther real estate owned /Total loans0.0000.0640.0030.0060.008BADLOANSSum of non-performing loans, loans past due more than 90 days, and OREO / Total loans0.0000.1730.0200.0280.024SIZELog( Market value of assets)6.912.910.110.11.1RTGWeighted average Moody's rating1.020.07.07.22.4

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Table 3-2. Simple and rank correlations. Correlations are for the sample of 2,060 firm-quarter observations over 1986-1999. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. V_EIAV, V_DIAV, and V_EDIAV are the corresponding estimates of the market value of assets. DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. All correlations are significantly different from 0 at the 1 percent level. Simple CorrelationsRank Correlations Panel A: Implied Market Value of AssetsV_EIAVV_DIAVV_EDIAVV_EIAVV_DIAVV_EDIAVV_EIAV1.001.00V_DIAV1.001.001.001.00V_EDIAV1.001.001.001.001.001.00Panel B: Implied Asset VolatilityEIAVDIAVEDIAVEIAVDIAVEDIAVEIAV1.001.00DIAV0.981.000.991.00EDIAV0.700.801.000.670.741.00Panel C: Market Measures of RiskDD_EIAVDD_DIAVDD_EDIAVDD_EIAVDD_DIAVDD_EDIAVDD_EIAV1.001.00DD_DIAV0.091.000.181.00DD_EDIAV0.140.981.000.320.971.00 132

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Table 3-3. Average market indicators of risk by Moodys credit rating. Average statistics are on the sample of 2,022 firm-quarters for the period 1986-1999. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. Prob of Default is the average one-year default rate over 1980-1999, obtained from Moodys Investors Service (2000). Prob of Default, Moody's Credit RatingN1980-1999 (%)DD_EIAVDD_DIAVDD_EDIAVEVYSInvestment GradeAaa-Aa1320.00-0.023.882.352.390.280.006A1,1010.024.062.322.390.270.006Baa6210.193.692.202.280.310.007Non-Investment GradeBa1181.402.861.651.720.400.028B426.601.691.551.560.630.046Caa-C825.351.411.491.480.710.060 133

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134 Table 3-4. Average market indicators of risk by asset quality deciles. Average statistics are on the sample of 2,022 firm-quarters for the period 1986-1999. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. LLAGL is the ratio of loan loss allowances to gross loans. BADLOANS is the sum of non-performing loans, past due loans, and other real estate owned as a proportion of gross loans. Asset QualityNobsDD_EIAVDD_DIAVDD_EDIAVEVYSLLAGL Decile1 (Healthy BHCs)2144.032.582.680.2930.01022044.022.342.420.2880.01132074.052.462.550.2950.00842053.962.442.540.3060.00852054.072.362.470.3040.00862073.922.292.380.3220.01172073.612.172.280.3580.01582054.132.232.370.3450.01092063.632.152.290.3900.01410 (Weak BHCs)2003.692.142.250.3740.015BADLOANS Decile1 (Healthy BHCs)2143.952.512.610.3060.00922044.152.462.580.3080.00932074.052.492.610.3040.00942054.062.342.440.3140.01152054.122.362.460.2980.01162074.112.352.450.3100.01072073.752.302.400.3290.01082053.682.232.350.3490.01292063.732.152.270.3570.01210 (Weak BHCs)2003.491.972.070.4010.019

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135 Table 3-5. Average market indicators of risk by SCORE deciles. Average statistics are on the sample of 2,022 firm-quarters for the period 1986-1999. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. SCORE is a composite index of the firms financial condition based on its capitalization, asset quality, management, earnings, and liquidity relative to other firms. It is a variable between 5 and 20 where a lower score indicates a healthier firm. SCORE DecileNobsDD_EIAVDD_DIAVDD_EDIA V EVYS1 (Healthy BHCs)3744.132.512.620.2970.008622194.012.432.520.3050.009432254.052.492.590.3000.008642444.282.252.340.2890.009351764.122.402.550.3000.008661863.772.272.370.3350.011371933.832.232.330.3320.010681533.792.252.360.3550.011891713.582.112.240.3790.014710 (Weak BHCs)1193.091.861.950.4520.0266

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Table 3-6. Analysis of Moodys credit ratings. We estimate ititititSizeRTGMktInd 210 via two-way fixed effects for the sample of 843 and 1,179 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable is one of the five market indicators: DD_EIAV, DD_DIAV, DD_EDIAV, EV, or YS. DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. The main independent variable, RTG, is the weighted average Moodys rating for the firms debt issues outstanding, RTG. Moodys ratings are coded as Aaa=1 to Caa=19, so that as ratings deteriorate, the variable RTG increases. SIZE is the log of the market value of assets. Fixed effects are excluded from the table for ease of exposition. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Fa is the F-statistic for the hypothesis that all time series effects are jointly zero. Fb is the F-statistic testing the hypothesis that all cross section fixed effects are jointly zero. EVYSDD_EIAVDD_DIAVDD_EDIAV Pre-FDICIA Period (Jun 1986 Sept 1991)RTG-0.158***-0.097***-0.103***0.032***0.006***(0.029)(0.013)(0.016)(0.003)(0.000)SIZE-0.065-0.393***-0.380***0.0030.001(0.255)(0.112)(0.145)(0.025)(0.002)R20.6170.7520.7100.7090.748Fa ( df = 22, [nobs-ncoef])37.10***5.42***5.34***55.38***14.15***Fb ( df = 68, [nobs-ncoef])5.55***23.67***18.89***5.09***12.29***Post-FDICIA Period (Dec 1991 Dec 1999)RTG-0.193***-0.056***-0.056***0.027***0.002***(0.033)(0.006)(0.005)(0.003)(0.000)SIZE-0.800***-0.111***-0.126***0.084***0.006***(0.227)(0.041)(0.037)(0.018)(0.002)R20.5610.7210.7460.6550.705Fa ( df = 32, [nobs-ncoef])14.03***13.68***19.00***16.57***10.57***Fb ( df = 66, [nobs-ncoef])6.85***13.10***9.96***6.19***12.47*** 136

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Table 3-7. Analysis of asset quality measures. We estimate ititmmitmitSizetyMeasuresAssetQualiMktInd 210 via two-way fixed effects using the sample of 860 and 1,200 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable is one of the five market indicators: DD_EIAV, DD_DIAV, DD_EDIAV, EV, or YS. DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. ROA is the ratio of net income (loss) to total assets. OREOGL, NALGL, and PDL90GL are asset-quality proxies defined in Table 3-1. ROALEV, OREOGLLEV, NALGLLEV, and PDL90GLLEV are ROA, OREOGL, NALGL, and PDL90GL interacted with leverage (LEV). LEV is the ratio of the market value of equity to the book value of debt. SIZE is the log of the market value of assets. Fixed effects are excluded from the table for ease of exposition. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. The R2 of the model with the highest explanatory power is in bold. Fa is the F-statistic testing that all fixed effects are jointly zero (df=nfe, [nobs-ncoeff]). Fb is the F-statistic for the hypothesis that all three interaction variables are jointly zero (df=3, [nobs=ncoff]). Fc is the F-statistics for testing that all six loan quality variables are jointly zero (df=6, [nobs-ncoeff]). Pre-FDICIA Period (Jun 1986 Sept 1991)Post-FDICIA Period (Dec 1991137 Intercept0.004.34***4.56***0.85***0.06***5.21**1.77***1.78***0.39**0.05***(2.19)(0.95)(1.23)(0.21)(0.02)(2.19)(0.39)(0.36)(0.16)(0.02)ROA30.83**-1.880.89-6.94***-0.98***-8.022.392.860.71-0.17(14.90)(6.47)(8.39)(1.42)(0.13)(14.71)(2.65)(2.42)(1.10)(0.11)OREOGL-50.23***-38.65***-42.94***11.50***2.09***-48.71***-2.97-4.23**6.06***0.38***(14.08)(6.12)(7.93)(1.34)(0.12)(14.09)(2.53)(2.31)(1.05)(0.10)NALGL-4.06-3.91*-3.65-0.48-0.05-9.26-5.40***-5.04***1.92***0.12**(5.49)(2.39)(3.09)(0.52)(0.05)(7.71)(1.39)(1.27)(0.58)(0.06)PDL90GL-21.800.08-0.45-1.030.09-16.85-1.46-1.99-0.330.49***(34.96)(15.18)(19.69)(3.33)(0.30)(20.83)(3.75)(3.42)(1.56)(0.15)ROALEV-289.00163.03*140.8044.35**9.45***12.77-1.33-3.37-2.240.45*(215.34)(93.53)(121.26)(20.54)(1.84)(35.37)(6.36)(5.81)(2.64)(0.25)OREOGLLEV318.66328.06***361.73**-79.88***-22.36***319.12*-8.043.19-47.37***-3.04**(259.63)(112.77)(146.20)(24.76)(2.22)(167.64)(30.14)(27.55)(12.53)(1.20)NALGLLEV-44.7853.9758.809.091.03-47.2182.38***70.70***-10.73*-1.44**(79.57)(34.56)(44.81)(7.59)(0.68)(79.04)(14.21)(12.99)(5.91)(0.57)PDL90GLLEV389.23-302.04-435.81*-4.68-2.0432.333.423.234.31-0.84*(455.96)(198.05)(256.76)(43.49)(3.89)(70.51)(12.68)(11.59)(5.27)(0.51)SIZE0.27-0.29**-0.32**-0.04*0.00**-0.43*-0.02-0.030.03*0.00(0.26)(0.11)(0.15)(0.03)(0.00)(0.23)(0.04)(0.04)(0.02)(0.00)DD_EIAV Dec 1999)DD_EIAVDD_DIAVDD_EDIAVEVYSDD_DIAVDD_EDIAVEVYS

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Table 3-7. Continued R20.6240.7610.7200.7210.7710.5730.7260.7480.6870.723Fa12.25***24.64***20.32***14.90***13.27***9.40***13.43***13.67***9.77***12.20***Fb0.825.17***3.84***3.51**36.78***1.8122.99***22.37***19.20***18.31***Fc4.13***10.82***8.19***14.41***58.29***9.71***16.26***18.20***31.95***19.93***Pre-FDICIA Period (Jun 1986 Sept 1991)DD_EIAVPost-FDICIA Period (Dec 1991Dec 1999)DD_EIAVDD_DIAVDD_EDIAVEVYSDD_DIAVDD_EDIAVEVYS 138

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Table 3-8. Analysis of financial health SCORE. We estimate ititititSizeSCOREMktInd 210 via two-way fixed effects for the sample of 860 and 1,200 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable is one of the five market indicators: DD_EIAV, DD_DIAV, DD_EDIAV, EV, or YS. DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. The main dependent variable is the firms financial health score, SCORE. This is a composite index of the firms financial condition based on its capitalization, asset quality, management, earnings, and liquidity relative to other firms. It is a variable between 5 and 20 where a lower score indicates a healthier firm. SIZE is the log of the market value of assets. Quarter indicators variables are included in the set of independent variables but excluded from the table for ease of exposition. Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Fa is the F-statistic testing that all fixed effects are jointly zero (df=nfe, [nobs-ncoeff]). Pre-FDICIA Period (Jun 1986 Sept 1991) Intercept-2.0911.927**1.6331.439***0.166***7.777***2.645***2.681***-0.1090.007(2.054)(0.897)(1.159)(0.204)(0.021)(2.136)(0.385)(0.355)(0.169)(0.016)SCORE-0.074***-0.064***-0.067***0.017***0.002***-0.076***-0.029***-0.027***0.011***0.001***(0.020)(0.009)(0.011)(0.002)(0.000)(0.020)(0.004)(0.003)(0.002)(0.000)SIZE0.578**0.0740.110-0.133***-0.020***-0.799***-0.096**-0.116***0.088***0.005***(0.257)(0.112)(0.145)(0.025)(0.003)(0.227)(0.041)(0.038)(0.018)(0.002)R20.6120.7510.7090.6890.6700.5500.7100.7290.6300.688Fa15.39***27.60***22.91***20.52***17.21***11.32***19.95***21.88***14.62***17.78***Post-FDICIA Period (Dec 1991Dec 1999)DD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAVDD_DIAVDD_EDIAVEVYS 139

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Table 3-9. Mean value tests of forecasting ability of market indicators. CHANGE equals 1 if the firm is downgraded from investment into non-investment grade by Moodys during quarter t; it equals 0 otherwise. DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. We test the hypothesis that the mean value of each market indicator is different for BHCs experiencing a material change in condition versus those that do not. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. One Quarter PriorTwo VariableCHANGEMeanStdDevMeanStdDevMeanStdDevMeanStdDevDD_EIAV 04.011.384.021.384.011.384.001.38 12.761.332.661.273.600.793.971.04Diff (0-1)1.25***1.36***0.410.03DD_DIAV 02.370.612.370.612.360.612.350.61 11.610.341.650.211.860.262.110.56Diff (0-1)0.76***0.72***0.51***0.25DD_EDIAV 02.480.732.480.732.470.732.470.73 11.680.351.700.211.950.242.341.02Diff (0-1)0.81***0.78***0.53***0.13EV 00.310.130.310.130.310.130.320.13 10.490.190.500.180.340.080.310.09Diff (0-1)-0.18***-0.19***-0.030.01YS 00.010.010.010.010.010.010.010.01 10.040.020.030.020.020.010.010.01Diff (0-1)-0.03***-0.02***-0.01***0.00Nobs 01,897 1,823 1,752 1,683 115 16 15 14 Quarters PriorThree Quarters PriorFour Quarters Prior 140

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141 Table 3-10. Logit analysis of material changes in firm condition. We estimate ktiktiktitiSIZERTGMktIndgChange ,3,2,10,1Pr via logistic regression for the samples of 1,912, 1,839, and 1,767 observations respectively 1, 2, or 3 quarters prior to the event during 1986-1999. The dependent variable CHANGE equals 1 if the firm is downgraded from investment to non-investment grade by Moodys during quarter t; it equals 0 otherwise. DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. DD_EIAV-0.80***-0.07(0.28)(0.25)DD_DIAV-6.84***-6.67***(1.25)(1.36)DD_EDIAV-6.52***(1.17)EV5.35***0.83(1.40)(2.26)YS95.97***92.05***(16.10)(19.20) R 2 0.0230.0440.0440.0240.0410.0440.041DD_EIAV-0.82***-0.32(0.24)(0.25)DD_DIAV-4.96***-4.42***(0.87)(0.94)DD_EDIAV-5.00***(0.84)EV4.88***2.57(1.18)(1.63)YS69.41***57.62***(12.48)(14.33) R 2 0.0250.0410.0430.0260.0340.0420.035DD_EIAV-0.100.04(0.23)(0.20)DD_DIAV-2.64***-2.69***(0.88)(0.91)DD_EDIAV-2.55***(0.87)EV0.09-2.19(2.14)(2.72)YS33.38**42.89**(16.82)(19.71) R 2 0.0040.0100.0100.0040.0060.0100.006Panel B: Two Quarters PriorPanel C: Three Quarters PriorModel 5Model 6Model 7Panel A: One Quarter PriorModel 1Model 2Model 3Model 4

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142 Table 3-11. Analysis of asset quality changes (LLAGL). We estimate via OLS for the sample of 555 and 1,000 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable dAQ is the change in asset quality as proxied by LLAGL. LLAGL is the ratio of loan loss allowances to gross loans. MktInd is one of the following equity (EInd), debt (DInd), or equity-and-debt (EDInd) indicators of risk: DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively; EV is the annualized daily equity volatility over the quarter; YS is the credit spread of the firms most recently issued subordinated debt. A change in variable X is denoted by dX. Control variables are excluded from the table for ease of exposition. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Fa is the F-statistic testing that all MktInd are jointly zero (df=4 or 8, [nobs-ncoeff]). Fb is the F-statistic for the hypothesis that all equity indicators are jointly zero (df=4, [nobs=ncoff]). Fc is the F-statistics for testing that all debt indicators are jointly zero (df=4, [nobs-ncoeff]). tititikktiktikktiktiSIZEAQdAQMktInddMktInddAQ,,54,431,,34,231,,10, dEInd_lag1-0.00020.0014-0.00020.0005(0.000)(0.002)(0.000)(0.002)dEInd_lag20.0003-0.00050.0003-0.0015(0.000)(0.002)(0.000)(0.002)dEInd_lag30.0002-0.00070.0002-0.0018(0.000)(0.003)(0.000)(0.003)EInd_lag40.0001-0.00270.0001-0.0035(0.000)(0.003)(0.000)(0.003)dDInd_lag1-0.00030.0473-0.00040.0455(0.001)(0.040)(0.001)(0.041)dDInd_lag2-0.00050.0448-0.00040.0441(0.001)(0.052)(0.001)(0.053)dDInd_lag3-0.00090.0675-0.00080.0649(0.001)(0.057)(0.001)(0.059)DInd_lag4-0.00020.0127-0.00020.0209(0.000)(0.034)(0.000)(0.035)dEDInd_lag1-0.0003(0.001)dEDInd_lag2-0.0004(0.001)dEDInd_lag3-0.0006(0.001)EDInd_lag40.0000(0.000)R 2 0.0340.0260.0260.0280.0300.0290.027R 2 (MktInd)0.003-0.004-0.004-0.002-0.001-0.001-0.004Fa1.480.390.390.670.880.910.72F b 0.340.76Fc1.420.55Pre-FDICIA Period (Jun 1986 Jan 1991)YSDD_EIAV and DD_DIAVEV and YSDD_EIAVDD_DIAVDD_EDIAVEV

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143 Table 3-11. Continued dEInd_lag1-0.0003***0.0067***-0.0003***0.0051***(0.000)(0.001)(0.000)(0.001)dEInd_lag2-0.0004***0.0083***-0.0004***0.0076***(0.000)(0.001)(0.000)(0.001)dEInd_lag3-0.0005***0.0078***-0.0005***0.0085***(0.000)(0.001)(0.000)(0.001)EInd_lag4-0.0004***0.0053***-0.0004***0.0067***(0.000)(0.001)(0.000)(0.001)dDInd_lag1-0.0035***0.0979***-0.0036***0.0757***(0.001)(0.014)(0.001)(0.015)dDInd_lag2-0.0029***0.0677***-0.0027***0.0278*(0.001)(0.014)(0.001)(0.015)dDInd_lag3-0.0016**0.0539***-0.0013**0.0050(0.001)(0.015)(0.001)(0.016)DInd_lag4-0.0014***0.0403***-0.0011***-0.0056(0.000)(0.011)(0.000)(0.013)dEDInd_lag1-0.0043***(0.001)dEDInd_lag2-0.0032***(0.001)dEDInd_lag3-0.0022***(0.001)EDInd_lag4-0.0018***(0.000)R 2 0.1280.1480.1630.1750.1560.1710.201R 2 (MktInd)0.0230.0440.0580.0700.0520.0670.096Fa6.95***12.42***16.41***19.90***14.60***9.91***14.38***F b 12.51***8.21***Fc7.05***13.34***DD_EIAVDD_EIAV and DD_DIAVEV and YSPost-FDICIA Period (Jan 1993 Dec 1999)DD_DIAVDD_EDIAVEVYS

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144 Table 3-12. Analysis of asset quality changes (BADLOANS). We estimate via OLS for the sample of 555 and 1,000 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable dAQ is the change in asset quality as proxied by BADLOANS. This is the sum of non-performing loans, past due loans, and other real estate owned as a proportion of gross loans. MktInd is one of the following equity (EInd), debt (DInd), or equity-and-debt (EDInd) indicators of risk: DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively; EV is the annualized daily equity volatility over the quarter; YS is the credit spread of the firms most recently issued subordinated debt. A change in variable X is denoted by dX. Control variables are excluded from the table for ease of exposition. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Fa is the F-statistic testing that all MktInd are jointly zero (df=4 or 8, [nobs-ncoeff]). Fb is the F-statistic for the hypothesis that all equity indicators are jointly zero (df=4, [nobs=ncoff]). Fc is the F-statistics for testing that all debt indicators are jointly zero (df=4, [nobs-ncoeff]). tititikktiktikktiktiSIZEAQdAQMktInddMktInddAQ,,54,431,,34,231,,10, dEInd_lag1-0.042***0.438***-0.043***0.232(0.016)(0.142)(0.016)(0.142)dEInd_lag2-0.040**0.416**-0.041**0.175(0.018)(0.180)(0.018)(0.177)dEInd_lag3-0.066***0.496**-0.072***0.331(0.021)(0.214)(0.020)(0.210)EInd_lag4-0.0310.220-0.042**0.110(0.020)(0.241)(0.020)(0.235)dDInd_lag1-0.160***19.481***-0.176***18.834***(0.052)(3.044)(0.052)(3.100)dDInd_lag2-0.163***14.212***-0.169***13.518***(0.055)(3.980)(0.055)(4.036)dDInd_lag3-0.188***11.873***-0.178***9.267**(0.055)(4.285)(0.055)(4.425)DInd_lag4-0.105***7.627***-0.106***7.402***(0.028)(2.704)(0.028)(2.726)dEDInd_lag1-0.112***(0.041)dEDInd_lag2-0.103**(0.044)dEDInd_lag3-0.147***(0.042)EDInd_lag4-0.092***(0.023)R20.0510.0630.0620.0490.1230.0840.125R2 (MktInd)0.0190.0310.0300.0170.0910.0520.094Fa3.76***5.50***5.31***3.42***15.07***4.83***8.27***Fb5.77***12.82***Fc4.04***1.42Pre-FDICIA Period (Jun 1986 Jan 1991)DD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAV and DD_DIAVEV and YS

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145 Table 3-12. Continued dEInd_lag1-0.047***0.877***-0.048***0.846***(0.014)(0.163)(0.014)(0.172)dEInd_lag2-0.0210.779***-0.0250.873***(0.017)(0.187)(0.017)(0.203)dEInd_lag3-0.055***0.934***-0.055***1.277***(0.018)(0.206)(0.018)(0.228)EInd_lag4-0.0250.482**-0.0270.851***(0.017)(0.198)(0.017)(0.229)dDInd_lag1-0.196**6.484***-0.244***3.589(0.092)(2.332)(0.093)(2.391)dDInd_lag2-0.411***4.882**-0.377***0.938(0.093)(2.245)(0.093)(2.384)dDInd_lag3-0.083-0.304-0.107-6.333**(0.100)(2.442)(0.099)(2.607)DInd_lag4-0.029-1.118-0.026-5.604***(0.068)(1.886)(0.068)(2.130)dEDInd_lag1-0.342***(0.100)dEDInd_lag2-0.415***(0.099)dEDInd_lag3-0.175(0.107)EDInd_lag4-0.062(0.076)R20.2250.2290.2320.2410.2230.2410.253R2 (MktInd)0.0130.0170.0200.0290.0110.0290.041Fa4.74***5.74***6.66***9.44***3.99***5.18***7.08***Fb5.52***4.57***Fc4.52***10.00***Post-FDICIA Period (Jan 1993 Dec 1999)DD_EIAVDD_EIAV and DD_DIAVEV and YSDD_DIAVDD_EDIAVEVYS

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146 Table 3-13. Logit analysis of SCORE changes. We estimate the logit model for the sample of 555 and 1,000 firm-quarters for the pre-FDICIA and post-FDICIA periods respectively. The dependent variable CHG equals 1 if a firms SCORE decreases, 0 if it remains the same, and -1 if it increases. SCORE is a composite index of the firms financial health. It is a number between 5 and 20 with a lower number indicating a healthier firm. MktInd is one of the following equity (EInd), debt (DInd), or equity-and-debt (EDInd) indicators of risk: DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively; EV is the annualized daily equity volatility over the quarter; YS is the credit spread of the firms most recently issued subordinated debt. A change in variable X is denoted by dX. Control variables are excluded from the table for ease of exposition. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively. Wa is the Wald statistic testing that all MktInd are jointly zero (df=4 or 8, [nobs-ncoeff]). Wb is the Wald statistic testing that all EInd are jointly zero (df=4, [nobs=ncoff]). Wc is the Wald statistics testing that all DInd are jointly zero (df=4, [nobs-ncoeff]). )(1Pr,54,431,,34,231,,10,titikktiktikktiktiSIZESCOREdSCOREMktInddMktIndgCHG dEInd_lag10.30***-2.97***0.32***-2.92***0.070.600.070.62dEInd_lag2-0.13*0.32-0.120.560.080.780.080.82dEInd_lag3-0.050.94-0.041.040.080.880.080.92Eind_lag40.020.630.030.590.080.970.081.00dDInd_lag10.21-25.59**0.33-15.230.2112.170.2112.54dDInd_lag20.34-15.970.32-27.07*0.2215.550.2216.25dDInd_lag30.20-14.790.07-2.250.2217.270.2218.52Dind_lag40.01-6.510.01-6.530.1110.770.1111.10dEDInd_lag10.230.16dEDInd_lag20.240.17dEDInd_lag30.080.16EDind_lag40.010.09R20.170.100.110.180.110.170.18R20.070.000.010.080.010.070.08Wa37.19***2.923.0639.19***6.0840.85***43.63***Wb3.594.21Wc38.09***37.95***Pre-FDICIA Period (Jun 1986 Jan 1991)YSDD_EIAV and DD_DIAVEV and YSDD_EIAVDD_DIAVDD_EDIAVEV

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147 Table 3-13. Continued dEInd_lag10.14*-1.63*0.12-0.150.070.840.080.93dEInd_lag20.02-3.25***0.00-1.370.080.910.091.04dEInd_lag30.17*-5.04***0.15*-4.36***0.090.980.091.15Eind_lag4-0.080.47-0.09-0.930.080.820.081.11dDInd_lag11.26***-35.89***1.37***-33.87***0.4811.790.4812.82dDInd_lag23.30***-68.81***3.15***-59.00***0.4912.360.5013.68dDInd_lag32.39***-61.11***2.62***-37.94**0.5314.010.5515.34Dind_lag40.399.780.4918.250.339.740.3412.34dEDInd_lag11.43***0.52dEDInd_lag23.15***0.52dEDInd_lag32.66***0.57EDind_lag40.150.34R20.340.370.370.360.380.380.39R20.010.040.040.030.040.050.06Wa15.35***56.24***56.69***42.00***52.14***66.94***68.27***Wb54.01***31.40***Wc13.65***18.56***DD_EIAV and DD_DIAVEV and YSPost-FDICIA Period (Jan 1993 Dec 1999)DD_DIAVDD_EDIAVEVYSDD_EIAV

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Table 3-14. Sensitivity of summary statistics to alternative input assumptions. EIAV is the equity-implied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. Implied asset volatilities are reported in percent per year. V_EIAV, V_DIAV, and V_EDIAV are the corresponding estimates of the market value of assets in billion dollars. DD_EIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default measures. Time to ResolutionDefault Point MedianMeanMedianMeanMedianMeanMedianMeanMedianMeanMedianMeanMedianMeanMedianMeanMedianMeanV_EIAV17.1631.6015.0127.1022.2840.2323.0941.1123.7642.2623.7642.2623.8242.3623.3741.9027.5244.85V_DIAV17.9332.7016.2229.0120.5738.1621.5939.3422.9440.8122.9940.8822.9140.7923.5242.2127.1343.68V_EDIAV17.4931.7815.4327.8421.3438.9122.1840.2423.7542.2623.7342.2523.8142.3523.4141.9328.0545.29EIAV3.955.124.846.722.813.182.733.102.663.022.663.022.653.012.683.052.683.04DIAV3.693.984.244.622.993.352.903.242.843.162.843.162.853.182.712.962.883.22EDIAV3.513.583.793.893.874.133.904.124.334.504.404.504.524.742.582.674.554.73DD_EIAV1.501.511.171.161.981.842.672.633.853.903.853.903.853.903.853.903.873.92DD_DIAV1.721.831.601.741.191.141.691.712.252.352.252.372.132.204.113.662.242.20DD_EDIAV1.711.871.591.751.551.421.951.882.332.462.332.502.212.314.824.272.322.27Nobs2,0301,9701,8321,9192,0592,0602,0602,0571,608Issuer YieldTax AdjustmentWeighted Average Duration of Traded DebtWeighted Average Maturity of Traded Debt95% of Total Debt97% of Total DebtCredit Spreads Calculated from Non Callable Bonds OnlyWeighted Average Issue YieldsLargest Issue YieldNoneAverage Yield on Moody's AAA-rated Bonds 148

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149 Table 3-15. Analysis of asset quality measures under alternative assumptions. We estimate via two-way fixed effects for the sample of 860 and 1,200 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable is one of the five market indicators: DD_EIAV, DD_DIAV, DD_EDIAV, EV, or YS. DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. EV is the annualized daily equity volatility over the quarter. YS is the credit spread of the firms most recently issued subordinated debt. ROA is the ratio of net income (loss) to total assets. OREOGL is the ratio of other real estate owned to gross loans. NALGL is the ratio of non-accruing loans to gross loans. PDL90GL is the ratio of loans past due more than 90 days to gross loans. ROALEV, OREOGLLEV, NALGLLEV, and PDL90GLLEV are the last four variables interacted with firm leverage. LEV is the ratio of the market value of equity to the book value of liabilities. SIZE is the log of the market value of assets. Each models fit is indicated by the R2. R2 is the contribution of all lags of DD and dDD to the pseudo R2 of a model including all but these variables. ititmmitmitSizetyMeasuresAssetQualiMktInd210 DD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAVDD_DIAVDD_EDIAVEVYSBase CaseR20.620.760.720.720.770.570.730.750.690.72Time to Resolution: Weighted Average Duration of Traded DebtR20.680.720.710.740.770.560.730.730.690.72Time to Resolution: Weighted Average Maturity of Traded DebtR20.710.720.670.720.800.590.740.750.680.72Default Point: 95% of Total DebtR20.760.530.880.720.790.710.750.900.660.72Default Point: 97% of Total DebtR20.700.500.830.740.750.630.750.860.660.72Issuer Yield: Weighted Average Issue YieldsR20.620.770.720.730.790.590.750.730.700.73Issuer Yield: Largest Issue YieldR20.620.610.670.730.760.590.720.690.700.71Tax Adjustment: NoneR20.620.760.730.730.780.590.750.780.700.71Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.620.670.620.730.670.590.680.560.700.66Non-callable Bonds OnlyR20.690.770.730.780.790.590.770.800.710.76Pre-FDICIA Period (Jun 1986 Jan 1991)Post-FDICIA Period (Jan 1993 Dec 1999)

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150 Table 3-16. Analysis of asset quality changes. We estimate via OLS for the sample of 555 and 1,000 firm-quarters for the pre-FDICIA and post-FDICIA period respectively. The dependent variable dAQ is the change in asset quality as proxied by BADLOANS. This is the sum of non-performing loans, past due loans, and other real estate owned as a proportion of gross loans. MktInd is one of the following equity (EInd), debt (DInd), or equity-and-debt (EDInd) indicators of risk: DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively; EV is the annualized daily equity volatility over the quarter; YS is the credit spread of the firms most recently issued subordinated debt. A change in variable X is denoted by dX. The models fit is indicated by the pseudo R2. R2 is the contribution of all lags of DD and dDD to the pseudo R2 of a model including all but these variables. tititikktiktikktiktiSIZEAQdAQMktInddMktInddAQ,,54,431,,34,231,,10, DD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAV and DD_DIAVEV and YSBase CaseR20.0510.0630.0620.0490.1230.0840.125R20.0190.0310.0300.0170.0910.0520.094Time to Resolution: Weighted Average Duration of Traded DebtR20.0550.0700.0690.0800.1940.0850.201R20.0160.0310.0310.0420.1550.0460.163Time to Resolution: Weighted Average Maturity of Traded DebtR20.0760.0660.0660.1030.2270.0990.239R20.0320.0230.0220.0590.1830.0550.196Default Point: 95% of Total DebtR20.0570.0200.1040.0430.0890.0770.104R20.0370.0000.0830.0230.0680.0570.084Default Point: 97% of Total DebtR20.1230.0870.1830.1290.3000.1370.307R20.0370.0010.0970.0430.2140.0510.222Issuer Yield: Weighted Average Issue YieldsR20.0510.0600.0550.0490.1420.0750.142R20.0190.0280.0230.0170.1100.0430.111Issuer Yield: Largest Issue YieldR20.0560.0450.0510.0540.1280.0660.133R20.0210.0100.0160.0180.0930.0310.098Tax Adjustment: NoneR20.0510.0590.0610.0490.1260.0810.129R20.0190.0280.0290.0170.0940.0490.097Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.0940.1070.1090.1020.1260.1360.147R20.0280.0420.0430.0360.0600.0700.081Non-callable Bonds OnlyR20.0630.0450.0420.0600.0630.0890.083R20.0490.0310.0280.0460.0490.0750.068Pre-FDICIA Period (Jun 1986 Jan 1991)

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151 Table 3-16. Continued DD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAV and DD_DIAVEV and YSBase CaseR20.2250.2290.2320.2410.2230.2410.253R20.0130.0170.0200.0290.0110.0290.041Time to Resolution: Weighted Average Duration of Traded DebtR20.2430.2420.2420.2560.2360.2520.262R20.0110.0100.0100.0240.0040.0200.030Time to Resolution: Weighted Average Maturity of Traded DebtR20.2150.2310.2310.2280.2450.2370.252R20.0130.0280.0290.0260.0420.0350.050Default Point: 95% of Total DebtR20.2620.2820.2910.2600.2670.2940.274R20.0090.0290.0380.0070.0140.0400.020Default Point: 97% of Total DebtR20.2460.2610.2670.2450.2410.2650.250R20.0110.0250.0320.0100.0050.0300.015Issuer Yield: Weighted Average Issue YieldsR20.2260.2290.2270.2420.2260.2400.255R20.0130.0160.0140.0290.0130.0280.042Issuer Yield: Largest Issue YieldR20.2250.2270.2230.2410.2190.2360.249R20.0130.0140.0110.0290.0070.0240.036Tax Adjustment: NoneR20.2250.2290.2330.2410.2230.2410.253R20.0130.0170.0210.0290.0100.0290.040Tax Adjustment: Average Yield on Moody's AAA-rated BondsR20.2260.2300.2370.2410.2240.2390.250R20.0130.0170.0250.0290.0120.0260.037Non-callable Bonds OnlyR20.2360.2460.2580.2610.2480.2650.278R20.0170.0270.0390.0420.0290.0460.060Post-FDICIA Period (Jan 1993 Dec 1999)

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Table 3-17. Logit analysis of SCORE changes. We estimate the logit model 33for the sample of 555 and 1,000 firm-quarters for the pre-FDICIA and post-FDICIA periods respectively. The dependent variable CHG equals 1 if the firms SCORE decreases, 0 if it remains the same, and -1 if it increases. SCORE is a composite index of the firms financial condition based on its capitalization, asset quality, management, earnings, and liquidity relative to other firms. It is a variable between 5 and 20 where a lower score indicates a healthier firm. MktInd is one of the following: DD_EIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively; EV is the annualized daily equity volatility over the quarter; YS is the credit spread of the firms most recently issued subordinated debt. A change in variable X is denoted by dX. Control variables are excluded from the table for ease of exposition. )(1Pr,54,41,,34,21,,10,titikktiktikktiktiSIZESCOREdSCOREMktInddMktIndgCHG DD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAV and DD_DIAVEV and YSDD_EIAVDD_DIAVDD_EDIAVEVYSDD_EIAV and DD_DIAVEV and YSBase CasePseudo R20.1670.1050.1050.1760.1090.1720.1820.3430.3740.3750.3640.3760.3830.388Time to Resolution: Weighted Average Duration of Traded DebtPseudo R20.1500.0980.0990.1630.1180.1580.1780.3450.3720.3730.3590.3710.3800.382Time to Resolution: Weighted Average Maturity of Traded DebtPseudo R20.1320.1010.1050.1450.1220.1360.1610.3570.3870.3880.3700.3840.3970.394Default Point: 95% of Total DebtPseudo R20.2140.1390.1590.2160.1310.2170.2290.3920.4000.4150.3960.3970.4160.407Default Point: 97% of Total DebtPseudo R20.2110.1220.1380.2040.1400.2140.2290.3930.3990.4060.3970.3940.4150.404Issuer Yield: Weighted Average Issue YieldsPseudo R20.1670.1100.1060.1760.1040.1740.1780.3440.3720.3700.3640.3800.3820.392Issuer Yield: Largest Issue YieldPseudo R20.1670.1080.1080.1760.1060.1740.1810.3430.3630.3590.3640.3770.3740.390Tax Adjustment: NonePseudo R20.1670.1060.1040.1760.1080.1690.1820.3430.3780.3800.3640.3760.3890.389Tax Adjustment: Average Yield on Moody's AAA-rated BondsPseudo R20.1620.0990.1000.1730.0970.1680.1790.3430.3560.3550.3640.3610.3660.377Non-callable Bonds OnlyPseudo R20.1200.1000.1030.1140.0840.1480.1200.3860.4120.4100.3970.4140.4230.421Pre-FDICIA PeriodPost-FDICIA Period 152

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153 0.010.030.050.070.090.11198606198612198706198712198806198812198906198912199006199012199106199112199206199212199306199312199406199412199506199512199606199612199706199712199806199812199909 EIAV_Median DIAV_Median EDIAV_Median Figure 3-1. Median implied asset volatility (IAV) through time for 1986-1999

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154 1234 EIAV_MedianDIAV_MedianEDIAV_Median 00.010.020.030.040.050.060.07IAVAsset/Debt Ratio Figure 3-2. Median implied asset volatility (IAV) by asset-to-debt ratio quartile

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155 11.522.533.544.555.5198606198612198706198712198806198812198906198912199006199012199106199112199206199212199306199312199406199412199506199512199606199612199706199712199806199812199909 DD_EIAV_Median DD_DIAV_Median DD_EDIAV_Median Figure 3-3. Median distance to default (DD) through time 1986-1999

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CHAPTER 4 CONCLUSION In chapters 2 and 3 we examine the ability to extract risk information from the prices of a firms equity and debt claims. In each case we use contingent claim models for firm valuation to construct risk measures from equity prices, debt prices, and a combination of both. We provide empirical evidence on the relative accuracy and forecasting ability of these measures for industrial firms (chapter 2) and financial firms (chapter 3). We now conclude by reviewing the main results from each chapter. In chapter 2, we compare a number of methodologies for constructing implied asset volatility estimates for industrial firms. We review the empirical properties of these estimates, assess their value as measures of firm risk, and document two important findings. First, while different methodologies produce different estimates of implied asset volatility, the analysis in the chapter suggests that these differences are not crucial in explaining realized asset volatility, Moodys credit ratings, Altmans (1968) Z scores, and default occurrences. Within each test, some estimates outperform others. But no estimate is consistently best. This implies that firm risk can be extracted from equity and debt prices equally accurately, thus suggesting that researchers and practitioners can use high-frequency and high-quality equity prices without losing much important information. The second important finding in chapter 2 concerns the impact of alternative model assumptions on estimates of implied asset volatility for industrial firms. While the choice of using equity or debt prices to extract firm risk information appears to be inconsequential, we find that the choice of model parameters is quite important. We show 156

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157 that the manner in which we adjust yield spreads to account for embedded call options, and tax differences between corporate and Treasury securities has a significant effect on the level and rank ordering of firm risk measures. In addition, assumptions about the maturity of debt and debt priority structure seem to affect the forecasting ability of both implied-volatility and distance-to-default estimates. In contrast, using alternative assumptions about each firms default point and alternative approaches to aggregating issue yields into issuer yields appear immaterial. This finding underscores the importance of robustness checks whenever equity and debt valuation is based on contingent-claim pricing models. It also provides researcher and practitioners with some direction as to the model parameters most likely to influence results. The analysis in chapter 3 offers valuable contribution to the literature on market discipline of banks and BHCs. While previous studies have successfully argued that government oversight should be supplemented with risk information from bank equity and debt prices, they have offered little guidance as to which set of prices to use and how to use it. Chapter 3 addresses both questions. First, we compare bank risk information extracted from equity prices to that extracted from debt prices in explaining bank credit ratings, asset portfolio quality, and overall financial health. We observe that default risk measures constructed from debt prices generally outperform those constructed from equity prices. This finding is in contrast to the commonly held belief that debt prices are too noisy for the information in them to be useful. We further document that models using information from both equity and debt prices improve on the explanatory power of equity-only or debt-only models and that the magnitude of the improvement depends on how similar the information in equity and debt prices is.

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158 A second dimension of the analysis in chapter 3 evaluates whether regulators should use market information as contemporaneous affirmation, or as a forecasting tool of a BHCs financial condition. We conclude that market information can be valuable in as both. The contemporaneous analysis suggests that risk measures constructed from equity and/or debt prices are related to indicators of BHC risk. This implies that regulators can use market information to reinforce their assessment of a BHCs current state. In that sense, it can also be used as a tripwire for supervisory actions, which might help reduce regulatory forbearance (Evanoff and Wall 2000). Our forecasting analysis indicates that market indicators can also be used to predict material changes in the firms default probability and quarter-to-quarter changes in the firms asset-portfolio quality and overall condition. Thus, market information can be used as an early warning signal of changes in a BHCs condition.

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LIST OF REFERENCES Allen, L., J. Jagtiani, and J. Moser, 2001, Further Evidence on the Information Content of Bank Examination Ratings: A Study of BHC-to-FHC Conversion Applications, Journal of Financial Services Research, 20, 213-232. Altman, E., 1968, Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy, Journal of Finance, 23, 589-609. Altman, E., 1989, Measuring Corporate Bond Mortality and Performance, Journal of Finance, 44, 909-922. Altman, E., 1993, Corporate Financial Distress and Bankruptcy: A Complete Guide to Predicting and Avoiding Distress and Profiting from Bankruptcy (Wiley, New York). Avery, R., T. Belton, and M. Goldberg, 1988, Market Discipline in Regulating Bank Risk: New Evidence from Capital Markets, Journal of Money, Credit, and Banking, 20, 597-610. Begley, J., J. Ming, and S. Watts, 1997, Bankruptcy Classification Errors in the 1980s: An Empirical Analysis of Altman and Ohlsons models, Review of Accounting Studies, 1, 267-284. Berger, A. and S. Davies, 1998, The Information Content of Bank Examinations, Journal of Financial Services Research, 14, 117-144. Berger, A., S. Davies, and M. Flannery, 2000, Comparing Market and Regulatory Assessments of Bank Performance: Who Knows What When? Journal of Money, Credit and Banking, 32, 641-667. Black, F. and J. Cox, 1976, Valuing Corporate Securities: Some Effects of Bond Indenture Provision, Journal of Finance, 31, 351-367. Black, F. and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 637-654. Bliss, R., 2000, The Pitfalls in Inferring Risk from Financial Market Data, Working Paper WP 2000-24, Federal Reserve Bank of Chicago. Bohn, J., 2000, A Survey of Contingent-Claims Approaches to Risky Debt Valuation, Journal of Risk Finance, 1, 53-70. 159

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160 Brown, B. and S. Maital, 1981, What do Economists Know? An Empirical Study of Experts Expectations, Econometrica, 49, 491-504. Burnett, A., K. S. Rao, and S. Tinic, 1991, Subsidizing of S&Ls Under the Flat-Rate Deposit Insurance System: Some Empirical Estimates, Journal of Financial Services Research, 5, 143-164. Calomiris, C. and B. Wilson, 1998, Bank Capital and Portfolio Management: The 1930s 'Capital Crunch' and Scramble to Shed Risk", NBER Working Paper No. 6649. Canina, L. and S. Figlewski, 1993, The Informational Content of Implied Volatility, Review of Financial Studies, 6, 659-681. Chernov, M., 2001, Implied Volatilities as Forecasts of Future Volatility, Time-Varying Risk Premia, and Return Variability, Working Paper, Columbia Business School. Cochrane, J., 1991, Volatility Tests and Efficient Markets: A Review Essay, Journal of Monetary Economics, 27, 463-485. Cooper, I. and S. Davydenko, 2002, Using Yield Spreads to Estimate Expected Returns on Debt and Equity, Working Paper, London Business School. Covitz, D., D. Hancock, and M. Kwast, 2002, Market Discipline in Banking Reconsidered: The Roles of Deposit Insurance Reform, Funding Manager Decisions and Bond Market Liquidity, Working Paper 2002-46, Board of Governors FED. Crosbie, P. and J. Bohn, 2002, Modeling Default Risk, Default Risk White Papers, KMV. Curry, T., P. Elmer, and G. Fissel, 2001, Regulator Use of Market Data to Improve the Identification of Bank Financial Distress, Working paper 2001-01, FDIC. Dale, W., J. Davis, K. Lehn, D. Malmquist, and H. McMillan, 1991, Estimating the Value of Federal Deposit Insurance, Policy Report by the Office of Economic Analysis, Securities and Exchange Commission. Day, T. and C. Lewis, 1992, Stock Market Volatility and the Information Content of Stock Index Options, Journal of Econometrics, 52, 267-287. Delianedis, G. and R. Geske, 2001, The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity, and Market Factors, Working Paper 22-01, Anderson School, UCLA. Diba, B., C. Guo, and M. Schwartz, 1995, Equity as a Call Option on Assets Some Tests for Failed Banks, Economic Letters, 48, 389-397.

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161 Dichev, I., 1998, Is the Risk of Bankruptcy a Systematic Risk? Journal of Finance, 53, 1131-1147. Elmer, P. and G. Fissel, 2001, Forecasting Bank Failure from Momentum Patterns in Stock Returns, Working paper, FDIC. Elton, E., M. Gruber, D. Agrawal, and C. Mann, 2001, Explaining the Rate Spread on Corporate Bonds, Journal of Finance, 56, 247-277. Evanoff, Douglas D. and Larry D. Wall, 2000, Subordinated Debt and Bank Capital Reform, Working paper WP 2000-07, Federal Reserve Bank of Chicago. Evanoff, Douglas D. and Larry D. Wall, 2001, Sub-Debt Yield Spreads as Bank Risk Measures, Journal of Financial Services Research 20(2/3) 121-146. Evanoff, Douglas D. and Larry D. Wall, 2002, Measures of the Riskiness of Banking Organizations: Subordinated Debt Yields, Risk-based Capital, and Examination Ratings, Journal of Banking and Finance, 26, 989-1009. Fama, E. and K. French, 1997, Industry Costs of Equity, Journal of Financial Economics, 43, 153-193. Flannery, M., 1998, Using Market Information in Prudential Bank Supervision: A Review of the U.S. Empirical Evidence, Journal of Money, Credit, and Banking, 30, 273-305. Flannery, M. and S. Sorescu, 1996, Evidence of Bank Market Discipline in Subordinated Debenture Yields: 1983-1991, Journal of Finance, 51, 1347-1377. Frank, J. and W. Torous, 1989, An Empirical Investigation of U.S. Firms in Reorganization, Journal of Finance, 44, 747-769. Frank, M. and V. Goyal, 2003, Capital Structure Decisions, Working Paper, Hong Kong University of Science and Technology. Giliberto, M. and D. Ling, 1992, An Empirical Investigation of the Contingent-Claims Approach to Pricing Residential Mortgage Debt, Journal of American Real Estate and Urban Economics Association, 20, 393-426. Goh, J. and L. Ederington, 1993, Is a Bond Rating Downgrade Bad News, Good News, or No News for Stockholders? Journal of Finance, 48, 2001-2008. Gorton, G. and A. Santomero, 1990, Market Discipline and Bank Subordinated Debt, Journal of Money, Credit and Banking, 22, 119-128.

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162 Greenspan, A., 2001, "The Financial Safety Net," Remarks to the 37th Annual Conference on Bank Structure and Competition of the Federal Reserve Bank of Chicago, Chicago, IL (May 10), http://www.federalreserve.gov/boarddocs/speeches/2001/20010510/default.htm Gropp, R., J. Vesala, and G. Vulpes, 2002, Equity and Bond Market Signals as Leading Indicators of Bank Fragility, Working paper, European Central Bank. Gunther, J., M. Levonian, and R. Moore, 2001, Can the Stock Market Tell Bank Supervisors Anything They Dont Already Know? Economic and Financial Review, Second Quarter, 2-9. Hall, J., T. King, A. Meyer, and M. Vaughan, 2002, Did FDICIA Enhance Market Discipline? A Look at Evidence from the Jumbo-CD Market, Working paper 2002-2, Federal Reserve Bank of St. Louis. Hancock, D. and M. Kwast, 2001, Using Subordinated Debt to Monitor Bank Holding Companies: Is It Feasible? Journal of Financial Services Research, 20, 147-188. Hand, J., R. Holthausen, and R. Leftwich, 1992, The Effect of Bond Rating Agency Announcements on Bond and Stock Prices, Journal of Finance, 47, 733-752. Harvey, K., M. Collins, and J. Wansley, 2003, The Impact of Trust-Preferred Issuance on Bank Default Risk and Cash Flow: Evidence from the Debt and Equity Securities Markets, The Financial Review, 38, 235-256. Hassan, M. K., 1993, Capital Market Tests of Risk Exposure of Loan Sales Activities of Large U.S. Commercial Banks, Quarterly Journal of Business and Economics, 32, 27-43. Hassan, M. K., G. Karels, and M. Peterson, 1993, Off-Balance Sheet Activities and Bank Default-Risk Premia: A Comparison of Risk Measures, Journal of Economics and Finance, 17, 69-83. Huang, J. and M. Huang, 2002, How Much of the Corporate-Treasury Yield Spread is Due to Credit Risk?, Working Paper, Pennsylvania State University. Jagtiani, J., G. Kaufman, and C. Lemieux, 2002, The Effect of Credit Risk on Bank and Bank Holding Companies Bond Yield: Evidence from the Post-FDICIA Period, Journal of Financial Research, 25, 559-576. Jagtiani, J. and C. Lemieux, 2000, Stumbling Blocks to Increasing Market Discipline in the Banking Sector: A Note on Bond Pricing and Funding Strategy Prior to Failure, Working paper S&R-99-8R, Federal Reserve Bank of Chicago. Jagtiani, J. and C. Lemieux, 2001, Market Discipline Prior to Failure, Journal of Economics and Business, 53, 313-324.

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163 Jones, P., S. Mason, and E. Rosenfeld, 1983, Contingent Claim Analysis of Corporate Capital Structure: An Empirical Investigation, Journal of Finance, 39, 611-625. Jordan, J., J. Peek, and E. Rosengren, 2000, The Market Reaction to the Disclosure of Supervisory Actions: Implications for Bank Transparency, Journal of Financial Intermediation, 9, 298-319. Jorion, P., 1995, Predicting Volatility in the Foreign Exchange Market, Journal of Finance, 50, 507-528. King, K. and J. OBrien, 1991, Market-based Risk-adjusted Examination Schedules for Depository Institutions, Journal of Banking and Finance, 15, 955-974. Krainer, J. and J. Lopez, 2002, Incorporating Equity Market Information into Supervisory Monitoring Models, Working paper, Federal Reserve Bank of San Francisco. Krainer, J. and J. Lopez, 2003, Using Security Market Information for Supervisory Monitoring, Working paper, Federal Reserve Bank of San Francisco. Krishnan, C., P. Ritchken, and J. Thomson, 2003, Monitoring and Controlling Bank Risk: Does Risky Debt Serve Any Purpose? Working paper, Case Western Reserve University. Lamoureux, C. and W. Lastrapes, 1993, Forecasting Stock-return Variance: Toward an Understanding of Stochastic Implied Volatilities, Review of Financial Studies, 6, 293-326. LeRoy, S. and R. Porter, 1981, The Present-Value Relation: Tests Based on Implied Variance Bounds, Econometrica, 49, 555-574. Longhofer, S. and J. Santos, 2003, The Paradox of Priority, Financial Mangement, 32, 69-81. Longstaff, F., 2002, The Flight-to-quality Premium in U.S. Treasury Bond Prices, Working paper 9312, NBER. Longstaff, F. and E. Schwartz, 1995, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance, 50, 789-820. Marcus, A. and I. Shaked, 1984, The Valuation of FDIC Deposit Insurance Using Option-Pricing Estimates, Journal of Money, Credit and Banking, 16, 446-459. Merton, R., 1974, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, 449-470.

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164 Merton, R., 1977, An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory, Journal of Banking and Finance, 1, 3-11. Moodys Investors Service, Historical Default Rates for Corporate Bond Issuers, 1985-1999, January 2000. Morgan, D. and K. Stiroh, 2001, Market Discipline of Banks: The Asset Test, Journal of Financial Services Research 20(2/3) 195-208. Nunn, K., J. Hill, and T. Schneeweis, 1986, Corporate Bond Price Data Sources and Return/Risk Measurement, Journal of Financial and Quantitative Analysis, 21, 197-208. Pennacchi, G., 1987, A Reexamination of the Over(or Under-) Pricing of Deposit Insurance, Journal of Money, Credit, and Banking, 19, 291-312. Poteshman, A., 2000, Forecasting Future Variance from Option Prices, Working Paper, University of Illinois at Urbana-Champaign. Ronn, E. and A. Verma, 1986, Pricing Risk-Adjusted Deposit Insurance: An Option-Based Model, Journal of Finance, 41, 871-895. Santomero, A. and E. Chung, 1992, Evidence in Support of Broader Bank Powers, Financial Markets, Institutions and Instruments, 1, 1-68. Sarig, O. and A. Warga, 1989, Some Empirical Estimates of the Risk Structure of Interest Rates, Journal of Finance, 44, 1351-1360. Saunders, A., 2001, Comment on Evanoff and Wall/Hancock and Kwast, Journal of Financial Services Research 20(2/3) 189-194. Saunders, A., A. Srinivasa, and I. Walter, 2002, Price Formation in the OTC Corporate Bond Markets: A Field Study of the Inter-Dealer Market, Journal of Economics and Business, 54, 95-110. Schellhorn, C. and L. Spellman, 1996, Subordinated Debt Prices and Forward-Looking Estimates of Bank Asset Volatility, Journal of Economics and Business, 48, 337-347. Severn, A. and W. Stewart, 1992, The Corporate-Treasure Yield Spread and State Taxes, Journal of Economics and Business, 44, 161-166. Shiller, R., 1981, Do Stock Prices Move Too Much to Be Justified By Subsequent Changes in Dividends? American Economic Review, 71, 421-436. Shrieves, R. and D. Dahl, 1992, The Relationship Between Risk and Capital in Commercial Banks, Journal of Banking and Finance, 16, 439-457.

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165 Sironi, A., 2002, Strengthening Banks Market Discipline and Leveling the Playing Field: Are the Two Compatible? Journal of Banking and Finance, 26, 1065-1091. Theil, H., 1966, Applied Economic Forecasting, Chicago: Rand McNally. Warga, A. and I. Welch, 1993, Bondholder Losses in Leveraged Buyouts, Review of Financial Studies, 6, 959-982. Wei, D. and D. Guo, 1997, Pricing Risky Debt: An Empirical Comparison of the Longstaff and Schwartz and Merton Models, Journal of Fixed Income, 7, 8-28. West, K., 1988, Bubbles, Fads, and Stock Price Volatility Tests, Journal of Finance, 43, 639-660.

PAGE 177

BIOGRAPHICAL SKETCH Stanislava (Stas) Nikolova is originally from Varna, Bulgaria, and has been pursuing her education in the U.S. for the last 9 years. She began her studies at SUNY College at Geneseo, where she earned a B.S. in management science. She started working toward a Ph.D. in finance at Georgia State University, and then transferred to the University of Florida. Her research interests include management and regulation of financial institutions, commercial banking, corporate finance, and fixed-income securities. 166


Permanent Link: http://ufdc.ufl.edu/UFE0006122/00001

Material Information

Title: Two essays in financial economics : firm risk reflected in security prices
Physical Description: xi, 166 p.
Language: English
Creator: Joncheray, Thomas Julien ( Dissertant )
Duran, Randolph ( Thesis advisor )
Flannery, Mark ( Reviewer )
Karceski, Jason ( Reviewer )
Nimalendran, Nimal ( Reviewer )
Brown, Dave ( Reviewer )
Ai, Chunrong ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Chemistry thesis, Ph.D   ( local )
Dissertations, Academic -- UF -- Chemistry   ( local )

Notes

Abstract: The two-dimensional self-assembly at the air/water (A/W) interface of various block copolymers (dendrimer-like polystyrene-b-poly(tert-butylacrylate) (PS-b-PtBA) and polystyrene-b-poly(acrylic acid) (PS-b-PAA), linear and five-arm star poly(ethylene oxide)-b-poly(epsilon-caprolactone) (PEO-b-PCL), and three-arm star triethoxysilane-functionalized polybutadiene-b-poly(ethylene oxide) (PB(Si(OEt)3)-b-PEO)) was investigated through surface pressure measurements (isotherms, isobars, isochores, and compression-expansion hysteresis experiments) and atomic force microscopy (AFM) imaging. The PS-b-PtBA and the PS-b-PAA samples formed well-defined circular surface micelles at low surface pressures with low aggregation numbers (~ 3-5) compared to linear analogues before collapse of the PtBA chains and aqueous dissolution of the PAA segments take place around 24 and 5 mN/m, respectively. The linear PEO-b-PCL samples exhibited three phase transitions at 6.5, 10.5, and 13.5 mN/m corresponding respectively to PEO aqueous dissolution, PEO brush formation, and PCL crystallization. The two PEO phase transitions were not observed for the star-shaped PEO-b-PCL samples because of the negligible surface activity of the star-shaped PEO core compared to its linear analogue. The PB(Si(OEt)3)-b-PEO sample was cross-linked at the A/W interface by self-condensation of the pendant triethoxysilane groups under acidic conditions, which resulted in the formation of a two-dimensional PB network containing PEO pores with controllable sizes. With a view toward drug detoxification therapy, the encapsulation abilities of oil core-silica shell nanocapsules and molecularly imprinted nanoparticles were also investigated by electrochemical (cyclic voltammetry) and optical (fluorescence and UV-vis spectroscopies) techniques. The core-shell nanocapsules were shown to efficiently remove large amounts of organic molecules present in aqueous solutions, with the silica shell acting analogously to a chromatographing layer. The molecularly imprinted nanoparticles were prepared by the non-covalent approach and by miniemulsion polymerization. Binding studies on the molecularly imprinted nanoparticles in aqueous solutions under physiological pH conditions indicated that, in the absence of specific imprinting, the uptake of toxic drugs was mainly driven by non-specific hydrophobic interactions. As demonstrated with the use of the antidepressant amitriptyline, in the presence of specific imprinting the uptake significantly increased as the amount of specific binding sites was increased.
Subject: Afm, amitriptyline, binding, blodgett, bupivacaine, copolymer, crosslinking, detoxification, drug, encapsulation, hydrosilylation, imprinting, interface, isotherm, langmuir, microemulsion, miniemulsion, nanocapsule, nanoparticle, paa, pbut, pcl, peo, polymerization, ps, ptba, silica, triethoxysilane, uptake
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 184 pages.
General Note: Includes vita.
Thesis: Thesis (Ph.D.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0006122:00001

Permanent Link: http://ufdc.ufl.edu/UFE0006122/00001

Material Information

Title: Two essays in financial economics : firm risk reflected in security prices
Physical Description: xi, 166 p.
Language: English
Creator: Joncheray, Thomas Julien ( Dissertant )
Duran, Randolph ( Thesis advisor )
Flannery, Mark ( Reviewer )
Karceski, Jason ( Reviewer )
Nimalendran, Nimal ( Reviewer )
Brown, Dave ( Reviewer )
Ai, Chunrong ( Reviewer )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2006
Copyright Date: 2006

Subjects

Subjects / Keywords: Chemistry thesis, Ph.D   ( local )
Dissertations, Academic -- UF -- Chemistry   ( local )

Notes

Abstract: The two-dimensional self-assembly at the air/water (A/W) interface of various block copolymers (dendrimer-like polystyrene-b-poly(tert-butylacrylate) (PS-b-PtBA) and polystyrene-b-poly(acrylic acid) (PS-b-PAA), linear and five-arm star poly(ethylene oxide)-b-poly(epsilon-caprolactone) (PEO-b-PCL), and three-arm star triethoxysilane-functionalized polybutadiene-b-poly(ethylene oxide) (PB(Si(OEt)3)-b-PEO)) was investigated through surface pressure measurements (isotherms, isobars, isochores, and compression-expansion hysteresis experiments) and atomic force microscopy (AFM) imaging. The PS-b-PtBA and the PS-b-PAA samples formed well-defined circular surface micelles at low surface pressures with low aggregation numbers (~ 3-5) compared to linear analogues before collapse of the PtBA chains and aqueous dissolution of the PAA segments take place around 24 and 5 mN/m, respectively. The linear PEO-b-PCL samples exhibited three phase transitions at 6.5, 10.5, and 13.5 mN/m corresponding respectively to PEO aqueous dissolution, PEO brush formation, and PCL crystallization. The two PEO phase transitions were not observed for the star-shaped PEO-b-PCL samples because of the negligible surface activity of the star-shaped PEO core compared to its linear analogue. The PB(Si(OEt)3)-b-PEO sample was cross-linked at the A/W interface by self-condensation of the pendant triethoxysilane groups under acidic conditions, which resulted in the formation of a two-dimensional PB network containing PEO pores with controllable sizes. With a view toward drug detoxification therapy, the encapsulation abilities of oil core-silica shell nanocapsules and molecularly imprinted nanoparticles were also investigated by electrochemical (cyclic voltammetry) and optical (fluorescence and UV-vis spectroscopies) techniques. The core-shell nanocapsules were shown to efficiently remove large amounts of organic molecules present in aqueous solutions, with the silica shell acting analogously to a chromatographing layer. The molecularly imprinted nanoparticles were prepared by the non-covalent approach and by miniemulsion polymerization. Binding studies on the molecularly imprinted nanoparticles in aqueous solutions under physiological pH conditions indicated that, in the absence of specific imprinting, the uptake of toxic drugs was mainly driven by non-specific hydrophobic interactions. As demonstrated with the use of the antidepressant amitriptyline, in the presence of specific imprinting the uptake significantly increased as the amount of specific binding sites was increased.
Subject: Afm, amitriptyline, binding, blodgett, bupivacaine, copolymer, crosslinking, detoxification, drug, encapsulation, hydrosilylation, imprinting, interface, isotherm, langmuir, microemulsion, miniemulsion, nanocapsule, nanoparticle, paa, pbut, pcl, peo, polymerization, ps, ptba, silica, triethoxysilane, uptake
General Note: Title from title page of source document.
General Note: Document formatted into pages; contains 184 pages.
General Note: Includes vita.
Thesis: Thesis (Ph.D.)--University of Florida, 2006.
Bibliography: Includes bibliographical references.
General Note: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0006122:00001


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TWO ESSAYS IN FINANCIAL ECONOMICS: FIRM RISK REFLECTED IN
SECURITY PRICES















By

STANISLAVA M. NIKOLOVA


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Stanislava M. Nikolova



























I would like to dedicate this dissertation to my parents, Margarita and Marincho
Nikolovi; and my brother, Roumen Nikolov.















ACKNOWLEDGMENTS

I would like to thank my supervisory committee members Mark Flannery, Jason

Karceski, Nimal Nimalendran, Dave Brown, and Chunrong Ai. All of them have made

the completion of this dissertation possible. I am grateful for their willingness to review

my doctoral research and to provide me with constructive comments.

I am especially thankful to Mark Flannery, my supervisory committee chair, who

has been a major source of academic and personal encouragement. I thank him for his

guidance, patience, and friendship through the painful process of writing this dissertation.

His contagious enthusiasm for research, and willingness to share his knowledge and

experience, stimulated me and kept me going. I also thank Jason Karceski for being an

invaluable mentor throughout my graduate studies, gladly helping anytime I requested

professional or research advice.

I am grateful to all the people of the Finance Department: the professors who

guided me through coursework and supported my research; and the fellow graduate

students, too numerous to name but instrumental in my growth as a scholar.

Finally, I want to thank my friends, without whom I would have finished this

dissertation much sooner.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST O F TA BLE S ......... ................... ... ............ .............. .. vii

LIST OF FIGURES ......... ............................... ........ ............ ix

A B STR A C T ................................................. ..................................... .. x

CHAPTER

1 IN T R O D U C T IO N ............................................................................. .............. ...

2 INDUSTRIAL-FIRM RISK REFLECTED IN SECURITY PRICES:
PREDICTING CREDIT RISK WITH IMPLIED ASSET VOLATILITY
E S T IM A T E S ................................................................................................................5

2 .1. T he State of the L literature ...................................................................... ...............9
2.1.1. Contingent Claim V aluation M odels.................................. .....................9
2.1.2. Applications of Contingent Claim Valuation..................... ................ 11
2.2. Methodologies for Constructing Risk Measures from Market Prices ..............15
2.2.1. Methodologies for Calculating Implied Asset Value and Volatility .........15
2.2.2. Calculating Credit Risk Measures from Implied Asset Value and
V olatility ..................................................................... 17
2.2.3. M ethodology A ssum ptions.................................... ........................ 18
2.3. D ata Sources ........................ ......... ........................... 20
2.3.1. Bond Prices and Characteristics ..................................... ............... 20
2.3.1.1. Tax adjust ent ........ ..................................... ............. ..... 22
2.3.1.2. Call-option adjustm ent .............. ............ ............. .............. 24
2.3.1.3. Y ield spread aggregation...................................... ............... 25
2.3.2. Equity Prices and Characteristics ................................... ............... ..26
2 .3 .3 A accounting D ata .................................................... .................. .... 26
2 .3.4 D default D ata ............................. .......... ... ..................... 28
2 .4 Sum m ary Statistics .............................. ...................... ............ ................28
2.5. Realized A sset V olatility Tests.................................................................... .... ... 32
2.5.1. Correlation between Implied Asset Volatility and Realized Asset
V o latility ........................................... ........................ ................. 3 4
2.5.2. Is Implied Asset Volatility a Rational Forecast of Realized Asset
V olatility ? .................................................................... 3 5









2.5.3. Is Implied Asset Volatility a Better Forecast Than Historical Asset
V o latility ? .................................................................................. 3 8
2.6. Default and Default Probability Tests ...................................... ............... 39
2.6.1. Tests Based on the Occurrence of Default ..............................................40
2.6.2. Tests Based on Credit Ratings........................................ ............... 43
2.6.2. Tests Based on Altman's (1968) Z ...... .... ................................. .......49
2.7. Sensitivity of Estimates to Alternative Model Assumptions............. ...............54
2.7.1. Sum m ary Statistics ............................................................................... 54
2.7.2. Realized A sset V olatility Tests ...................................... ............... 55
2.7.3. Default and Default Probability Tests..................... .................. .......... 56
2.8. Sum m ary and C onclusion......................................................... ............... 58

3 BANK RISK REFLECTED IN SECURITY PRICES: EQUITY AND DEBT
MARKET INDICATORS OF BANK CONDITION.....................................87

3.1. Introduction .................. ........ .............. ........................... .. ................ ... ........ 87
3.2. Extracting Information about Firm Risk from Security Prices..........................94
3.2.1. Review of Contingent Claim Valuation Models .....................................94
3.2.2. Methodologies for Calculating Implied Asset Value and Volatility .........97
3.2.3. Distance-to-Default M easures................................. ............. ........... 101
3.3. D ata Sources .......... .. ......... ......... .. ................ .............. 102
3.3.1. Bond Prices and Characteristics ................................ ........103
3.3.1.1. Tax adjust ent ........................................... .... .. ........ ...... 105
3.3.1.2. Call-option adjustment ..... ...................... ............107
3.3.1.3. Y ield spread aggregation.................................... ............... 108
3.3.2. Equity Prices and Characteristics ................................ ................. 109
3 .3 .3 A ccou noting D ata ......... ................. ....................................... ...............109
3.4. Sample Selection and Summary Statistics................................. ... ................ 109
3.4. Relative Accuracy of Market Indicators of Risk ........................ ............13
3.5. Relative Forecasting Ability of Market Indicators of Risk .............................119
3.5.1. Forecasting Material Changes in Default Probability ...........................119
3.5.2. Forecasting Changes in Asset Quality............................. ... ................. 122
3.6. Sensitivity of Market Indicators to Alternative Model Assumptions................125
3 .7 C on clu sion s............................................................................... ............... 12 8

4 C O N C L U SIO N .......... .................................................................... ......... ... .... 156

LIST OF REFEREN CE S ......... .................................. ........................ ............... 159

B IO G R A PH ICA L SK ETCH ......... ................. ...................................... .....................166
















LIST OF TABLES

Table p

2 -1. Su m m ary statistics ............................................................................ ....................6 1

2-2. Sim ple and rank correlations ............................................. ............................. 62

2-3. Simple and rank correlations of implied and historical asset volatility with
realized asset v volatility ................................................................ .......... .... 63

2-4. Analysis of IAV and HAV forecasting properties..............................................64

2-5. Analysis of the relative informational content of IAV and HAV in forecasting
R A V ............................................................................. 6 5

2-6. Average DD statistics by default status............................... ... .......... ................. 67

2-7. Logit analysis of defaults....... ................................................ .................... 68

2-8. Median distance-to-default estimates by Moody's credit rating .............................69

2-9. Median changes in distance-to-default estimates by Moody's credit rating
change .............. ....... ........................................ .................. .. 70

2-10. Analysis of M oody's credit ratings ..................................................... ............... 71

2-11. Logit analysis of credit rating changes. .............. ......... ................... ............... 72

2-12. Average statistics by Z-score deciles................................. ......................... 73

2-13. A analysis of Z-score......... .......... ....................................................... .............. 74

2-14. A analysis of Z-score changes..................... ......... .......... ................. ............... 75

2-15. Sensitivity of summary statistics to alternative input assumptions ........................77

2-16. Analysis of IAV and HAV forecasting properties under alternative
assume options ........................................... ............................ 79

2-17. Logit analysis of defaults under alternative assumptions................. ................80

2-18. Analysis of Moody's credit ratings under alternative assumptions........................81









2-19. Analysis of credit rating changes under alternative assumptions..........................83

3-1. Sum m ary statistics ......................................................... ........... ..... 131

3-2. Sim ple and rank correlations ....................................................... ............... 132

3-3. Average market indicators of risk by Moody's credit rating..................................133

3-4. Average market indicators of risk by asset quality deciles .................................... 134

3-5. Average market indicators of risk by SCORE deciles ............................................ 135

3-6. Analysis of M oody's credit ratings ..................................................... ............... 136

3-7. A analysis of asset quality m measures ................................................ ........ ....... 137

3-8. Analysis of financial health SCORE .............................................. .................. 139

3-9. Mean value tests of forecasting ability of market indicators.............. ..................... 140

3-10. Logit analysis of material changes in firm condition. .........................................141

3-11. Analysis of asset quality changes (LLAGL) ....................................................142

3-12. Analysis of asset quality changes (BADLOANS)................................................144

3-13. Logit analysis of SCORE changes...................................... ........................ 146

3-14. Sensitivity of summary statistics to alternative input assumptions ........................148

3-15. Analysis of asset quality measures under alternative assumptions ......................149

3-16. Analysis of asset quality changes ..................................... ........... ............... 150

3-17. Logit analysis of SCORE changes...................................... ........................ 152
















LIST OF FIGURES


Figure page

2-1. M edian implied asset volatility over 1975-2001 ................................... ...............84

2-2. Median implied asset volatility by assets-to-debt ratio quartile ...............................85

2-3. Median distance to default over 1975-2001 .... ................................. 86

3-1. Median implied asset volatility (IAV) through time for 1986-1999 ....................153

3-2. Median implied asset volatility (IAV) by asset-to-debt ratio quartile...................154

3-3. Median distance to default (DD) through time 1986-1999 .................................... 155















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

TWO ESSAYS IN FINANCIAL ECONOMICS: FIRM RISK REFLECTED IN
SECURITY PRICES

By

Stanislava M. Nikolova

August 2004

Chair: Mark J. Flannery
Major Department: Finance, Insurance, and Real Estate

We examine the ability to extract risk information from the market prices of a

firm's securities. We use contingent claim models for firm valuation to construct risk

measures from equity prices, debt prices, and a combination of both. We provide

empirical evidence on the relative accuracy and forecasting ability of these measures for

industrial and financial firms.

We compare a number of methodologies for constructing implied asset volatility

estimates for industrial firms. We document that while different methodologies produce

different estimates, these differences are not crucial in explaining realized asset volatility,

Moody's credit ratings, Altman's Z scores, or default occurrences. Within each test, some

estimates outperform others, but no estimate is consistently best. We also show that,

while the choice of using equity or debt prices to extract firm risk information appears to

be inconsequential, the choice of model parameters is quite important. The manner in

which we adjust yield spreads to account for embedded call options, and tax differences









between corporate and Treasury securities as well as assumptions about the maturity of

debt and debt priority structure have a significant effect on the level and rank ordering of

firm risk measures.

Finally, we address the value of market information in the government oversight of

U.S. bank holding companies. We construct risk measures obtained from equity prices

alone, debt prices alone, and a combination of both. We observe that default risk

measures constructed from debt prices generally outperform those constructed from

equity prices in both contemporaneous and forecasting models. We further document that

models using information from both equity and debt prices improves on the explanatory

power of equity-only or debt-only models. Risk measures constructed from both equity

and debt prices are more closely related to bank credit ratings, asset-portfolio quality

indicators, and overall financial health. In addition, models using both equity and debt

price information can better predict material changes in the firm's default probability, and

quarter-to-quarter changes in the firm's asset-portfolio quality and overall condition.














CHAPTER 1
INTRODUCTION

The ability to accurately assess firm total asset risk has important applications in

many areas of finance risk management, bank lending practices, and regulation of

financial firms, among others. Thus, improving this ability can have important

implications for both finance researchers and practitioners. Although considerable

research effort has been put toward extracting firm risk information from either equity or

debt prices, to the best of our knowledge, no previous study has assessed the relative

informational quality of firm risk measures obtained from equity and debt prices; or the

impact of alternative model assumptions on the accuracy of these measures.

Financial theory suggests that in a world of complete and frictionless markets, both

equity and debt prices fully reflect the available information about a firm's condition. We

can value firm equity as a call option written on the market value of the firm's assets

(Black and Scholes 1973), and we can value risky debt as a riskless bond with an

embedded put (default) option (Merton 1974). Since both the equity-call and debt-put

options are written on the same underlying the firm's total assets they are functions of

the same set of variables: the market value of firm's assets, the volatility of the firm's

assets, the face value of debt, short-term interest rates, and the time to firm resolution

(debt maturity). A firm's credit risk should then be reflected in both equity and debt

prices, if markets were perfect. However, both equity and debt markets are characterized

by frictions. Which of these is characterized by fewer frictions, and which market's

frictions have lower impact on firm risk measures?









Debt markets are notorious for their lack of transparency and data availability.

While some corporate bonds trade on NYSE and Amex, they account for no more than

2% of market volume (Nunn et al. 1986). In addition, data quotes on OTC trades tend to

be diffused and based on matrix valuation rather than on actual trades. Warga and Welch

(1993) document that there are large disparities between matrix prices and dealer quotes.

Hancock and Kwast (2001) compare bond-price data from four sources and find that

correlation between bond yields from the different sources are in the 70-80% range. Even

if bond data were readily available, extracting firm risk information can be difficult. The

typical approach is to use debt prices, and calculate yield spreads as the difference

between a corporate yield and the yield on a Treasury security of the same maturity. This

spread is assumed to be a measure of credit risk. However, corporate yields will differ

from Treasury yields for a number of reasons other than credit risk (Delianedis and Geske

2001, Elton et al. 2001, Huang and Huang 2002). These include premiums for tax and

liquidity differences between corporate and Treasury securities, as well as compensation

for common bond-market factors. Yield spreads reflect not only default probability but

also expected losses, which requires an adjustment for recovery rates. Adjustments are

also needed for redemption and convertibility options, sinking fund provisions, and other

common bond features. Finally, yield spreads reflect differences in duration/convexity,

because cash flows of corporate and Treasury bonds are not perfectly matched. Despite

all of these shortcomings, yield spreads are commonly used as a proxy for firm risk.

In contrast to debt markets, equity markets are liquid and deep. Equity prices of

high frequency and quality can be easily obtained. Nevertheless, these markets are also

characterized by imperfections. Stock prices have been documented to overreact or









underreact to news, and have been shown to appear too volatile than a basic dividend

model would predict (Cochrane 1991, LeRoy and Porter 1981, Shiller 1981, West 1988).

Also, while yield spreads are easily interpreted as a measure of firm risk, there is no

analogous measure obtained from equity prices. Although some researchers have used

equity abnormal returns as a measure of firm risk, these are not immediately interpreted

as such: an increase in abnormal return might be the result of an increase in firm

profitability and/or increase in firm risk.

Since both equity and debt markets are characterized by frictions, and since both

equity and debt prices impose challenges in extracting information about firm risk,

whether one of these two information sources is better than the other is an empirical

question. We evaluate the relative informational content and accuracy of firm risk

measures obtained from equity or debt prices, and examine whether combining

information from both markets can produce more accurate risk measures.

We construct alternative estimates of asset volatility for a large set of U.S. firms,

and tests their value as forecasting and risk-valuation variables. Chapter 2 focuses on

industrial firms. We start by constructing asset volatility estimates for a set of 1,264 U.S.

industrial firms. We then test the information content of these estimates by using them to

predict defaults, credit-rating changes, and asset-return features. The result is specific

information on the value of alternative methods for estimating a firm's asset volatility.

Chapter 3 applies general insights from the industrial-firm analysis to the specific case of

assessing the condition of large financial firms. The value of market prices to assess bank

risk has become an important issue among banks and their government supervisors.

Banks also provide a valuable opportunity to expand our tests of asset volatility









estimates: their extensive supervisory reports provide homogeneous and detailed

financial information that can be used to help infer the properties of estimated asset

volatilities. We start by constructing three implied asset volatility estimates for a set of 84

U.S. bank holding companies (BHCs) over the period 1986-1999. These asset volatilities

are then combined with firm leverage to produce three versions of a single measure of

default risk distance to default (DD). We then investigate the contemporaneous

association among the three DD measures and other indicators of bank risk, and their

ability to foresee changes in bank risk. Results of this analysis will have important

implications for the regulation of large financial firms.














CHAPTER 2
INDUSTRIAL-FIRM RISK REFLECTED IN SECURITY PRICES: PREDICTING
CREDIT RISK WITH IMPLIED ASSET VOLATILITY ESTIMATES

The ability to accurately assess firm total asset risk has important applications in

many areas of finance claim pricing, risk management, and bank lending practices

among others. Thus, improving this ability can have important implications for both

finance researchers and practitioners. Although considerable research effort has been put

toward extracting firm risk information from either equity or debt prices, to the best of

our knowledge no previous study has assessed the relative informational quality of

industrial-firm risk measures obtained from equity and debt prices, and the impact of

alternative model assumptions on the accuracy of these measures.

Since both equity and debt markets are characterized by frictions, and since both

equity and debt prices impose challenges in extracting information about firm risk,

whether one of these two information sources is better than the other is an empirical

question. In this chapter, we evaluate the relative informational content and accuracy of

firm risk measures obtained from equity or debt prices, and examine whether combining

information from both price sources can produce more accurate risk measures. First,

using information from equity and/or debt prices, we construct four asset volatility

estimates for a set of 1,264 U.S. industrial firms over the period 1975-2001. Second, we

test the information content of these asset volatility estimates by using them to predict

defaults, credit ratings, Altman's (1968) Z scores, and asset-return features. The result is

specific information on the value of alternative methods for estimating a firm's total asset









volatility. Finally, we investigate the effect of alternative-model assumptions on the

quality of the firm risk measures.

Four estimates of asset volatility are analyzed in this chapter:

* Asset volatility obtained by de-levering equity-return volatility: simple implied
asset volatility (SIAV).

* Asset volatility implied by equity prices alone (EIAV).

* Asset volatility implied by debt prices alone (DIAV).

* Asset volatility implied by contemporaneous equity and debt prices (EDIAV).

Our analysis indicates that implied asset volatility estimates can differ dramatically

across methodologies. The low correlations of these estimates indicate that if they are to

be used as measures of total firm risk, then risk rankings will depend significantly on the

method used to calculate asset volatility. The correlations are even lower when asset

volatilities are combined with leverage, to produce a measure of each firm's distance to

default (DD) the number of standard deviations required to push a firm into insolvency.

These differences justify a closer look at the relative forecasting and risk-valuation ability

of the implied asset volatility and corresponding DD estimates.

Because implied asset volatility is the market's forecast of future volatility, the first

set of tests examines the association among the four implied asset volatility (IAV)

estimates and the subsequent realized volatility of total asset returns. We document that

all of the IAV estimates are biased forecasts of realized volatility. Furthermore, they do

not seem to incorporate all of the historical information available at the time they are

calculated. Fit statistics indicate that SIAV and EIAV tend to outperform the others when

it comes to forecasting realized volatility. Also, of the four IAV estimates, DIAV seems

to add the most new information to historical asset volatility in forecasting realized









volatility. This is contrary to the conventional assumption that debt prices are extremely

noisy.

The second set of tests examines if any of the four DD estimates successfully

distinguishes firms that default from those that do not. We find that a decrease in any of

the four DD estimates increases the probability that a firm will then default. We replicate

the tests for the subsample of non-investment grade firms, in an attempt to achieve a

more balanced sample. For non-investment grade firms, we find that only the DD

estimates based on EDIAV and SIAV help forecast default. Judging by the fit statistics of

the four models in both sets of tests, we conclude that the DD calculated from SIAV

contains the most relevant information about an upcoming default.

Because previous studies indicate that credit ratings can reliably proxy for default

probability, our third test investigates the relation between a firm's DD and its Moody's

credit rating. Although all four DD measures are statistically significant, the one based on

EIAV seems to be the most accurate, as indicated by its marginal contribution to the

model's fit. It is outperformed by DDEDIAV when we limit ourselves to the subset of

non-investment grade firms, and by DD_DIAV when we limit ourselves to the subset of

investment-grade firms. We also examine the ability of changes in DD to predict

credit-rating upgrades and downgrades. Although only some lags of the DD estimates are

statistically significant in explaining Moody's upgrades, all of them successfully predict

credit downgrades a decrease in DD increases the probability that a firm will be

downgraded. The DD calculated from EIAV seems to be the most accurate predictor, as

judged by the model's fit statistics.









Finally, we replicate the credit-rating tests above using another proxy for default

probability Altman's (1968) Z score. We find that variations in DD successfully explain

variations in Z but only for low-Z (high default probability) firms. This is consistent with

Dichev (1998) who shows that Z is a better measure of default risk when the ex ante

default probability is high. Of the four DD estimates, those calculated from EIAV and

DIAV seem to add the most explanatory power to a base model that includes only control

variables. We analyze the relationship between changes in DD and changes in Z

separately for negative and positive changes, analogously to our separate analysis of

rating downgrades and upgrades. Consistent with our rating-change results, we find that

lagged changes in DD have more explanatory power for negative Z-score changes than

for positive ones. The fit statistics of these models indicate that DD adds little-to-no new

information to lagged Z changes, and that the most new information is added by the DD

estimate calculated from EIAV.

In summary, different methodologies produce different estimates of implied asset

volatility. These differences are even larger when compounded by leverage differences to

produce DD measures. However, the analysis in this chapter suggests that these

differences are not crucial in explaining realized asset volatility, Moody's credit ratings,

Altman's (1968) Z scores, or default occurrences. Within each test, some IAV and DD

measures outperform others, but no estimate is consistently "best." This implies that firm

risk can be extracted from equity and debt prices equally accurately, thus suggesting that

researchers and practitioners can use high-frequency and high-quality equity prices

without losing much important information.









While the choice between equity and debt prices as a source of firm risk

information appears to be inconsequential, the choice of contingent-claim-model

assumptions does not. The informational content of risk measures is significantly affected

by tax and call-option adjustments, as well as time-to-firm-resolution and debt-priority-

structure assumptions. This provides an important checklist of robustness tests for those

conducting empirical research using contingent-claim pricing models.

2.1. The State of the Literature

2.1.1. Contingent Claim Valuation Models

Black and Scholes (1973) were the first to recognize that their approach to valuing

exchange-traded options could also be used to value firm equity. With limited liability the

payoff to equityholders is equivalent to the payoff of a call option written on the firm's

assets with an exercise price equal to the face value of the firm's debt. Consider a non-

dividend paying firm with homogeneous zero-coupon debt that matures at time T.

Assume that the market value of the firm's assets follows a continuous lognormal

diffusion process with constant variance. Then the current equity value of the firm is

E = VN(d,) De R N(d2) (2-1)
where
In(V/D)+ (Rf +0.502)c
1 VT
d2 = d -ol.V
E is the current market value of the firm's equity,
V is the current market value of the firm's assets,
D is the face value of the firm's debt,
o is the instantaneous standard deviation of asset returns,
z is the time remaining to maturity,
Rf is the risk-free rate over z,
N(x) is the cumulative standard normal distribution of x.









Merton (1974) uses the same insight to derive the value of a firm's risky debt. He

demonstrates that under limited liability, the payoff to debtholders is equivalent to the

payoff to holders of a portfolio consisting of riskless debt with the same characteristics as

the risky debt, and a short put option written on the firm's assets with an exercise price

equal to the face value of debt. Re-arranging the formula used by Merton (1974) allows

us to express the credit-risk premium as the spread between the yield on risky debt, R,

and the yield on risk-free debt with otherwise the same characteristics:


R-R =-In V eRf N(- d)+N(d2) / r (2-2)

One of the basic assumptions underlying Merton's (1974) derivation is that the firm

issues a single homogenous class of debt. In reality, the characteristics of debt are highly

variable, which makes his model intuitively useful, but not precisely applicable to risky

debt valuation.

The single-class debt assumption is relaxed by Black and Cox (1976), who analyze

the debt-valuation effect of having multiple classes of debtholders. Consider a firm

financed by equity and two types of debt differentiated by their priority. Although the

probability of default is the same for senior and subordinated debtholders, their expected

losses differ; and that is reflected in the valuation of their claims. Assume that all of the

firm's debt matures on the same date. If at maturity the value of the firm is less than D,

(the face value of senior debt) then senior debtholders receive the value of the firm, while

subordinated debtholders (along with equityholders) receive nothing. If at maturity the

value of the firm is greater than D, but less than the face value of all debt (D, +D,) then

senior debtholders get paid in full, subordinated debtholders receive the residual firm

value, and equityholders receive nothing. Note that the payoff to equityholders is the









same, whether there is one or two classes of debtholders if the value of the firm at

maturity is higher than the face value of all debt, they receive the residual after debt

payments are made; and if the value of the firm at maturity is lower than the face value of

all debt, they receive nothing. Thus, while knowing the precise breakdown of debt into

priority classes is crucial for debt valuation, it does not affect the valuation of equity.

Following Black and Cox (1976), the value of a firm's subordinated debt is given

by

x2 = V[N(d,) N(d,) De -Rf'N(d2)+(D1 + D2 )e R'N(d2) (2-3')
where
_ln(V/D,)+(Rf +0.502 )
1, V

d2 =d1 C2VC

ln(V/(D + D2))+(Rf +0.5V2)T

2 1 V

D, is the face value of the firm's senior debt,
D2 is the face value of the firm's subordinated debt,
X2 is the current value of subordinated debt.
The Black-Cox model most frequently appears in the literature as the spread between the

yield on subordinated debt (R2 ) and the risk-free rate (R ) of the same maturity:


R2 -R, = -In eRf [N(d,)-N(d)] D N(d2) +D N(2) / (2-3)
D2 D2 D2
2.1.2. Applications of Contingent Claim Valuation

The above contingent-claim approach to pricing firm debt has many applications in

the literature on credit-risk analysis. Bohn (2000) surveys some of the main theoretical

models of risky debt valuation that built on Merton (1974) and Black and Cox (1976).

The empirical validity of these models has been rarely and poorly tested because of the

unavailability and low quality of bond data. Jones, Mason, and Rosenfeld (1983) and









Frank and Torous (1989) find that contingent-claim models yield theoretical credit

spreads much lower than actual credit spreads. Sarig and Warga (1989) estimate the term

structure of credit spreads, and show it to be consistent with contingent-claim model

predictions. Wei and Guo (1997) test the models of Merton (1974) and Longstaff and

Schwartz (1995), and find the Merton model to be empirically superior. It is important to

note that in calculating theoretical credit spreads, all of these studies require an estimate

of the variance of firm assets. One way to obtain such an estimate is by constructing a

historical time series of firm asset values and calculating the variance. Asset value is

typically the sum of market value of equity and book value of debt; or alternatively, the

sum of market value of equity, market value of traded debt and the estimated market

value of nontraded debt. Another way to estimate the variance of asset returns is by de-

levering the historical variance of equity returns, as in a simple version of the boundary

condition in Merton (1974):


o- = OE (2-4')
V
where aE is the historical standard deviation of equity returns, E is the market value of

equity, and V is the sum of E and book value of debt. We call this the simple implied

asset volatility (SIAV). It is important to note that any test of the contingent-claim

models to debt valuation is a test of the joint hypothesis that the model and the estimate

of ca are both correct. Nevertheless, the relative accuracy of different ca estimates has

not been explored in any of the above studies.

Contingent-claim valuation of equity has been used extensively in the literature on

bank deposit insurance where the equity-call model is 'reversed' to generate estimates of

the market value of assets from observed stock prices. This approach, along with the









observation in Merton (1977) that deposit insurance can be modeled as a put option,

allows the calculation of fair deposit insurance premia. This insight is used by Marcus

and Shaked (1984), Ronn and Verma (1986), Pennacchi (1987), Dale et al. (1991), and

King and O'Brien (1991) in the analysis of deposit insurance premia. The approach of

these researchers is to solve a system of equations that consists of Eq. 2-1 and Merton's

boundary condition


V = E E (2-4)
VN(d )
for the market value and volatility of assets. Their proxy for cE is the historical standard

deviation of equity returns. We will refer to the volatility estimate produced by this

approach as the equity-implied asset volatility (EIAV); and the asset value obtained along

with it is VEIAV. In addition to calculating the market value of assets for banks and

bank holding companies, this methodology has also been used to calculate the market

value of assets for savings and loan associations, by Burnett et al. (1991); and for

insurance companies and investment banks, by Santomero and Chung (1992). Despite its

wide use, the accuracy of the estimates it produces has rarely been questioned. We are

aware of only one study that investigates whether the market value estimates obtained

through this methodology are correct. Diba et al. (1995) use a contingent-claim model to

calculate the equity values of failed banks and find that these greatly exceed the negative

net-worth estimates of the FDIC. They conclude that the equity-call model produces poor

estimates of the market value of assets. The accuracy of the asset volatility estimates,

however, has not been previously examined.

While the literature on deposit insurance uses the contingent-claim equity-pricing

model, the literature on market discipline of bank and bank holding companies makes use









of the contingent-claim debt-pricing model. Starting with Avery, Belton, and Goldberg

(1988), yield spreads on bank subordinated notes and debentures have been examined for

information about the bank's risk profile. However, Gorton and Santomero (1990)

recognize that subordinated yield spreads are a nonlinear function of risk, and insist that

researchers focus on the variance of bank assets instead. They use the methodology of

Black and Cox (1976) to estimate a, from subordinated debt prices under the

assumption that book value is a good proxy for the market value of assets. Their

methodology insight has since been used by Hassan (1993) and Hassan et al. (1993) who

apply contingent-claim valuation techniques to calculate implied asset volatilities; and by

Flannery and Sorescu (1996), who use it to obtain theoretical default-risk spreads. We

refer to the asset volatility estimate calculated from subordinated debt prices as the debt-

implied asset volatility (DIAV); and the market value of assets obtained along with it is

V DIAV.

The last methodology we analyze is closest in spirit to the one used by Schellhorn

and Spellman (1996). They examine four banks over 1987-1988, and calculate two

estimates of implied asset volatility for each bank. The first estimate is EIAV and is

based on the methodology of Ronn and Verma (1986) described earlier. The second

estimate solves Equations 2-1 and 2-3 simultaneously for the market value of assets and

the standard deviation of asset returns. We refer to this volatility estimate as the equity-

and-debt implied asset volatility (EDIAV); and the corresponding asset value estimate is

V_EDIAV. Schellhorn and Spellman (1996) conclude that the two a, estimates can

differ substantially over the studied period, and that the estimates obtained from

contemporaneous equity and debt prices are on average 40% higher than those obtained









using historical information. The difference between the two estimates increases even

more when the banks are perceived to be insolvent. This suggests that if asset volatility is

to be used as a proxy for the total risk of a firm, then using historical equity variance can

substantially underestimate firm risk.

We expand the work of Schellhom and Spellman (1996) in three ways. First, we

use a larger and more-diverse sample. We obtain data on industrial firms for the period

1975-2001. Second, we compare a broader range of asset value and volatility estimates.

We judge the EDIAV and corresponding V EDIAV against estimates calculated using

three more traditional methodologies (SIAV, EIAV, DIAV) and the corresponding asset

value estimates. Third, we set up "horse-race" tests to determine the relative

informational content and accuracy of the four asset volatility estimates.

2.2. Methodologies for Constructing Risk Measures from Market Prices

This section summarizes the three methodologies traditionally used to estimate the

market value and volatility of assets. It then proposes one that relies on contemporaneous

equity and debt prices to obtain V and y. Finally, it explains the construction of

default-risk measures from implied asset value and volatility estimates.

2.2.1. Methodologies for Calculating Implied Asset Value and Volatility

The simple implied asset volatility (SIAV) is the most popular estimate of asset

volatility found in the finance literature. This is likely due to the ease of computation

since it uses a simplified version of the boundary condition


oV = GE (2-4')
where all variables are as previously defined. This methodology assumes that the

instantaneous standard deviation of equity returns at the end of quarter t is the standard









deviation of equity returns over the quarter. It uses the sum of the market value of equity

and book value of debt as a proxy for the market value of assets. This is equivalent to

assuming that the firm's debt is risk-free, which implies that we will overestimate its

market value by the value of the put option embedded in risky debt. Thus, we expect this

methodology to produce a market-value-of-assets estimate higher than those produced by

the three simultaneous-equation methodologies that follow.

The equity-implied asset volatility (EIAV) is calculated by solving the system

E = VN(d,) De Rf N(d2) (2-1)
E
(SV =p---- -------
= VN(d,) (2-4)

for c- and V. This is done using the Newton iterative method for systems of nonlinear

equations. For the starting value of V, we use the sum of the market value of assets and

book value of debt; and for the starting value of oy we use SIAV. Adhering to previous

studies, we assume that the instantaneous standard deviation of equity at the end of

quarter t is the standard deviation of equity returns over the quarter.

The debt-implied asset volatility (DIAV) is calculated by solving the system of

nonlinear equations:1

V R D D, +D
R, R = -In e [N(,) -N(d,)] 2) / (2-3)
1D2 D) 2 D(2
E
Oy V~ ---- ------
V VN(d,) (2-4)
for oa and V using the Newton iterative method. Once again, for the starting value of

V we use the sum of the market value of assets and book value of debt; but for the


1 We use the subordinated-debt valuation model, because we assume that publicly traded debt is likely to be
last in a firm's debt-priority structure. We discuss the reasonableness of this assumption later and explore
the sensitivity of our results to alternative assumptions.









starting value of a, we use the theoretically more-accurate EIAV. As in the calculation

of equity-implied asset volatilities, we assume that the historical standard deviation of

equity over quarter t is a good approximation for the instantaneous standard deviation of

equity returns at the end of the quarter.

The equity-and-debt implied asset volatility (EDIAV) is obtained by solving the

system of nonlinear equations

E = VN(d,) De R'fN(d2) (2-1)

R, -R, = -ln e d)-N(d )] N(d )+ + N(d2) /c (2-3)

for a, and V using the Newton iterative method. We use the same starting values for a,

and V as in the calculation of DIAV, and later ensure that the solutions are not sensitive

to the starting values. Note that unlike the previous three methodologies, this one needs

no historical information about the standard deviation of equity returns.

2.2.2. Calculating Credit-Risk Measures from Implied Asset Value and Volatility

Three elements determine the probability that a firm will default the market value

of its assets, the portion of liabilities due, and the volatility of asset returns. The first two

determine the default point of the firm, which as explained earlier is at first set to 97% of

total debt. The last element, asset volatility, captures business, industry, and market risks

faced by the firm. If the implied asset volatility estimates calculated in our study are

correct assessments of the firm's future risk exposure, then along with the firm's asset

and liability values they should reflect default probability accurately. We combine asset

volatility with the value of assets and liabilities, into a single measure of default risk, and

refer to it as the distance-to-default (DD). This measure compares a firm's net worth to

the size of one standard deviation move in the asset value, and is calculated as









ln(V/D)+(R 0.5cr ) T
DD =


Intuitively, a DD value of X tells us that a firm is X standard deviations of assets away

from default. Thus, a low DD indicates that a firm has a high probability of default.

2.2.3. Methodology Assumptions

The methodologies above are based on contingent-claim valuation, and as a result

require that the standard assumptions of Black and Scholes (1976) and Black and Cox

(1979) be met. Bliss (2000) lists a series of deviations from these assumptions. However,

it is an empirical question whether these deviations make the estimates of asset value and

volatility less meaningful. In addition to the standard assumptions, applying contingent-

claim valuation techniques requires that we know the time left to equityholders exercising

their option, and the default point of each firm. In obtaining estimates for these we

initially adhere to previous studies, but later examine the sensitivity of our results to

alternative assumptions. Our study aims to determine which of the simplifying

assumptions made in calculating asset values and volatilities affect the informational

content and accuracy of the estimates.

Starting with Marcus and Shaked (1984) and Ronn and Verma (1986) the time to

exercising the equity call option is typically assumed to be 1 year. Banking researchers

claim that the 1-year expiration interval is justified because of the annual frequency of

regulatory audits. If after an audit, the market value of assets is found to be less than the

value of total liabilities, regulators can choose to close the bank. An alternative

resolution-time assumption is used by Gorton and Santomero (1990), who set the time to

expiration equal to the average maturity of subordinated debt, and find that the DIAV

estimates calculated under this assumption are significantly higher than the ones









calculated under the 1-year-to-maturity assumption. However, they offer no evidence as

to which maturity assumption produces the better estimate of asset volatility. In the

application of contingent-claim models to the valuation of industrial firms there is much

less uniformity in the time-to-expiration assumption. Huang and Huang (2002) use the

actual maturity of debt, Delianedis and Geske (2001) use the duration of debt, and

Crosbie and Bohn (2002) use an interval of 1 year. Since the empirical properties of

implied total asset volatility are not the focus of these studies, they offer little evidence on

the sensitivity of their results to alternative time-to-expiration assumptions. To start with,

we assume that the time to resolution equals 1 year. We later explore the effects of two

alternative assumptions time to resolution equals to either the weighted average

duration or the weighted average maturity of the firm's bond issues.

Although we often assume that firms default as soon as their asset value reaches the

value of their liabilities, this is true only if the firm's debt is due immediately. In reality,

firms issue debt of various maturities and as a result their true default point is somewhere

between the value of their short-term and long-term liabilities. Unfortunately, while

previous studies recognize this (Crosbie and Bohn 2002), they offer little guidance on

choosing each firm's default point. The banking literature adheres to the assumptions

made by Ronn and Verma (1986) who set the default point at 97% of the value of total

debt. They originally experiment with default points in the range of 95-98% of debt and

determine that rank orderings of asset values are significantly affected by the choice of

default point. However, they do not examine the relative accuracy of the estimates

obtained under alternative default-point assumptions.









2.3. Data Sources

To construct the above estimates of asset value and volatility, we combine a

number of data sources for the period of December 1975 December 2001. Data on

equity prices and characteristics is obtained from the Center for Research in Security

Prices (CRSP). Data on bond prices and characteristics is obtained from the Warga-

Lehman Brothers Fixed Income Database (WLBFID) and the Warga Fixed Investment

Securities Database (FISD). Both sources are used since neither database alone covers the

whole study period. Finally, balance sheet and income statement data comes from the

Compustat Database. Combining these four data sources is nontrivial since (1) each

database has its own unique identifier with only some of them overlapping across

databases, and since (2) some of the identifiers are recycled. Therefore, the merging

process that we use requires further explanation.

We start with information from WLBFID and FISD, which use issuer CUSIP as

one of their identifiers. We then match the issuer CUSIP against those obtained from

CRSP making sure that the date on which the bond data is recorded falls within the date

range for which the CUSIP is active in the CRSP database. Merging the WLBFID and

FISD data with that from the CRSP database allows us to add one more identifier to our

list PERMNOs. We use them to acquire Compustat data from the Merged

CRSP/Compustat database. These matching procedures result in data on at least 1,264

unique industrial firms which give us 28,262 firm-quarter observations for 1975-2001.

2.3.1. Bond Prices and Characteristics

The initial sample includes all firms from the WLBFID and FISD whose bonds are

traded during the period of 1975-2001. The WLBFID reports monthly information on the

major private and government debt issues traded in the United States until March 1997.









We identify all U.S. corporate fixed-rate coupon-paying debentures that are not

convertible, putable, secured, or backed my mortgages/assets. We collect data on their

month-end yield, prepayment options, and amount outstanding.2 While most prices

reflect "live" trader quotes, some are "matrix" prices estimated from price quotes on

bonds with similar characteristics. Yields calculated from "matrix" prices are likely to

ignore the firm-specific changes we are trying to capture, so we exclude them from our

sample.

The FISD contains comprehensive data on public U.S. corporate and agency bond

issues with reasonable frequency since 1995. We use the same procedures for retaining

observations as we do with the WLBFID in an attempt to make the two databases as

comparable as possible we identify all fixed, non-convertible, non-putable, and non-

secured debentures issued by U.S. corporations. The main difference between the two

databases is the source and type of pricing information. The WLBFID reports bond trader

quotes as made available by Lehman Brothers traders. The FISD reports actual

transaction prices recorded electronically by Reuters/Telerate and Bridge/EJV who

collectively account for 83% of all bond trader screens. In the spirit of making data from

the two databases comparable, we calculate each issue's month-end yield using the price

closest to the end of the month. A cursory examination of the small number of debt issues

that have both WLBFID and FISD data available indicates that yields across the two

databases are extremely similar. Nevertheless, when combining the WLBFID with the





2 Data for December 1984 is substantially incomplete and produces no viable observations for the fourth
quarter of that year. We use the November data to match it against balance sheet data for the last quarter of
1984.









FISD sample, we choose actual trade prices over quotes only if the trade occurs in the last

five days of the month.

In order to compute a credit-risk spread, we need to subtract from each corporate

yield the yield on a debt security that is risk-free but otherwise has the same

characteristics as the corporate bond. The most common approach to calculating a credit-

risk spread is to difference the yield on a corporate bond with that on a Treasury bond of

the same remaining maturity. To do so we collect yields on Treasury bonds of different

maturities from the Federal Reserve Board's H. 15 releases. For each corporate debt issue

in our sample we identify a Treasury security with approximately the same maturity as

the remaining maturity on the corporate debenture. When there is no precise match, we

interpolate to obtain a corresponding Treasury yield. The difference between a corporate

yield and a corresponding Treasury yield is our first measure of the raw credit-risk

spread.

2.3.1.1. Tax adjustment

There is growing evidence that corporate yield spreads calculated as above cannot

be entirely attributed to the risk of default. Huang and Huang (2002) and Delianedis and

Geske (2001) demonstrate that at best less than half of the difference between corporate

and Treasury bonds is due to default risk. Elton et al. (2001) suggest that this difference

can be explained by the differential taxation of the income from corporate and Treasury

bonds. Since interest payments on corporate bonds are taxed at the state and local level

while interest payments on government bonds are not, corporate bonds have to offer a

higher pre-tax return to yield the same after-tax return. Thus, the difference between the

yield on a corporate and the yield on a Treasury bond must include a tax premium. Elton

et al. (2001) illustrate that this tax premium accounts for a significantly larger portion of









the difference than does a default risk premium. For example, they find that for 10-year

A-rated bonds, taxes account for 36.1% of the yield spread over Treasuries compared to

the 17.8% accounted for by expected losses. Cooper and Davydenko (2002) derive an

explicit formula for the tax adjustment proposed by Elton et al. (2001). They calculate

that the tax-induced yield spread over Treasuries is:


A 1 I 1 -
Ayt = 1 n
tM r exp(- rt)
where t, is the time to maturity for both the corporate and the Treasury bonds, r is the

applicable tax rate, and rrf is the Treasury yield.3 We use this formulation along with the


estimated relevant tax rate of 4.875% from Elton et al. (2001) to calculate a hypothetical

Treasury yield if Treasuries were to be taxed on the state and local level.4 The difference

between a corporate yield and a corresponding "taxable" Treasury rate is a measure of the

tax-adjusted raw credit-risk spread.

Alternatively, we can difference corporate yields with the yield on the highest rated

bonds under the assumption that these almost never default. We obtain Moody's average

yield on AAA-rated bonds from the Federal Reserve Board's H. 15 releases. It is

important to note that differencing a corporate yield with the AAA yield might allow us

to extract a more accurate estimate of the credit-risk premium by controlling for liquidity

as well as tax differential between corporate and Treasury bonds. However, it is also the


3 This formulation of the yield spread due to taxes assumes that capital gains and losses are treated
symmetrically and that the capital gain tax is the same as the income tax on coupons.

4 Corporate bonds are subject to state tax with maximum marginal rates generally between 5% and 10%
depending on the state. This yields an average maximum state tax rate in the U.S. of 7.5%. Since in most
states, state tax for financial institutions (the main holder of bonds) is paid on income subject to federal
taxes, Elton et al. (2001) use the maximum federal tax rate of 35% and the maximum state tax rate of 7.5%
to obtain an estimate for r of 4.875%. An alternative estimate is produced by Severn and Stewart (1992)
and equals to 5%.









case that the AAA yield has a number of drawbacks it averages the yields on bonds of

different maturity and different convertibility/callability options. Nevertheless, for the

non-AAA-rated bonds in our sample we use the difference between their yield and the

average AAA yield as an alternative tax adjustment for the raw credit-risk spread. We

start by differencing the corporate yields with the hypothetical taxable Treasury yields.

However, in the spirit of this study we later investigate whether using the average AAA

yields significantly affects the accuracy and informational content of the implied asset

volatility estimates.

2.3.1.2. Call-option adjustment

The tax-adjusted yield spreads calculated above might still contain some non-credit

related components. Perhaps the most important of these is the value of call options

embedded in many corporate yield spreads. Since the value of a call option is always

non-negative, the spread over Treasuries whether adjusted for taxes or not, will exceed

the credit-risk spread unless we adjust for the option's value. We follow the approach

presented in Avery, Belton, and Goldberg (1988) and Flannery and Sorescu (1996) to

estimate an option-adjusted credit spread. For each callable corporate bond in our sample,

we use the maturity-corresponding "taxable" Treasury bond to calculate a hypothetical

callable Treasury yield. That is, we calculate the required coupon rate on a Treasury bond

with the same maturity and call-option parameters as the corporate bond but the same

market price as the non-callable Treasury bond adjusted for taxes. The difference

between the yield on the hypothetical callable and the actual non-callable Treasury bond

is the value of the option to prepay. We subtract these option values from the tax-adjusted

spreads calculated earlier to obtain option-adjusted credit spreads.









The required yield on the hypothetical Treasury is computed following the method

of Giliberto and Ling (1992). They use a binomial lattice based on a single factor model

of the term structure to value the prepayment options of residential mortgages. Their

methodology uses the whole term structure of interest rates to estimate the drift and

volatility of the short-term interest rate process. These two parameters are then used to

determine the interest rates at every node of the lattice, which are in turn used to calculate

the value of the mortgage prepayment option. Following Flannery and Sorescu (1996)

this methodology is adjusted to calculate the call option value of the Treasury bonds

instead.

In a small number of cases these credit spreads turn out to be negative. A cursory

examination of these occurrences indicates that when the term structure of interest rates is

relatively flat and interest rate volatility high, our option-adjustment methodology

produces higher option values. When combined with an initially low yield (high-rated

bonds) these high option values lead to negative credit spreads. Since the theoretical

motivation used in this study does not allow for negative credit spreads and since

negative credit spreads are heavily concentrated in highly rated bonds, we winsorize our

set of credit spreads at zero.

2.3.1.3. Yield spread aggregation

To obtain a firm yield spread, YS, we aggregate yield spreads on bonds issued by

the same firm using three approaches. The first approach is to construct a weighted-

average yield spread by averaging the spreads on same-firm bonds and weighing them by

the bonds' outstanding amount. The other approaches use the findings in Hancock and

Kwast (2001) and Covitz et al. (2002) that due to higher liquidity larger and more

recently issued debentures have more reliable prices. To minimize the liquidity









component of yield spreads, for each firm we take the spread on its largest issue (based

on amount outstanding) as our second measure of firm yield spread, and the spread on its

most recent issue as our third measure. We investigate whether different aggregation

approaches produce significantly different IAV estimates.

2.3.2. Equity Prices and Characteristics

For all firms that have bond data available, we collect equity information from the

daily CRSP Stock Files. We calculate the quarterly equity return volatility oE as the

annualized standard deviation of daily returns during the quarter. The market value of

equity is the last stock price for each quarter multiplied by the number of shares

outstanding.

We exclude from our sample all stocks with a share price of less than $5 and for

which oE is computed from fewer than fifty equity-return observations in a quarter.

These data filters attempt to reduce the effect of the bid-ask bounce on the estimate of

equity-return volatility, while providing enough observations to make the quarterly

volatility estimate meaningful.

2.3.3. Accounting Data

Quarterly accounting data is obtained from the CRSP/COMPUSTAT Merged

Database using PERMNOs. For each firm we collect information on the book value of

total assets VB, and the book value of total liabilities, D, at the end of each calendar

quarter during 1975-2001. We also obtain industry classification codes to construct 48-

industry indicator variables following Fama and French (1997).

Our methodology requires information on the priority structure of total debt in

addition to its amount. For industrial firms there is no information on the amount of









senior versus subordinated debt, so we use the following approach for obtaining an

estimate of the priority breakdown. Using the two bond databases described earlier, we

aggregate the amount outstanding of each firm's bonds at each quarter-end during 1975-

2001. We use this as one estimate of the firm's face value of subordinated debt and input

it into Eq. 2-3. This simplification is based on the fact that firms tend to take out bank

loans before they turn to the public debt markets, and is supported by the findings of

Longhofer and Santos (2003) that most bank debt is senior. We investigate the sensitivity

of our findings to two alternative assumptions about debt priority structure. The first one

treats all debt as of a single priority class and as of homogeneous risk. That is, credit

spreads calculated earlier are assumed to reflect the default probability on total debt and

not only the default probability on bond issues outstanding. We use the credit spread, YS,

and total debt as inputs into Eq. 2-2. The second alternative assumption allows for at least

two priority and risk classes of debt. If YS is of a bond issue explicitly described as

senior, then the spread is assumed to reflect the risk of the firm's most senior debt. Along

with the face value of the firm's senior bonds outstanding it is inputted in Eq. 2-2. If YS

is instead that of a non-senior bond issue, then it is assumed to reflect the risk of the

firm's most junior debt claims. This credit spread and the face value of subordinated

bonds are then used as inputs in Eq. 2-3. This second alternative assumption is equivalent

to assuming that senior bonds are the company's most senior debt compared to the base

assumption that senior bonds might be subordinated to bank loans and private debt. If this

generalization is incorrect and a firm has debt senior to the senior bond issues, then YS

will overestimate the riskiness of the firm's assets and produce IAV estimates higher than

those produced by the base case.









2.3.4. Default Data

We use two proxies for the event of default the firm's delisting date from the

exchange that it trades on and the firm's bankruptcy filing date. We obtain delisting dates

from CRSP for the period 1975-2001 and retain those that are associated with

bankruptcy, liquidation, and other financial difficulties (delisting codes greater than 400).

We collect bankruptcy-filing dates from FISD for the period 1995-2001. Since an

extremely small portion of the firms in our sample default and since there is a large

overlap between the CRSP delisting dates and FISD bankruptcy-filing dates, we combine

the two data sources.5 We construct an indicator variable DFLT that equals one for

quarter t if a firm is either delisted or files for bankruptcy during the three years following

that quarter. It equals zero otherwise.

2.4. Summary Statistics

We use the methodologies described earlier to compute four estimates of implied

asset value and volatility. The base input assumptions are: the time to debt resolution

equals one year; the default point is at 97% of total debt; the issuer's yield is the yield on

the most recently issued bonds; the adjustment for taxes is based on Cooper and

Davydenko (2002); and, subordinated debt's face value is the face value of the firm's

bonds outstanding. For a small set of firm-quarter observations, the Newton iterative

procedure had difficulties converging. We experimented with different starting values

and different methods for solving a system of nonlinear equations (the Jacobi method and

the Seidel method). We were successful in calculating all four implied asset value and

volatility estimates for 27,723 out of the 28,557 original observations.


5 Estimating two separate logit models, one for delistings and one for bankruptcy filings, yields identical
results.









Table 2-1 presents summary statistics on the sample of 27,723 firm-quarters. The

average market value of assets is in the range of $6.3-8.1 billion and is very similar

across methodologies. The highest value is produced by the simple method of summing

the market value of equity and the book value of debt. This is not a surprise since this

methodology does not account for the riskiness of debt. When the value of the debt put

option is subtracted, then the market value of assets is reduced as indicated by the

estimates obtained from any of the system-of-equations methodologies.

Unlike the estimates of asset value, the estimates of asset volatility are significantly

different across methodologies. The average implied volatility is the lowest, 16.9%, when

calculated by the simple method of de-levering equity volatility using the market value of

equity and book value of debt. Once a system-of-equations methodology is used, the

average estimate becomes higher it is 17.9% for EIAV, 22.9% for DIAV, and 31.9%

for EDIAV. The magnitude of the EIAV and DIAV estimates is consistent with that

documented in Cooper and Davydenko (2002) and Huang and Huang (2002) both of who

rely on historical equity volatility in computing IAV.

We investigate whether the IAV differences vary across quarters. Figure 2-1 plots

median implied asset volatility for each quarter during 1975-2001, and makes four

noteworthy points. First, the four IAV measures appear to follow a similar time pattern.

The one notable exception is the last quarter of 1987 when median EIAV, DIAV, and

SIAV dramatically increase, while EDIAV falls. This is likely due to the reliance of the

first three estimates on historical equity volatility calculated over the three-month period

that includes the October 1987 crash. On the other hand, EDIAV is not affected by the

crash-induced historical equity volatility and as a result is a more forward-looking









assessment of asset volatility. In fact, EDIAV increases in the second quarter of 1986

possibly in anticipation of the 1987 events. Third, the plot shows that the median SIAV is

consistently the lowest estimate of IAV. This is an important observation given the wide

use of the estimate in finance research. Finally, the plot shows that the four IAV

estimates have significantly increased and the differences among them decreased since

the latter part of 1998.

We also explore whether our estimates of implied asset volatility are affected by

firm leverage. At the end of each quarter, we use firm assets-to-debt ratio ranking to

assign them to one of four quartiles. Figure 2-2 shows median implied asset volatilities

from our four methodologies by assets-to-debt ratio quartile. It is apparent that the higher

the amount of debt relative to assets, the lower the implied volatility. A possible

explanation for this finding is that firm capital structure and asset volatility are

simultaneously determined. Firms financed with relatively less debt might be willing to

take on more risk since they have a significant equity cushion to absorb changes in asset

value. Conversely, those that have relatively more debt in their capital structure might be

more risk averse since small fluctuations of total asset value can push them into default.

The distance-to-default (DD) measure can possibly avoid problems resulting from

the endogenous relationship between implied volatility and leverage since it combines

them into a single measure of default probability. Table 2-1 present summary statistics on

DD calculated from the four estimates of asset volatility. The average DD is 5.08 if

calculated from SIAV, 4.66 if calculated from EIAV, 2.17 if calculated from DIAV, and

2.23 if calculated from EDIAV.









The time series behavior of the median of the four DD measures can be seen in

Figure 2-3. While the DD estimates calculated from SIAV and EIAV are very volatile,

the ones calculated from DIAV and EDIAV are relatively stable. For instance, during

1980-1997 the DD calculated from EDIAV has fluctuated only in the range of 1.50-2.50

while the median DDEIAV has fluctuated in the range of 1.00-6.50. Once again, the

medians of the four DD estimates seem to be converging towards the end of the sample

period.

Table 2-2 examines more closely the correlation among the four IAV estimates.

The table indicates that market value of assets estimates are largely independent of the

methodology used to compute them the simple and rank correlations among all of the

four estimates are extremely close to 1.

Three out of the four asset volatility estimates are also highly correlated. SIAV,

EIAV, and DIAV have simple and rank correlations in the 90% range. Two of the three

measures however have lower simple correlations with EDIAV 67.5% for SIAV and

62.4% for EIAV with the rank correlations only slightly higher. In contrast, EDIAV is

highly correlated with DIAV as indicated by the simple (rank) correlation of 90.5%

(88.3%).

The simple and rank correlations among the four estimates of DD indicate a strong

association between DD SIAV and DD EIAV on one hand, and DD DIAV and

DD_EDIAV on the other. Correlations between the first two are 91.3% (simple) and

92.3% (rank), and those between the second two are 94.7% (simple) and 90.9% (rank). In

contrast, the DD calculated from DIAV has the lowest simple and rank correlation with

the DD calculated from SIAV 19.1% and 21.7%. The correlation of DD EDIAV with









DD_SIAV and DD_EIAV is always less than 50%. Interestingly enough, the differences

in DD measures do not simply reflect differences in IAV as indicated by the high

correlation of DIAV with EIAV and SIAV, and relatively low correlations of DD_DIAV

with DD EIAV and DD SIAV.

The wide range of implied asset volatility and distance to default correlations

reported in Table 2-2 suggests that different methodologies produce very different

estimates. Although all of the simple and rank correlations are statistically different from

zero, all of them are also statistically different from one. By using information from

different sources the four methodologies discussed in this study produce total risk and

default measures not only of different magnitude but also of different ranking. However,

whether any of the estimates are superior to the others is an empirical question that

requires a comparison of their informational content and accuracy. We conduct such

comparisons in the two sections that follow.

2.5. Realized Asset Volatility Tests

We start our comparison of the implied volatility measures by examining the

relationship between them and realized asset volatility. We explore whether implied asset

volatility is a rational forecast of realized asset volatility. This test is similar in spirit to

tests used to examine the ability of equity-return volatility implied by equity option prices

to predict realized volatility. These studies (Canina and Figlewski 1993, Chernov 2001,

Day and Lewis 1992, Jorion 1995, Lamoureux and Lastrapes 1993, Poteshman 2000)

yield different results depending on the time period, observation frequency, and data

source used. However, their overall conclusion is that implied equity-return volatility is a

biased forecast of realized volatility and that it does not use available information

efficiently. It will be interesting to relate these findings on the informational content of









implied equity volatility with our findings on the informational content of implied total

asset volatility.

Our difficulty in comparing implied to realized volatility stems from the fact that

unlike the market value of equity which is easily and frequently observed, the market

value of total assets can not be directly obtained and requires estimation. We construct a

hypothetical monthly time series of the market value of assets as the sum of the market

value of common equity, the last available book value of preferred equity, and an

estimate of the last available market value of debt. We use two alternative estimates for

the market value of debt. The first estimate uses the monthly price of each bond issue and

the amount outstanding of all bond issues tracked in the two bond databases to calculate

an estimate of each issuer's total bond market value. It then substitutes the bonds' market

value for their face value in the amount of total debt available from quarterly balance

sheet reports. That is, the first estimate is the sum of the market value of each firm's

publicly traded debt and the book value of its non-traded debt. The second estimate

assumes that the yield on non-traded debt is the same as that on traded debt, and

discounts the book value of total debt accordingly.

We use the monthly series of the market value of assets to calculate continuously

compounded total asset returns. We define realized asset volatility, RAVt, as the

annualized standard deviation of these monthly returns over the two years following the

end of quarter t. Historical asset volatility, HAVt, is the annualized standard deviation of

monthly returns over the year prior to quarter t. RAVland HAV1 use our first estimate of

the market value of debt, and RAV2 and HAV2 use the second.









2.5.1. Correlation between Implied Asset Volatility and Realized Asset Volatility

Table 2-3 presents the simple and rank correlations of the implied asset volatility

(IAV) and historical asset volatility (HAV) estimates with realized volatility. The table

suggests that IAV is significantly correlated with RAV with simple and rank correlation

coefficients in the range of 25.1-31.2% and 42.5-56.7% respectively.6 Among the four

IAV estimates the DIAV has the highest simple correlation with RAV closely followed

by SIAV and EIAV. The rank correlation of SIAV with RAV is the highest with the

correlation of EIAV and DIAV with RAV coming in a close second and third. That is,

none of the four implied volatilities appears to be a consistent winner with respect to its

correlation with realized volatility. However, there is a consistent looser the correlation

between EDIAV and RAV is always the lowest. It is interesting to note that the HAV

estimate is very highly correlated with RAV. It has the highest simple and rank

correlation coefficient among all the volatility forecast measures.

Since a previous section of this study demonstrates that median implied asset

volatilities vary with firm leverage, we investigate whether this variation occurs in the

correlation between IAV and RAV as well. We calculate simple and rank correlations

separately for each asset-to-debt ratio quartile and present these in Table 2-3. We find

that as the amount of debt decreases (assets-to-debt ratio increases) simple correlations

tend to increase. So do rank correlations of EDIAV and DIAV with RAV. On the other

hand, rank correlations of EIAV and SIAV with RAV at first increase but then decrease

as asset-to-debt ratio increases.



6 The correlations become smaller when the market value of debt is calculated under the assumption that all
of a firm's debt is of the same risk class. This implies that such a generalization introduces additional noise
in the implied volatility estimates.









2.5.2. Is Implied Asset Volatility a Rational Forecast of Realized Asset Volatility?

Theoretically, the estimates of implied total asset volatility calculated earlier are the

market's forecasts of future asset volatility. We can assess the accuracy of these forecasts

by examining the relation between them and realized asset volatility. Note that realized

volatility can be viewed as its expected value conditional on information available at

quarter-end t plus a zero-mean random error that is orthogonal to this information. That is

RA V,, = E[RAV I I,, + 0t,, where E[E I,,l= 0.
This formulation leads to the regression test for forecast rationality7:

RAVt,~ = 0S + 1Volatility Forecastt, + Et, (2-5)
where Volatility Forecastt,n is one of the four implied asset volatility (IAV) estimates at

the end of quarter t for firm n. If IAVt is the true expected value of realized asset

volatility conditional on information available at t, then regressing realized asset

volatilities on their expectations should produce estimates of 0 and 1 for 68 and 6,

respectively. Deviation from these values will be evidence of bias and inefficient use of

information in the market's forecasts. Note that the forecast error must be orthogonal to

any rationally formed forecast for any information set available at t. Thus, estimating the

above regression for each of our IAVt should produce 68 = 0 and 6, = 1 regardless of the

quality of the information that IAVt is based on. However, a more inclusive information

set will produce a forecast that explains a relatively larger portion of the variation in the

realization. That is, an implied asset volatility estimate derived from a more appropriate

model will produce a higher R2





7 Theil (1966) is credited with introducing this test for forecast rationality. The test has be successfully used
in economics research, see Brown and Maital (1981) for an example.









The above tests might lead us to reject the null hypothesis that implied volatility is

an unbiased forecast of realized volatility, if realized volatility is simply difficult to

predict. That is, if the market's information set at quarter-end t contained very little useful

information, then our results would be driven by estimation errors. To investigate

whether realized asset volatility is at all predictable using information available at

quarter-end t, we use yet another volatility forecast historical asset volatility, HAV. We

calculate this from a time series of historical asset values under the assumption that past

volatility trends will continue in the future. We then estimate the model above with HAV

as the Volatility Forecast.

Table 2-4 presents the results from the estimation of Eq. 2-5 for the whole sample

of 21,570 firm-quarter observations. All of the intercepts are statistically different from

zero which implies that both forward-looking and historical forecasts of asset volatility

are positively biased. This bias is the smallest for the DIAV estimate (0.089) and the

largest for the HAV estimate (0.137). The volatility forecasts do not appear to use

information optimally as indicated by their coefficient estimates in all of the

estimations these are significantly different from one. The relative magnitude of the

coefficients suggests that DIAV and SIAV make the best use of available information

with coefficients of 0.453 and 0.460. The lowest forecast efficiency is displayed by the

EIAV estimate with a coefficient of 0.293. The whole-sample results indicate that there is

some variation in the quality of information on which each of the forecasts is based. Out

of the four IAVs, the SIAV, EIAV and DIAV seem to be the most informative RAV

forecasts as indicated by their R2 of 9.6, 8.1, and 9.7% respectively. However, the R2









produced by the HAV is even higher (10.3%) implying that this forecast is based on even

better information.

Our conjecture that assets-to-debt ratio might affect the forecasting abilities of IAV

is supported by the results from estimating Eq. 2-5 for each of the four assets-to-debt

quartiles. The first and fourth quartiles display relatively higher intercepts and lower

coefficient estimates compared to the second and third quartiles. This suggests that biases

in the IAV forecasts tend to be larger for firms with extremely low or extremely large

amount of debt in their capital structures. The explanatory power of the models also

varies across assets-to-debt ratio quartiles. The IAV measures produce an R2 that is

extremely low in the first quartile in the range of 0.7-3.5% but increases as we move

to higher quartiles. Nevertheless, explanatory power is always the highest for the model

in which HAV is the independent variable. Its R2 starts at 8.2 and increases to 15.5%.

It is interesting to note that the fourth assets-to-debt-ratio quartile is characterized

by the highest explanatory power which implies that IAV estimates contain better

information for low-debt firms. One possible explanation for this surprisingly high R2 is

that the realized volatility of firms in that quartile is simply easier to predict since a larger

proportion of their total asset volatility comes from equity volatility. Since equity markets

are characterized by higher trading volume and more transparency than debt markets,

equity volatility might be easier to estimate and forecast than debt volatility. However,

the results in Table 2-4 suggest that information from equity prices alone is not enough to

form a good asset volatility forecast. Except for the first quartile DIAV always

outperforms EIAV it has the lower intercept implying lower bias, the higher coefficient

implying higher informational efficiency, and the higher R2 implying better information.









It is disappointing that EDIAV is a considerably worse forecast of RAV than any of the

other IAV measures. This can be due to the fact that EDIAV is calculated from a single

equity and debt value pair observed at the end of each quarter. This approach might

produce measurement errors which can be reduced by using historical equity volatility

calculated from equity prices over a whole quarter. As a result any of the IAV measures

calculated from historical equity volatility might contain better information than EDIAV.

2.5.3. Is Implied Asset Volatility a Better Forecast Than Historical Asset Volatility?

Having both implied asset volatility and realized asset volatility available allows us

to examine their relative informational content by estimating a model that includes both:

RA V,, = p, + p,IA Vt, + 2HA V,,, + t, (2-6)
If the information that is used to calculate one of the forecasts is a subset of the

information used to calculate the other, then the coefficient on the more informative

forecast will be statistically 1 and the coefficient on the redundant forecast will tend to 0.

On the other hand, if the two forecasts are based on different subsets of information then

both p, and p2 will be significantly different from 0 with the larger coefficient

corresponding to the more informative forecast. The difference between the R2 of Eq. 2-6

and that of Eq. 2-5 when the Volatility Forecast is HAV will indicate the relative

contribution of implied asset volatility to historical data in forecasting future asset

volatility.

We estimate Eq. 2-6 for the whole sample of 21,570 firm-quarters and then

separately for each of the asset-to-debt-ratio quartiles. The whole-sample results in Table

2-5 indicate that the coefficient estimates on both asset volatility forecasts are

significantly different from zero. This implies that rather than being redundant, IAV and

HAV are based on largely different information sets. Adding IAV to the regression of









RAV on HAV significantly increases the R2. This suggests that implied asset volatility

contributes a statistically and economically significant amount of information to a

forecast based on historical asset values alone. The marginal contribution is the highest

for the DIAV estimate. Interestingly enough, the coefficient estimate on HAV remains

significant which suggests that markets do not fully impound historical asset-return

volatility in their forecasts of future volatility. No matter the methodology used to extract

implied asset volatility from equity and/or debt prices, these prices do not appear to

reflect all of the information available. Day and Lewis (1992) and Lamoureux and

Lastrapes (1993) reach the same conclusion when examining the relative informational

content of implied and historical equity volatility. They document that information

available at the time that market prices are set can be used to predict realized return

variance better than the variance forecast embedded in stock option prices.

The results by assets-to-debt ratio quartiles in Table 2-5 confirm that IAV adds a

significant amount of information to HAV. The marginal information contribution does

not appear to be systematically related to leverage. However, it is interesting to note that

DIAV estimates display the largest marginal increase in R2 in all but the lowest assets-to-

debt ratio quartile. Along with the results in Table 2-4, this suggests that for all but the

highly levered firms DIAV is not only based on better information than any of the other

IAV estimates but that a larger portion of that information is new and different from the

information contained in historical asset-return volatility.

2.6. Default and Default Probability Tests

To compare the relative default-forecasting accuracy of DD computed from the

four asset value and volatility estimates, we design three tests. The first one is based on

the occurrence of default and the other two on default probability. We use two proxies for









default probability Altman's (1968) Z score and Moody's credit ratings. The two

measures are likely to complement each other well because they are derived using

different sets of information. The Z score is calculated from financial ratios that are

publicly available, while credit ratings are believed to be based on proprietary models and

inside information.

2.6.1. Tests Based on the Occurrence of Default

The relative default-forecasting accuracy of the distance-to-default (DD) measures

can be best examined through their ability to successfully distinguish between firms that

default and those that do not. The analysis relates a firm's default status over a three-year

period to its DD prior to the beginning of that three-year period. We divide the data into

eight subperiods: 1983-85, 1986-88, 1989-91, 1992-94, 1995-97, 1998-2000, and 2001-

03. 8,9 The December 1982 estimate of the DD measure is used to explain whether or not

the firm defaults in 1983, 1984, or 1985. A three-year period is chosen to balance the

need for a short window to capture the DD-default relationship with the need for a long

window to obtain sufficient number of defaults in each subperiod.

We limit our sample to firms that have data available as of the beginning of at least

one of the non-overlapping three-year periods defined earlier. This leaves us with 1,795

firm-quarter observations out of which only 35 are for defaulted firms.10 Being aware of


8 We exclude from our original sample observations prior to 1982 for two reasons. First, the Bankruptcy
Reform Act of 1978 revised the administrative and, to some extent, the procedural, legal, and economic
aspects of corporate bankruptcy filings in the United States. The Act went into effect on October 1st, 1979.
Second, only one of the firms in our sample defaults before 1982.

9 We chose to split our sample into the above listed three-year periods because this particular split allowed
us to retain the maximum number of default occurrences. Either of the other two possible splits (starting in
1982 or 1984) yields identical results.

10 Rather than having observations for 52 quarters as in our original sample of 23,857 firm-quarters, we
now have observations for 4 quarters. This explains the large reduction in sample size from 23,857 firm-
quarters to 1,795.









the econometrics issues that such a 'lop-sided' sample creates, we conduct the

occurrence-of-default tests not only on the whole sample but also on the subsample of

non-investment grade firms. This allows us to achieve a more balanced dataset 519

observations out of which 30 for distressed firms while biasing our results against

detecting a relationship between DD and default occurrences.

Table 2-6 provides summary statistics on the average distance-to-default estimates

by financial distress status. It shows that independent of the asset volatility estimate used

to calculate it, average DD is significantly lower for financially distressed firms. If we

look at the subsample of non-investment grade firms, the differences in average DD

persist but become smaller and less significant for DD_EIAV and DD_DIAV.

We estimate a Logit model in which the dependent variable DFLTt equals 1 if the

firm defaults in the three-year period following quarter t, and zero otherwise. The main

independent variables are the four DDt calculated from the four implied asset volatility

estimates. That is,

Pr(DFLT,,, = 1) = g(a + aDD,,, + aControls,, ) (2-7)
The control variables include period indicator variables intended to absorb the

effect of macroeconomic changes on instances of default. It also includes an indicator

variable, SMALLt that equals 1 if during quarter t a firm is in the bottom equity-value

decile of all traded firms. Since for the purposes of our study we define default as a

bankruptcy filing, or delisting due to bankruptcy or performance, our set of defaulted

firms might include firms that are delisted for non-liquidation reasons (e.g., violation of

price limits, not enough market makers, and infrequent trading). We believe that this is

more likely to be a problem for relatively small firms and thus employ the variable

SMALLt to control for the effects of miscategorizing firms into the set of defaulted ones.









Table 2-7 presents the results from the estimation of Eq. 2-7. The whole-sample

results indicate that all four DD measures are statistically significant in explaining the

occurrence of financial distress. Their negative sign indicates that a decrease in the

distance to default increases the probability that a firm will experience financial

difficulties in the following three years. The fit of all four models as indicated by the max

re-scaled pseudo R-square, R2, is in the range of 19.01-22.26%. The best fit is provided

by the DD calculated from SIAV, which contributes 7.30% to R 2 of a base logit model

that includes period and size indicator variables only. The second best performance is

displayed by DDEDIAV with R2 of 20.88% and marginal contribution of 5.92% to a

base model's R2.

The DD coefficient estimates, produced by fitting a logit model to the subsample of

non-investment-grade firms, are still negative but of less statistical significance. The DD

measures based on EIAV and DIAV are no longer statistically significant, the one based

on EDIAV is significant at the 10% level, and the one based on SIAV at the 5% level.

The change in statistical significance might be the result of the sample being smaller and

more balanced. Alternatively, it might indicates that while methodology choice is not

essential for the ability of DD to explaining default probability, it is important when

predicting default probability conditional on non-investment grade rating. We examine

R2 of the four models and not surprisingly the best fit is obtained when using SIAV

closely followed by EDIAV. The marginal contribution of SIAV and EDIAV to R2 of a

base logit model is 2.91% and 1.83% respectively.

In summary, whether analyzing the whole sample or the subsample of non-

investment grade firms, the DD estimates calculated from SIAV and EDIAV are better









than the ones calculated from EIAV or DIAV at distinguishing between firms that default

and those that do not. However, we should be cautious in interpreting these results as

conclusive since they are based on a sample characterized by an extremely small

percentage of defaults.

2.6.2. Tests Based on Credit Ratings

Credit rating agencies, such as Moody's and Standard & Poor, assess the

uncertainty surrounding a firm's ability to service its debt and assign ratings designed to

capture the results of these assessments. Credit ratings are revisited and revised often to

ensure that they reflect the most recent information on the probability that a firm will

default. Although the accuracy of credit ratings is difficult to judge, Altman (1989) shows

that bond mortality rates are significantly different across credit ratings and that higher

ratings imply higher bond mortality rates over a horizon of up to ten years. Based on

these findings we interpret a Moody's credit rating as a proxy for the default probability

of a firm and examine the relationship between credit ratings and DD. If implied asset

volatility is a reliable estimate of firm risk, then the corresponding DD measure will be

highly correlated with the firm's credit rating. The stronger this relationship, the more

accurate the asset volatility estimate. We allow for the DD estimates produced by the four

IAV methodologies to differ for the subsamples of investment and non-investment grade

firms.

Table 2-8 breaks down the original sample of 20,298 observations by Moody's

average credit rating and offers median DD statistics by rating category. A cursory

examination suggests that credit rating rankings are generally consistent with average DD

- as ratings deteriorate, DD falls. This relationship is much more pronounced for non-

investment grade firms and seems to be independent of the implied asset volatility that










DD is based on. Table 2-9 investigates whether quarterly changes in firm DD over the

period of 1975-2001 are consistent with subsequent quarterly changes in Moody's credit

rating. The median DDEDIAV and DD_DIAV changes seem consistent with the

subsequent credit upgrades and downgrades. Moody's appear to downgrade a firm after

its DD has fallen. This fall is larger if when downgraded the firm moves from investment

into non-investment grade. Similarly, when a firm's credit rating is adjusted upwards then

its DD has just increased with the increase being larger for firms upgraded into

investment grade. The average DD calculated from EIAV or SIAV do not follow this

pattern. In fact, for the firms whose credit rating changes from investment into non-

investment grade, the beginning-of-the-quarter DD is higher than that of the previous

quarter. This counter-intuitive association between average DD and credit rating changes

holds true for the firms downgraded from investment grade into non-investment grade

when DD is based on SIAV.

In order to control for the effect of other variables on firm credit rating, we estimate

a multivariate regression model separately for investment and non-investment grade

firms. That is, we estimate via OLS: 1

RTGinvest invest invest Controls + invest
t,n 0 1 t,n k k,t,n t,n
k (2-8)
junk junk junk
RTG junk junk + junk DD + junk Controls + junk
t,n 0 1 t,n k k k,t,n t,n
The set of controls includes industry indicator variables and a measure of firm size. It is

possible that credit rating agencies pay different attention to the financial health of small



1 Credit ratings are categorical variables which would suggest that the above model is better estimated via
logit or probit model. We choose to use OLS for two reasons. First, although issue credit ratings are
discrete, issuer credit ratings are not since they are the average issue ratings for that issuer. Second, the fact
that issuer credit ratings are not discrete leaves us with more than 100 issuer rating categories and that
creates convergence problems for an ordered logit model.









versus large firms. We control for such differences by including the natural logarithm of

the market value of assets corresponding to each volatility estimate in the logit

estimations above. It might also be the case that the credit ratings of regulated firms

contain different information compared to those of non-regulated firms. If government

agencies intervene to correct problems as soon as they are detected, then all else equal the

default risk of a regulated firm is less than that of a non-regulated one. We allow for this

possibility by including an indicator variable REG that equals 1 if a firm operates in a

regulated industry during the quarter in question, and equals 0 otherwise. Finally, the set

of controls includes industry indicator variables that are designed to control for default-

point variations among industry groupings.

The results from estimating Eq. 2-8 via OLS are presented in Table 2-10. They

indicate that DD measures calculated from any of the four IAV estimates are an accurate

assessment of firm default risk as proxied by Moody's credit rating. The coefficient on

DD is always negative and statistically significant which implies that higher distance to

default is associated with a higher-number rating (lower credit rating is denoted by a

higher number).

In evaluating the relative accuracy of the four DD estimates we focus on the

marginal contribution of each measure to the explanatory power of a regression that

includes control variables only. The whole-sample results indicate that the increase in R2

is the highest (7%) when we add DD_EIAV to the set of independent variables. The

second highest marginal contribution is provided by DD_SIAV (5.8%) and then by

DDEDIAV (3.6%). Assuming that Moody's credit rating is an accurate proxy of the

probability that a firm defaults, then our results indicate that EIAV is the most precise









forecast of future volatility. It is interesting to note that the accuracy ranking among the

four estimation methodologies changes when we split our sample into investment and

non-investment grade firms. The biggest surprise comes from the relative performance of

EDIAV. This estimate produces a DD measure with the highest marginal contribution to

R2 for the set of non-investment-grade firms 6.0%. For this set of firms relying on

historical equity volatility appears to reduce the informational content of the IAV

estimates as judged by the marginal contribution of any of the other three DD measures.

In addition to investigating the accuracy of DD, we also investigate whether the

information it contains is distinct from and timelier than that contained in credit ratings.

We do so by employing a Granger-causality test. We examine whether credit rating

upgrades and downgrades can be forecasted with information contained in lagged

distance-to-default changes. We allow for a change in firm default probability to be

reflected in its debt and equity valuation up to three quarters before it is reflected in a

credit rating change. That is, we use up to three lags of DD in the models below. We also

allow for the possibility that credit rating downgrades convey more information than

credit rating upgrades. Hand et al. (1992) and Goh and Ederington (1993) investigate the

informational content of credit ratings and conclude that downgrades contain negative

information while upgrades contain little or no information as indicated by bond and

stock price reactions. Thus, to test our conjecture we estimate two Logit models one for

downgrades versus no changes, and another for upgrades versus no changes. That is, we

estimate:









3
Pr(dRTG t= =) g() o + IidDDti + DD 4, n
t,n / o 1 t-i,n 2 t-4,n
i 1 (2-9)
3
+ ZE 3 .dRTG +4 RTG-, + ElkControls n)
1 t-j,n 4 t-4,n k tn
j=1 k
where dRTGt,, = 1 if firm n's credit rating has been upgraded in quarter t from its rating

in quarter t-1, and dRTG,, = 0 if the rating has remained the same. Similarly, we

estimate:

3
Pr(dRTGn = 0)= g(7 + 7 .dDD +yDD
t,n o Ti t-i,n 2 t-4,n
(2-10)
3
+ E y .3dRTG +7.RTG 4, + 7k Controls )
j 3 t- !,n 4 t-4,n k tIn
j=1 k
where dRTG,,, = 0 if the rating has remained the same and dRTG,,, = -1 if firm n's

credit rating has been downgraded in quarter t from its rating in quarter t-1. In addition to

the control variables described earlier, we include two more in the estimation of the

above models. The literature on the informational content of credit ratings documents that

highly rated firms are very rarely downgraded. This implies that a firm's starting credit

rating affects the probability of a subsequent downgrade/upgrade. Since the logit models

include three lags of DD and rating changes, we choose to include the firm's rating four

quarters prior to t. We also include the contemporaneous DD estimate.

Table 2-11 presents the results from a logit analysis that examines the relation

between credit rating upgrades/downgrades and DD changes. The relationship between

changes in credit rating and changes in distance to default appears to be of the expected

direction. The negative sign on the coefficient estimates indicates that the larger the

decrease in distance to default, the larger the probability of a credit rating downgrade. All

three lags of all four estimates of DD are statistically significant in explaining the









probability of credit rating downgrades. This suggests that the DD estimates capture

increases in default probability up to a year before these increases are reflected in an

actual credit rating change. This information appears to be distinct from information

contained in previous credit rating changes as indicated by the persistent statistical

significance of some of the lagged rating change variables. In fact, it can be argued that

the information contained in the DD estimates is better since adding DD into the model

reduces the statistical significance of some of the lagged ratings. We compare the fit of

the four models to that of a base model, which includes only control variables. We

discover that the DD calculated from EIAV provides the highest marginal contribution to

the R2 (1.6%) and is closely followed by the marginal contribution of the DD calculated

from SIAV (1.3%).

While changes in DD are highly significant in predicting credit rating downgrades,

Table 2-11 shows that they lack forecasting power when it comes to rating upgrades.

Only some of the lagged variables' coefficients are statistically significant and

significance levels are generally lower. While the explanatory power of the model is

higher for upgrades than it is for downgrades, the marginal contribution of the lagged DD

changes to the R2 is economically zero. On one hand this suggests that credit rating

upgrades are easier to forecast than credit rating downgrades. On the other, it appears that

lagged changes in DD do not aid in this forecasting process. This could be the result of

credit rating upgrades containing little or no new information as documented in Hand et

al. (1992) and Goh and Ederington (1993). Thus, the decrease in default probability that

we use them to proxy for has been incorporated in the firm's valuation earlier than the









three quarter lags that we include. This is consistent with the fact that the most recent DD

changes have the lowest statistical significance.

To sum up, all four DD estimates are able to detect credit rating downgrades up to a

year before they occur. The estimate based on EIAV seems to be better at explaining

subsequent downgrades than are the estimates based on EDIAV, DIAV, and SIAV.

Although some of the DD estimates' lags are statistically significant in explaining credit

rating upgrades, none of them improve our ability to distinguish between upgrades and

no-changes as indicated by their marginal contribution to the R2 of a base regression.

2.6.2. Tests Based on Altman's (1968) Z

Altman's (1968) Z-model provides an alternative proxy for default probability.

This is probably the most popular model of bankruptcy prediction and has been

extensively used in empirical research and in practice. 12 The Z-model is obtained

through multiple discriminant analysis of the financial ratios of industrial firms. It is

given by:

S= 1.2 WrkCapital +1.4 RetainedErngs +3.3 EBIT +0.6 MktValEquity Sales
Z = 1.2 ---- n ti ------- + 3.3 ----- +0.6 ------ +----
S TotalAssets) TotalAssets ) TotalAssets) BookValEquity TotalAssets
The Z thus obtained is a measure of financial health and a higher Z implies a lower

probability of default. If IAV is the market's rational expectation of future total asset

volatility, then the DD it implies should reflect expected default probability. Since Z is a

measure of the same expectation then a higher DD should be associated with a higher Z.

Although Z has been documented to predict default occurrences quite accuratelyl3,

the evidence in Dichev (1998) suggests that Z is a better predictor of default when the ex


12 See Altman (1993) for an extensive review of empirical studies citing and using the Z-model.

13 See Altman (1993) and Begley, Ming, and Watts (1997) for tests of Z's predictive abilities.









ante probability of default is high. He forms portfolios based on Z deciles and finds that

the correlation between the number of distress delistings in each portfolio and the

portfolio's rank is high when Z is low (portfolio 1-5). In contrast, when Z is high

(portfolios 6-10) the correlations are low and sometimes with a sign reversed from

expected. To account for this asymmetry in the predictive abilities of the measure, we

allow the relationship between Z and DD to differ across ex ante default probability.

Following the approach in Dichev (1998) we use each firm's Z-score at the end of each

quarter and assign the firm to one often Z-decile portfolios.

We start our analysis with simple univariate comparisons between Z-Scores and

DD estimates. Each quarter we assign firms in our sample to one often Z-score deciles.

Table 2-12 presents medians of the four DD estimates by Z-Score deciles and shows that

higher deciles are typically associated with higher DDs. It is interesting to note that the

two DD estimates that incorporate information from debt prices, DD_EDIAV and

DD_DIAV, are more consistent over the low-Z deciles, while the ones that incorporate

information from equity prices are more consistent over the high-Z deciles.

We then estimate a model separately for low-Z (portfolios 1-5) and high-Z

(portfolios 6-10) firms. That is,

Slow low low DD + low Controls + low
t,n 0 t,n k k,t,n t,n (2
k (2-11)
Z high = high + high D + high Controls + C high
t,n 0 i tn k k t,n t,n
Table 2-13 contains the results from this OLS estimation. All four DD estimates are

highly statistically significant in explaining Z whether the model includes industry or

firm fixed effects. The positive sign on the DD coefficient indicates that a larger distance

to default is on average associated with a higher Z score. This implies that all four of the









DD estimates contain accurate information about a firm's default probability if Z is a

good proxy of this probability. The relative accuracy of the four measures can be

determined by their marginal contribution to the explanatory power of a base model that

includes control variables only. In the regression that includes industry fixed effects,

DD_DIAV produces the highest increase in R2 (2.74%). It is followed by DD_EIAV with

2.11%. This accuracy ranking is reversed when the regression includes firm fixed effects

with DD_EIAV containing better information than DD_DIAV.

For the subset of high-Z firms, the coefficient estimates of DD are less significant

and/or of a sign opposite to the one expected. Also, these variables add little or no

explanatory power when included among the explanatory variables. These results might

indicate that DD is a poor estimate of a firm's true distance to default, or perhaps Z is

simply a poor measure of default risk. Although we cannot unambiguously distinguish

between these two alternatives, the results in Dichev (1998) suggest that Z might be the

flawed measure. He shows that Z score is a less accurate measure of default risk when the

ex ante default risk is low.

We also examine whether changes in default probability, as proxied by Z, can be

predicted by changes in the four DD estimates. Since an increase in a firm's distance to

default implies that its financial condition is improving, then changes in DD should be

associated with same-direction changes in Z. To examine whether this is the case, we

estimate a model in which the dependent variable is dZt: the change in Z from quarter-

end t-1 to quarter-end t. The main independent variable is the change in one of the four

distance-to-default estimates, dDDt. The four DDt are calculated from the four implied

asset value and volatility estimates in quarter t and the change dDDt is from quarter-end t-









1 to quarter-end t. We include up to three lags of dDDt to investigate whether financial

markets detect changes in default probability before these are reflected in a firm's

accounting reports.

We allow for our DD estimates to have different predictive power for positive and

negative changes in Z. There is circumstantial evidence that when it comes to credit risk,

investors tend to be surprised by negative information but not by positive information.

Studies document that bank regulators' and credit rating agencies' downgrades are

regarded as news while upgrades seem to have no new informational content. It has been

maintained that the reason behind this asymmetry is managers' willingness to share

favorable and withhold unfavorable private information. Thus, the release of the latter is

eventually forced by regulators and rating agencies. We extend this argument to quarterly

reports. We contend that while managers might reveal good news as soon as it becomes

available, they might wait to disclose bad news until their quarterly reports are due. We

estimate a model separately for increases and decreases in Z to allow for a possible

asymmetry in informational content:

3
dZ = 0++ 0 + dDD + E Controls + s
t,n 0 1 t- i,n k k,t,n t,n (2-12)
3
dZ =0 + C 0. dDD +O9, Controls
t,n =0 + t-i,n k k,t,n +t,n
i=1 k
All of the models in this subsection are estimated via ordinary least squares. The set of

control variables includes the natural logarithm of the market value of assets, SIZEt, since

previous research has established that smaller firms are more likely to default all else

equal. It also includes an indicator variable, REGt, which equals 1 if the firm operates in a









regulated industry during the quarter in question, and 0 otherwise.14 We include quarterly

indicator variables designed to absorb the effect of macroeconomic changes on default

probability. Finally, we include either industry or firm indicator variables in order to

capture default-point differences across industries or firms respectively. In essence, this is

identical to estimating a panel regression with industry or firm fixed effects.15

Table 2-14 presents the results from estimating Eq. 2-12. DD changes are

statistically significant only for the subset of negative Z changes with industry fixed

effects, and the subset of positive Z changes with firm fixed effects. When significant

their coefficients are positive indicating that the larger the increase in DD, the larger the

increase in Z. The marginal contribution of DD changes to the R2 of a regression

including lagged Z changes and control variables only, indicates that the former add little

to no new information the marginal contribution is always less than 0.2%. However,

there is a DD estimate that stands out. An assessment of each of the four DD estimates'

statistical significance and marginal explanatory power suggest that the DD calculated

from EIAV performs best.

In summary, the results presented in this section indicate that when the ex ante

probability of default is high all four DD estimates accurately reflect a firm's default risk.

It seems that the DD estimate calculated from EIAV is more accurate and timely than the

other DDs. Furthermore, it appears to add the most new information to the firm's lagged

Z-score changes.

14 Regulated industries include railroads (SIC code 4011) through 1980, trucking (4210 and 4213) through
1980, airlines (4512) through 1978, telecommunications (4812 and 4813) through 1982, and gas and
electric utilities (4900 and 4939). See Frank and Goyal (2003) for more. We estimate the regressions
excluding regulated firms from the sample and the results remain unchanged.
15 Our sample contains more than one industries represented by a single firm. To ensure that the model is
identified we do not include both industry and firm indicator variables in the same estimation.









2.7. Sensitivity of Estimates to Alternative Model Assumptions

The analysis above examines the properties of implied asset values, volatilities, and

distance-to-default measures calculated under a set of base assumptions. In this section

we assess the sensitivity of the estimates to changes in the assumptions. To do so, we

repeat the realized asset volatility, and the default and default probability tests discussed

earlier using alternative-assumption estimates of IAV and DD. We include a sample of

our results below.

2.7.1. Summary Statistics

Table 2-15 presents summary statistics under alternative assumptions. The sample

statistics are largely unaffected when we use different default points, different issuer

yields, or limit ourselves to non-callable bonds only. In contrast, employing alternative

time-to-resolution, tax-adjustment, or debt-priority assumptions makes a significant

difference.

As the time to resolution increases from one year to the duration and then the

maturity of debt, median EIAV considerably increases from 15.7% to 24.2% Median

DIAV is almost unchanged when instead of one year we assume that the time to

resolution equals the average duration of debt. However, if time to resolution is assumed

to equal the average debt maturity, then average DIAV increases. It is interesting to note

that increasing the time to resolution at first decreases but then slightly increases the

EDIAV estimate. While under the one-year to resolution assumption the three system-of-

equations IAV estimates are significantly different, increasing the time to resolution has

the effect of making their magnitudes very similar and changing their relative ranking. In

fact, if the time to resolution is assumed to equal the average maturity of debt then









average EIAV is the highest, while under the one year to resolution assumption it is the

lowest.

Since DIAV and EDIAV are the only estimates calculated from credit spreads, they

are the only estimates affected by employing an alternative tax adjustment. Table 2-15

shows that if we do not adjust for the differential taxation of corporate and Treasury

securities altogether, both DIAV and EDIAV increase. This effect is expected since not

adjusting for taxes overestimates the portion of yield spreads due to default risk, which in

turn overestimates the implied volatility of total assets. On the other hand, when we

adjust for taxes by differencing corporate yields with the average yield on Moody's

AAA-rated bonds, the two IAV estimates significantly decrease.

Finally, the sample summary statistics are most dramatically affected by changes in

the debt priority assumption. Table 2-15 indicates that the DIAV and EDIAV estimates

increase to unreasonable levels whenever we assume that bond yields are representative

of the default risk of total debt. The increase is even more striking when we assume that

senior bonds are senior to all remaining debt, and junior bonds are junior to all remaining

debt. It is important to note that this latter result might be due to the loss observations.

Under the second alternative debt-priority assumption the algorithm used to solve for the

DIAV and EDIAV fails to converge for about 500 additional observations that tend to be

characterized by low credit spreads.

2.7.2. Realized Asset Volatility Tests

Table 2-16 presents the results from re-estimating Eq. 3-5. As suggested by the

summary statistics in Table 2-15, alternative assumptions about each firm's default point

and credit spread do not considerable affect the informational content of the IAV

estimates. Three alternative assumptions that significantly worsen the forecasting ability









of the IAV estimates are that (1) time to resolution equals the weighted average maturity

of traded debt, (2) differencing corporate yields with the average yield on Moody's AAA-

rated bonds is a proper tax adjustment, and (3) senior (junior) bonds are the firm's most

senior (junior) debt. When we limit our sample to non-callable bonds we lose almost two-

thirds of our observations. These seem to be observations that contain high-quality

information, since the explanatory power for this subsample is quite lower than in our

base case. Only two alternative assumptions produce IAV estimates which forecast RAV

better than the base IAV estimates. Assuming that time to resolution equals the weighted

average duration of each firm's traded debt or assuming that all debt is of the same

priority and homogeneous default risk produces the IAV estimates with the highest

explanatory power. The former assumption also generates some of the highest coefficient

estimates on IAV suggesting that these estimates use information most efficiently.

2.7.3. Default and Default Probability Tests

The results from re-estimating the default forecasting model Eq. 2-7 are shown in

Table 2-17. Increasing the time to resolution has the effect of decreasing the explanatory

power of the DD estimates obtained through any of the system-of-equations IAV

methodologies. Consistent with our realized asset volatility test, we find that alternative

assumptions about default point or issuer yield do not significantly impact the

explanatory power of the model. Employing no tax adjustment reduces the explanatory

power of the two estimates whose calculation requires bond yields DIAV and EDIAV.

Adjusting for taxes by using the average yield on Moody's AAA-rated bonds reduces

explanatory power for the whole sample but produces some of the highest R2 for the

subsample of non-investment grade firms. The sensitivity results in Table 2-17 indicate









that some of the alternative assumptions employed affect the explanatory power of our

model. However, DD_SIAV consistently produces the highest marginal contribution to

R2 and is typically followed by DDEDIAV. Assuming that all debt is senior and of

homogeneous risk is the only assumption under which the distance to default obtained

from EDIAV is relatively more informative than that produced by SIAV judging by

AR2.

Table 2-18 presents the results from re-estimating the credit ratings model (Eq.

2-9). Most of the alternative assumptions preserve the performance ranking of the four

DD measures. The equity DD measure, DDEIAV, outperforms the others in the whole

sample and the investment-grade subsample estimation. For the subsample of junk firms,

the DD measures which combines information from equity and debt prices typically

outperforms the other DD measures. Both DD_EIAV and DD_EDIAV have the highest

explanatory power when constructed under the assumption that a firm's default point

equals 95% of its total debt.

The results from re-estimating the downgrade/upgrade logit model (Eq. 2-10) can

be seen in Table 2-19. As we already established, the market measures are statistically

significant but improve the fit of forecasting models only marginally. Table 2-19 points

out that this relatively poor forecasting ability is not significantly worsened or improved

by alternative model assumptions. The DD measures that rely on debt price information,

DD_DIAV and DDEDIAV, produce the best fit when credit spreads are calculated

using the average yield on Moody's AAA-rated bonds rather than the yield on Treasury

securities.









2.8. Summary and Conclusion

The results reported in this study have important implications for financial theory

and practice. Researchers and practitioners have employed a variety of methods to obtain

estimates of asset volatility for the purpose of valuing corporate debt and derivative

products written on it, measuring total firm risk, or pricing deposit insurance. However,

despite the variety in available methods, we know very little about the empirical

properties of the implied asset volatility estimates they produce. We address this gap in

the literature in two steps. First, we examine whether the source of information debt

versus equity prices, and historical versus implied equity volatility impacts the

informational content and accuracy of implied asset volatility. Second, we explore

whether assumptions about the model parameters time to resolution, default point, debt

priority structure, and tax and call option adjustments appear to be important.

To address the first issue we construct four estimates of implied asset volatility. We

obtain the simplest one by de-levering historical equity volatility using the market value

of equity and the book value of debt. To construct the other three we use contingent-

claim pricing models to simultaneously solve for the market value and volatility of assets.

The first estimate reflects information from equity prices and historical equity volatility,

and the second one reflects information from debt prices and historical equity volatility.

The last estimate incorporates information from contemporaneous equity and debt prices

without relying on past equity volatility information. We assess the relative performance

of the four implied asset volatility estimates by using them to forecast realized asset-

return volatility, defaults, credit ratings, and Z scores.

We document that the implied asset volatility calculated from debt prices best

explains variations in realized asset volatility. This is contrary to the commonly held









belief that debt markets are characterized by many frictions and as a result debt prices are

too noisy to be useful. In addition to directly examining the relation between implied and

realized volatility of asset returns, we perform a number of indirect tests that draw on the

intuition that, all else equal, firms with highly volatile assets have a higher default

probability. For the purpose of these tests we use firm leverage and asset volatility to

construct a default risk measure, distance to default, that represents the number of asset-

value standard deviations required to push a firm into default. We find that this default

risk measure can successfully forecast defaults, and is highly correlated with a firm's

credit rating and Z score. However, none of our four implied-asset-volatility

methodologies produces a default risk measure that consistently outperforms the others.

When we examine whether the distance-to-default measures are able to forecast changes

in credit ratings and Z scores, we find that their predictive power is limited to negative

changes in the dependent variables. This is consistent with the findings of previous

studies that market participants rarely regard decreases in default probability as news. In

determining which of the four methodologies analyzed in this study produces the most

informative and accurate estimate of total firm risk, we examine the marginal

contribution of each methodology's default risk measure to the explanatory power of a

base regression. We find that although there is no consistent winner, the measure

calculated from equity prices and historical equity volatility has slightly better forecasting

abilities than do measures constructed through other methodologies.

The second contribution of this study is that it documents the impact of alternative

model assumptions on estimates of implied asset volatility. While the choice of using

equity or debt prices to extract firm risk information appears to be inconsequential, we









find that the choice of model parameters is quite important. We show that the manner in

which we adjust yield spreads to account for embedded call options, and tax differences

between corporate and Treasury securities has a significant effect on the level and rank

ordering of firm risk measures. In addition, assumptions about the maturity of debt and

debt priority structure seem to affect the forecasting ability of both implied-volatility and

distance-to-default estimates. In contrast, using alternative assumptions about each firm's

default point and alternative approaches to aggregating issue yields into issuer yields

appear immaterial. This finding underscores the importance of robustness checks

whenever equity and debt valuation is based on contingent-claim pricing models. It also

provides researcher and practitioners with some guidance as to the model parameters

most likely to influence results.









Table 2-1. Summary statistics. Summary statistics are for the sample of 27,723 firm-
quarter observations over 1975-2001. SIAV is the simple implied asset
volatility calculated by de-levering historical equity volatility. EIAV is the
equity-implied asset volatility calculated from equity prices and historical
equity volatility. DIAV is the debt-implied asset volatility calculated from
debt prices and historical equity volatility. EDIAV is the equity-and-debt-
implied asset volatility calculated from contemporaneous equity and debt
prices. Implied asset volatilities are reported in percent per year. VSIAV,
V_EIAV, VDIAV, and VEDIAV are the corresponding estimates of the
market value of assets in billion dollars. DD SIAV, DD EIAV, DD DIAV,
and DD EDIAV are the corresponding distance-to-default measures.
Variable Minimum Maximum Median Mean StdDev
V SIAV 0.03 404.07 2.90 8.14 20.52
V EIAV 0.02 383.08 2.77 7.76 19.37
V DIAV 0.02 395.20 2.21 6.31 16.93
V EDIAV 0.02 383.08 2.77 7.75 19.37

SIAV 0.6 154.6 14.8 16.9 10.6
EIAV 0.7 208.0 15.7 17.9 11.6
DIAV 1.1 141.2 20.2 22.9 12.8
EDIAV 1.9 172.4 29.5 31.9 15.3

DD SIAV 0.05 20.34 4.83 5.08 2.12
DD EIAV -1.38 18.24 4.36 4.66 2.20
DD DIAV -0.70 19.26 1.90 2.17 1.40
DD EDIAV -0.34 32.56 2.02 2.23 1.26













Table 2-2. Simple and rank correlations. Correlations are for the sample of 27,723 firm-quarter observations over 1975-2001. SIAV is
the simple implied asset volatility calculated by de-levering historical equity volatility. EIAV is the equity-implied asset
volatility calculated from equity prices and historical equity volatility. DIAV is the debt-implied asset volatility calculated
from debt prices and historical equity volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from
contemporaneous equity and debt prices. VSIAV, VEIAV, VDIAV, and VEDIAV are the corresponding estimates of
the market value of assets. DD_SIAV, DDEIAV, DD_DIAV, and DD_EDIAV are the corresponding distance-to-default
measures. All correlations are significantly different from 0 at the 1 percent level.
Simple Correlations Rank Correlations
V SIAV V EIAV V DIAV V EDIAV V SIAV V EIAV V DIAV V EDIAV
V SIAV 1.000 1.000
V EIAV 1.000 1.000 1.000 1.000
V DIAV 0.985 0.982 1.000 0.990 0.989 1.000
V EDIAV 1.000 1.000 0.982 1.000 1.000 1.000 0.989 1.000

SIAV EIAV DIAV EDIAV SIAV EIAV DIAV EDIAV
SIAV 1.000 1.000
EIAV 0.987 1.000 0.996 1.000
DIAV 0.907 0.871 1.000 0.937 0.923 1.000
EDIAV 0.675 0.624 0.905 1.000 0.693 0.664 0.883 1.000

DD SIAV DD EIAV DD DIAV DD EDIAV DD SIAV DD EIAV DD DIAV DD EDIAV
DD SIAV 1.000 1.000
DD EIAV 0.913 1.000 0.923 1.000
DD DIAV 0.191 0.315 1.000 0.217 0.331 1.000
DD EDIAV 0.348 0.426 0.947 1.000 0.417 0.473 0.909 1.000












Table 2-3. Simple and rank correlations of implied and historical asset volatility with realized asset volatility. Correlations are for the
sample of 21,570 firm-quarter observations over 1975-2001. SIAV is the simple implied asset volatility calculated by de-
levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and historical
equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity volatility.
EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices. HAV1 and
HAV2 are two estimates of annualized historical asset volatility calculated over the year prior to the end of each quarter.
RAV1 and RAV2 are two estimates of annualized realized asset volatility over the year following each quarter-end. HAVI
and RAVi assume that the market value of debt is the sum of the market value of traded debt and the book value of non-
traded debt. HAV2 and RAV2 assume that the yield to maturity on non-traded debt is the same as the yield to maturity on
traded debt. All correlations are significantly different from 0 and 1 at the 1 percent level.
Simple Correlations Rank Correlations
EDIAV EIAV DIAV SIAV HAVI HAV2 EDIAV EIAV DIAV SIAV HAVI HAV2

Whole Sample, N=21,570
RAV1 0.251 0.285 0.312 0.310 0.321 0.320 0.425 0.533 0.514 0.567 0.563 0.490
RAV2 0.206 0.272 0.274 0.267 0.316 0.334 0.328 0.489 0.430 0.463 0.512 0.499

Assets-to-Debt Ratio, Quartile 1, N=5,428
RAV1 0.084 0.178 0.170 0.189 0.287 0.303 0.249 0.405 0.386 0.422 0.505 0.425
RAV2 0.076 0.180 0.165 0.160 0.287 0.324 0.191 0.374 0.330 0.310 0.458 0.470

Assets-to-Debt Ratio, Quartile 2, N=5,380
RAV1 0.207 0.289 0.304 0.333 0.344 0.308 0.262 0.520 0.450 0.537 0.562 0.501
RAV2 0.181 0.284 0.285 0.313 0.330 0.311 0.220 0.492 0.404 0.471 0.528 0.517

Assets-to-Debt Ratio, Quartile 3, N=5,410
RAV1 0.241 0.266 0.306 0.303 0.369 0.375 0.350 0.455 0.453 0.478 0.474 0.455
RAV2 0.227 0.271 0.297 0.297 0.358 0.374 0.300 0.455 0.415 0.449 0.452 0.463

Assets-to-Debt Ratio, Quartile 4, N=5,352
RAV1 0.337 0.332 0.391 0.366 0.394 0.386 0.405 0.431 0.459 0.446 0.422 0.411
RAV2 0.320 0.351 0.383 0.373 0.406 0.404 0.358 0.435 0.423 0.429 0.419 0.420










Table 2-4. Analysis of IAV and HAV forecasting properties. We estimate via OLS
RA V,,, = o + d Voaltility Forecast,,, + ,, .Volatility forecast is one of the
five: SIAV, EIAV, DIAV, EDIAV, or HAV. SIAV is the simple implied asset
volatility calculated by de-levering historical equity volatility. EIAV is the
equity-implied asset volatility calculated from equity prices and historical
equity volatility. DIAV is the debt-implied asset volatility calculated from
debt prices and historical equity volatility. EDIAV is the equity-and-debt-
implied asset volatility calculated from contemporaneous equity and debt
prices. HAV is an estimate of annualized historical asset volatility calculated
over the year prior to the end of each quarter. RAV is an estimate of
annualized realized asset volatility over the two years following each quarter-
end. Standard errors are reported in parenthesis. All coefficient estimates are
statistically significant at the 1 percent level.
IAV Methodology

Sample Used in Estimation EDIAV EIAV DIAV SIAV HAV
Whole Sample, N=21,570
Intercept 0.108 0.122 0.089 0.113 0.137
(0.002) (0.018) (0.003) (0.024) (0.014)
Slope 0.343 0.293 0.453 0.460 0.273
(0.009) (0.006) (0.015) (0.014) (0.003)
R2 0.063 0.081 0.097 0.096 0.103
Assets-to-Debt Ratio, Quartile 1, N=5,428
Intercept 0.133 0.126 0.099 0.106 0.134
(0.009) (0.003) (0.010) (0.005) (0.012)
Slope 0.202 0.233 0.427 0.649 0.186
(0.002) (0.008) (0.004) (0.024) (0.016)
R2 0.007 0.031 0.029 0.035 0.082
Assets-to-Debt Ratio, Quartile 2, N=5,380
Intercept 0.091 0.109 0.063 0.079 0.107
(0.010) (0.005) (0.013) (0.015) (0.004)
Slope 0.379 0.302 0.557 0.685 0.385
(0.001) (0.024) (0.003) (0.004) (0.014)
R2 0.043 0.083 0.092 0.111 0.118
Assets-to-Debt Ratio, Quartile 3, N=5,410
Intercept 0.098 0.128 0.080 0.103 0.114
(0.005) (0.003) (0.013) (0.028) (0.015)
Slope 0.398 0.280 0.505 0.514 0.448
(0.002) (0.014) (0.003) (0.015) (0.003)
R2 0.058 0.071 0.094 0.092 0.136
Assets-to-Debt Ratio, Quartile 4, N=5,352
Intercept 0.123 0.144 0.107 0.130 0.131
(0.009) (0.005) (0.014) (0.005) (0.015)
Slope 0.309 0.264 0.391 0.373 0.426
(0.005) (0.024) (0.006) (0.021) (0.016)


0.113 0.110 0.153 0.134 0.155


0.113 0.110 0.153


0.134 0.155









Table 2-5. Analysis of the relative informational content of IAV and HAV in forecasting
RAV. We estimate via OLS RAV, n = po + plA ,V, + p2HAVt, + Et, .The
independent variable IAV is SIAV, EIAV, DIAV, or EDIAV. SIAV is the
simple implied asset volatility obtained by de-levering historical equity
volatility. EIAV is the equity-implied asset volatility obtained from equity
prices and historical equity volatility. DIAV is the debt-implied asset volatility
obtained from debt prices and historical equity volatility. EDIAV is the
equity-and-debt-implied asset volatility obtained from contemporaneous
equity and debt prices. HAV is an estimate of historical asset volatility
calculated over the year prior to the end of each quarter. RAV is an estimate
of realized asset volatility over the 2 years following each quarter-end.
Standard errors are reported in parenthesis. All coefficient estimates are
statistically significant at the 1 percent level. AR2 (IAV) is the marginal
contribution of the corresponding IAV to the model's R2 when compared to a
base model including HAV only.
IAV Methodology

Sample Used in Estimation EDIAV EIAV DIAV SIAV
Whole Sample, N=21,570
Intercept 0.079 0.099 0.069 0.091
(0.002) (0.034) (0.004) (0.003)
IAV 0.279 0.218 0.362 0.357
(0.007) (0.005) (0.012) (0.014)
HAV 0.245 0.223 0.222 0.218
(0.002) (0.046) (0.003) (0.015)
R2 0.143 0.144 0.161 0.157
AR2(IAV) 0.041 0.041 0.058 0.054
Assets-to-Debt Ratio, Quartile 1, N=5,428
Intercept 0.100 0.102 0.073 0.082
(0.002) (0.004) (0.031) (0.016)
IAV 0.209 0.193 0.388 0.576
(0.007) (0.026) (0.008) (0.004)
HAV 0.186 0.175 0.180 0.177
(0.006) (0.003) (0.004) (0.014)
R2 0.089 0.103 0.106 0.110
AR2 (IAV) 0.007 0.021 0.024 0.028
Assets-to-Debt Ratio, Quartile 2, N=5,380
Intercept 0.060 0.083 0.048 0.063
(0.002) (0.014) (0.017) (0.017)
IAV 0.263 0.192 0.384 0.475
(0.009) (0.005) (0.008) (0.005)
HAV 0.353 0.306 0.303 0.279
(0.005) (0.022) (0.006) (0.022)
R2 0.138 0.146 0.156 0.162


AR2 (IAV)


0.020 0.028


0.038 0.044










Table 2-5. Continued


IAV Methodology


Sample Used in Estimation E
Assets-to-Debt Ratio, Quartile 3, N=5,410
Intercept
(i
IAV
(i
HAV
(i
R2
AR2 (IAV)
Assets-to-Debt Ratio, Quartile 4, N = 5,352
Intercept
(i
IAV
(i
HAV
(R
R2


DIAV EIAV DIAV SIAV


0.062
0.002)
0.253
0.010)
0.398
0.006)
0.158
0.022

0.085
0.006)
0.206
0.033)
0.340
0.004)
0.199


0.092
(0.004)
0.145
(0.014)
0.379
(0.005)
0.152
0.016

0.115
(0.021)
0.130
(0.004)
0.328
(0.022)
0.174


0.059
(0.032)
0.317
(0.008)
0.358
(0.005)
0.167
0.031

0.084
(0.044)
0.263
(0.008)
0.291
(0.005)
0.208


0.079
(0.016)
0.295
(0.004)
0.354
(0.024)
0.160
0.024

0.107
(0.017)
0.214
(0.004)
0.297
(0.012)
0.185


0.044 0.019


0.053 0.029


AR2 (IAV)









Table 2-6. Average DD statistics by default status. A firm is considered 'Defaulted' if it
is delisted due to liquidation or performance, or files for bankruptcy in the
three years following the fourth quarter of 1982, 1985, 1988, 1991, 1994,
1997, and 2000. SIAV is the simple asset volatility, EIAV is the equity-
implied asset volatility, DIAV is the debt-implied asset volatility, and EDIAV
is the equity-an-debt-implied asset volatility. DD is the distance to default
measure calculated from the corresponding asset values and volatilities, and
represents the number of standard deviations required to push a firm into
default. Statistical significance at the 1, 5, and 10 percent level is denoted by
***, **, and respectively.
Average DD Calculated from
Default Status N SIAV EIAV DIAV EDIAV
Investment and Non-investment Grade Observations
All 1,795 3.29 2.89 1.30 1.39
Non-defaulting 1,760 3.32 2.91 1.32 1.40
Defaulting 35 2.06 1.65 0.72 0.89
Difference 1.25 *** 1.26 *** 0.59 *** 0.51 ***

Non-investment Grade Observations
All 519 2.45 1.92 0.86 1.01
Non-defaulting 489 2.48 1.94 0.87 1.02
Defaulting 30 1.90 1.52 0.68 0.83
Difference 0.58 *** 0.42 ** 0.19 0.19 ***












Table 2-7. Logit analysis of defaults. We estimate DFLT,,, = o + aDD,, + aControls, + s,, .These are the results from a logistic
regression on the sample of all 1,795 observations and the subsample of 519 non-investment-grade observations. The
dependent variable DFLT equals 1 if the firm is delisted due to liquidation or performance, or files for bankruptcy in the
three years following the fourth quarter of 1982, 1985, 1988, 1991, 1994, 1997, and 2000; it equals 0 otherwise.
DD_SIAV, DDEIAV, DD DIAV, and DDEDIAV are the distance-to-default measures calculated from the simple,
equity-implied, debt-implied, and equity-and-debt-implied asset volatilities respectively. P3-P8 are period indicator
variables. R2 is max-rescaled pseudo R2, which is an indicator of fit for logit models. A R2 is the marginal contribution of
each DD to R2. It is measured as the difference between R2 of a model including DD, and that of a base model excluding it.
Standard errors are reported in parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **
and respectively.
Investment and Non-investment Grade Observations Non-investment Grade Observations
SIAV EIAV DIAV EDIAV SIAV EIAV DIAV EDIAV
Intercept -3.350 *** -4.424 *** -4.590 *** -3.318 *** -3.028 *** -3.917 *** -3.817 *** -3.365 ***
(0.867) (0.789) (0.760) (0.887) (0.904) (0.777) (0.773) (0.855)
DD -1.001 *** -0.599 *** -0.932 *** -1.923 *** -0.659 ** -0.209 -0.451 -0.870 *
(0.240) (0.180) (0.253) (0.478) (0.306) (0.176) (0.290) (0.463)
P3 2.143 *** 1.973 ** 1.516 1.578 1.435 1.155 0.978 1.040
(0.816) (0.813) (0.808) (0.808) (0.874) (0.859) (0.852) (0.851)
P4 2.300 *** 1.776 ** 1.281 1.384 1.420 0.965 0.763 0.786
(0.842) (0.846) (0.843) (0.848) (0.913) (0.888) (0.900) (0.906)
P6 2.053 ** 1.811 ** 1.394 1.507 1.560 1.247 1.074 1.154
(0.832) (0.826) (0.827) (0.825) (0.859) (0.841) (0.835) (0.834)
P7 2.920 *** 3.056 *** 2.900 *** 2.833 *** 2.595 *** 2.519 *** 2.463 *** 2.512 ***
(0.837) (0.834) (0.834) (0.833) (0.881) (0.875) (0.872) (0.872)
P8 2.949 *** 3.291 *** 3.597 *** 3.249 *** 2.579 *** 2.852 *** 2.912 *** 2.830 ***
(0.830) (0.819) (0.809) (0.819) (0.852) (0.837) (0.831) (0.833)
SMALL 1.464 *** 1.299 ** 1.394 ** 1.055 1.273 ** 1.167 1.078 0.961
(0.562) (0.609) (0.603) (0.621) (0.616) (0.639) (0.650) (0.668)

R2 0.223 0.196 0.190 0.209 0.156 0.134 0.138 0.145
AR2 (DD) 0.073 0.046 0.040 0.059 0.029 0.007 0.011 0.018











Table 2-8. Median distance-to-default estimates by Moody's credit rating. Median
statistics are on the sample of 20,298 firm-quarters for the period 1975-2001.
SIAV is the simple asset volatility, EIAV is the equity-implied asset volatility,
DIAV is the debt-implied asset volatility, and EDIAV is the equity-an-debt-
implied asset volatility. DD is the distance to default measure calculated from
the corresponding asset values and volatilities. 'Prob of Default' comes from
Moody's Investors Service (2000) and is the average one-year default rate
over 1983-1999. For B3 and below average rates are calculated over 1998-
1999, the only two cohort years available so far for the Caa subcategories.
Prob of Default,
Moody's Credit Rating N 1983-1999 (%) DD_EDIAV DD_EIAV DD_DIAV DD_SIAV
Investment Grade
Aaa 1,070 0.00 2.11 3.71 2.16 4.02
Aal 358 0.00 1.48 3.63 1.56 3.89
Aa2 2,164 0.00 1.59 3.46 1.66 3.81
Aa3 1,151 0.10 1.53 3.18 1.58 3.53
Al 2,083 0.00 1.49 3.26 1.54 3.59
A2 4,532 0.00 1.54 3.04 1.52 3.48
A3 2,176 0.00 1.49 3.10 1.48 3.47
Baal 1,496 0.00 1.48 3.09 1.44 3.44
Baa2 2,283 0.10 1.41 2.88 1.34 3.32
Baa3 1,360 0.30 1.38 2.73 1.30 3.14

Non-Investment Grade
Bal 696 0.60 1.30 2.37 1.21 2.81
Ba2 914 0.50 1.21 2.13 1.16 2.57
Ba3 1,090 2.50 1.15 2.10 1.09 2.44
B1 2,905 3.50 1.01 1.62 0.91 2.18
B2 882 6.90 0.99 1.67 0.91 2.10
B3 479 8.04 0.95 1.53 0.88 1.87
Caal 17 10.78 0.74 0.95 0.54 1.64
Caa2 42 15.79 0.70 1.27 0.46 2.04
Caa3 1 28.87 0.71 1.15 0.58 1.68
Ca 2 N/A -0.26 0.14 -0.93 2.96












Table 2-9. Median changes in distance-to-default estimates by Moody's credit rating change. Median statistics are on the sample of
20,298 firm-quarters for the period 1975-2001. SIAV is the simple asset volatility, EIAV is the equity-implied asset
volatility, DIAV is the debt-implied asset volatility, and EDIAV is the equity-an-debt-implied asset volatility. dDD is the
quarterly change in the distance-to-default measure calculated from the corresponding asset values and volatilities.
Credit Rating Change N dDD EDIAV dDD EIAV dDD DIAV dDD SIAV
Downgrade Crossing the Investment Grade Boundary 107 -0.0483 0.0123 -0.0786 0.1546
Downgrade Without Crossing the Investment Grade Boundary 1,009 -0.0048 -0.0256 -0.0027 -0.0265
No Change 18,228 0.0036 0.0182 0.0038 0.0130
Upgrade Without Crossing the Investment Grade Boundary 855 0.0071 0.0434 0.0104 0.0541
Upgrade Crossing the Investment Grade Boundary 99 0.0509 0.0746 0.0889 0.0680










Table 2-10. Analysis of Moody's credit ratings. We estimate via OLS

RTGn = X + IDDt +n + kControlsk +e for the sample of
t,n 0 t,n k k,t,n t,n

25,701 firm-quarters for the period 1975-2001. Moody's rating of Aaa to Caa
is coded as 1 to 19 respectively, so that as ratings deteriorate, the dependent
variable increases. The dependent variable is not discrete since firm rating is
the average rating of its debt issues which does not have to be the same.
DD SIAV, DD EIAV, DD DIAV, and DD EDIAV are the distance-to-
default measures calculated from the simple, equity-implied, debt-implied,
and equity-and-debt-implied asset volatilities respectively. SIZE is the log of
the market value of assets. REG is an indicator variable that equals 1 if the
firm operates in a regulated industry during that quarter and 0 otherwise. AR2
is the contribution of DD to the R2 of a model including control variables
only. Standard errors are reported in parenthesis. Statistical significance at the
1, 5, and 10 percent level is denoted by ***, **, and respectively.
EDIAV EIAV DIAV SIAV
Investment and Non-Investment Grade Firms
Intercept 21.36 *** 21.23 *** 21.30 *** 21.60 ***
(0.25) (0.24) (0.25) (0.24)
DD -0.72 *** -0.65 *** -0.65 *** -0.60 ***
(0.01) (0.01) (0.01) (0.01)
SIZE -1.64 *** -1.56 *** -1.65 *** -1.56 ***
(0.01) (0.01) (0.01) (0.01)
REG -1.34 *** -1.06 *** -1.32 *** -0.92 ***
(0.21) (0.20) (0.21) (0.21)
R2 0.611 0.645 0.610 0.633
AR2 (DD) 0.036 0.070 0.035 0.058
Investment Grade Firms
Intercept 13.65 *** 14.08 *** 13.62 *** 14.18 ***
(0.23) (0.23) (0.23) (0.23)
DD -0.37 *** -0.33 *** -0.35 *** -0.31 ***
(0.01) (0.01) (0.01) (0.01)
SIZE -0.85 *** -0.87 *** -0.85 *** -0.85 ***
(0.01) (0.01) (0.01) (0.01)
REG -0.90 *** -0.74 *** -0.90 *** -0.62 ***
(0.17) (0.17) (0.17) (0.17)
R2 0.403 0.420 0.405 0.413
AR2 (DD) 0.032 0.049 0.034 0.042
Non-Investment Grade Firms
Intercept 16.48 *** 16.38 *** 16.26 *** 16.42 ***
(0.26) (0.26) (0.27) (0.27)
DD -0.75 *** -0.24 *** -0.43 *** -0.19 ***
(0.03) (0.01) (0.02) (0.01)
SIZE -0.41 *** -0.45 *** -0.45 *** -0.45 ***
(0.01) (0.01) (0.01) (0.01)
REG 0.20 -1.09 *** -0.40 -1.32 ***
(0.30) (0.29) (0.30) (0.29)
R2 0.366 0.351 0.342 0.337
AR2 (DD) 0.060 0.045 0.036 0.031










Table 2-11. Logit analysis of credit rating changes. We estimate
3 3
dRTG = o+ fli dDDti + 2DD 4, + f3j dRTGt +l4RTGt + fkControlst, +
t,n lo t-,,n 2 t-4,n 3j t-,n 4 t-4,n tn tn
i-- j=1 k
for the sample of 20,298 firm-quarters during the period 1975-2001. Moody's
rating change, dRTG, equals -1 if a firm is downgraded, 0 if the credit rating
remains the same, and 1 if the firm is upgraded. When credit rating change is
the dependent variable, we further distinguish between upgrades/downgrades
that cross the investment grade threshold (dRTG=2/dRTG=-2) and those that
do not (dRTG=1/dRTG=-1). The model estimates the probability of the lower
rating change values. dDD_SIAV, dDDEIAV, dDD_DIAV, and
dDD EDIAV are quarterly changes in the distance-to-default measures
calculated from the simple, equity-implied, debt-implied, and equity-and-debt-
implied asset volatilities respectively. SIZE is the log of the market value of
assets. Lags of variables are so indicated. Indicator variables are not presented
for ease of exposition. The model's fit is indicated by the max rescaled pseudo
R2. AR2 is the contribution of all lags of DD and dDD to R2 of a model
including all but these variables. Standard errors are reported in parenthesis.
Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **,
and respectively.
Credit Rating Downgrades Credit Rating Upgrades
Variable SIAV EIAV DIAV EDIAV SIAV EIAV DIAV EDIAV
Intercept -5.77 *** -5.72 *** -5.82 *** -5.84 *** 9.29 *** 9.91*** 9.75 *** 9.71 ***
(1.11) (1.11) (1.11) (1.11) (0.61) (0.62) (0.61) (0.61)
dDD lagl -0.25 *** -0.30 *** -0.25 *** -0.33 *** 0.02 -0.06 -0.07 -0.06
(0.04) (0.04) (0.06) (0.08) (0.05) (0.05) (0.06) (0.07)
dDD lag2 -0.44 *** -0.48 *** -0.29 *** -0.41 *** 0.06 -0.05 -0.13 ** -0.12
(0.05) (0.05) (0.07) (0.09) (0.05) (0.05) (0.07) (0.09)
dDD lag3 -0.34 *** -0.34 *** -0.39 *** -0.45 *** 0.02 -0.12 ** -0.19 *** -0.18 **
(0.05) (0.05) (0.07) (0.09) (0.05) (0.05) (0.07) (0.09)
DD lag4 -0.28 *** -0.29 *** -0.47 *** -0.50 *** 0.04 -0.11*** -0.13 ** -0.12
(0.04) (0.04) (0.06) (0.08) (0.04) (0.04) (0.06) (0.08)
SIZE 0.18 *** 0.15 *** 0.16 *** 0.17 *** -0.62 *** -0.62 *** -0.61 *** -0.61 ***
(0.03) (0.03) (0.03) (0.03) (0.04) (0.04) (0.04) (0.04)
dRTG lagI -0.07 -0.04 -0.07 -0.08 0.05 0.06 0.06 0.06
(0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08)
dRTG lag2 -0.25 *** -0.23 *** -0.24 *** -0.25 *** 0.05 0.06 0.07 0.06
(0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08)
dRTG lag3 -0.23 *** -0.22 *** -0.22 ** -0.23 *** -0.10 -0.08 -0.08 -0.08
(0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08)
RTG lag4 -0.01 -0.02 -0.02 -0.01 -0.27 *** -0.29 *** -0.28 *** -0.28 ***
(0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01)

R2 0.096 0.099 0.092 0.090 0.155 0.156 0.156 0.155
AR2 (dDD and DD) 0.013 0.016 0.009 0.007 0.000 0.001 0.001 0.001











Table 2-12. Average statistics by Z-score deciles. Z-score is a measure of default
probability proposed by Altman (1969) where a higher Z implies lower
default probability. SIAV is the simple implied asset volatility, EIAV is the
equity-implied asset volatility, DIAV is the debt-implied asset volatility, and
EDIAV is the equity-an-debt-implied asset volatility. DD is the distance to
default measure calculated from the corresponding asset values and
volatilities.
Z-Score Decile N DD EDIAV DD EIAV DD DIAV DD SIAV
All 23,600 1.40 2.79 1.36 3.14
1 2,409 1.11 2.37 0.85 2.93
2 2,354 1.28 3.29 1.03 3.72
3 2,364 1.31 2.63 1.11 3.19
4 2,358 1.36 2.48 1.22 3.02
5 2,344 1.45 2.59 1.37 3.04
6 2,373 1.48 2.73 1.44 3.10
7 2,369 1.49 2.81 1.49 3.12
8 2,352 1.50 2.89 1.55 3.17
9 2,366 1.46 2.98 1.56 3.18
10 2,311 1.38 3.06 1.54 3.17













Table 2-13. Analysis of Z-score. We estimate via OLS Z n = O +. DD, + Y Ok Controlsk + n for the sample of 23,600
t,n 0 i t, n + kok k,t,n t,fn

firm-quarter observations for 1975-2001. The dependent variable is Z-Score as calculated in Altman (1969) and is a
measure of default probability based on accounting reports. A higher Z-Score implies lower probability of default. SIZE is
the log of market value of assets. REG is an indicator variable that equals one if the firm operates in an industry regulated
during the quarter in question. DD_SIAV, DDEIAV, DD DIAV, and DD_EDIAV are the distance-to-default measures
calculated from the simple, equity-implied, debt-implied, and equity-and-debt-implied asset volatilities and values
respectively. Control variables (industry and year-quarter indicator variables) are not presented for ease of exposition. AR2
(DD) is the contribution of DD to the R2 of a model including all but these variables. Standard errors are reported in
parenthesis. Statistical significance at the 1, 5, and 10 percent level is denoted by ***, **, and respectively.
Industry Fixed Effects Firm Fixed Effects
EDIAV EIAV DIAV SIAV EDIAV EIAV DIAV SIAV
Low Z-Score Firms
DD 0.090 *** 0.053 *** 0.082 *** 0.039 *** 0.029 *** 0.042 *** 0.032 *** 0.022 ***
(0.005) (0.003) (0.004) (0.003) (0.004) (0.003) (0.003) (0.003)
SIZE 0.011 *** 0.012 *** 0.012 *** 0.015 *** 0.090 *** 0.081 *** 0.089 *** 0.085 ***
(0.003) (0.003) (0.003) (0.003) (0.009) (0.009) (0.009) (0.009)
REG -0.003 -0.006 -0.001 -0.013 -0.084 -0.082 -0.077 -0.094 *
(0.032) (0.032) (0.032) (0.032) (0.049) (0.049) (0.049) (0.049)

R2 0.240 0.241 0.247 0.231 0.709 0.714 0.710 0.709
AR2 (DD) 0.021 0.021 0.027 0.011 0.002 0.007 0.003 0.002

High Z-Score Firms
DD -0.111 *** 0.019 ** 0.024 ** -0.058 *** -0.036 *** 0.049 *** 0.014 0.012 *
(0.014) (0.009) (0.011) (0.008) (0.010) (0.007) (0.008) (0.006)
SIZE 0.147 *** 0.123 *** 0.123 *** 0.142 *** 0.611 *** 0.613 *** 0.611 *** 0.613 ***
(0.007) (0.007) (0.007) (0.006) (0.017) (0.017) (0.017) (0.017)
REG 0.275 0.194 0.176 0.204 -0.354 -0.345 -0.337 -0.347 *
(0.210) (0.210) (0.210) (0.210) (0.190) (0.190) (0.190) (0.190)

R2 0.218 0.214 0.214 0.217 0.730 0.731 0.729 0.729
AR2 (DD) 0.004 0.000 0.000 0.003 0.000 0.001 0.000 0.000













Table 2-14. Analysis of Z-score changes. We estimate via OLS d2


3
,n 0 + E dDD +0 Controls,
t,n = 0 0 1 t-i, n k k, t, n
i=1 k


+ E on the


sample of 19,800 firm-quarter observations for 1975-2001. The dependent variable is Altman's (1969) Z-Score. A higher
Z-Score implies a lower probability of default. SIZElag is the one quarter lag of the log of market value of assets. REG is
an indicator variable that equals one if the firm operates in an industry regulated during the quarter in question. DD_SIAV,
DDEIAV, DD_DIAV, and DD_EDIAV are the distance-to-default measures calculated from the simple, equity-implied,
debt-implied, and equity-and-debt-implied asset volatilities and values respectively. Control variables (industry and year-
quarter indicator variables) are not presented for ease of exposition. AR2 (DD) is the contribution of all lags of dDD to the
R2 of a model including all but these variables. Standard errors are reported in parenthesis. Statistical significance at the 1,
5, and 10 percent level is denoted by ***, **, and respectively.
Industry Fixed Effects Firm Fixed Effects
SIAV EIAV DIAV EDIAV SIAV EIAV DIAV EDIAV
Negative Z Score Changes
dDD_lagI 0.010 *** 0.013 *** 0.008 ** 0.008 0.000 0.003 0.001 0.001
(0.003) (0.003) (0.004) (0.005) (0.003) (0.002) (0.003) (0.002)
dDD_lag2 0.008 ** 0.011 *** 0.007 0.009 0.002 0.004 0.002 0.000
(0.003) (0.004) (0.004) (0.005) (0.003) (0.003) (0.003) (0.002)
dDD_lag3 0.004 0.006 0.003 0.004 0.001 0.003 0.001 0.002
(0.003) (0.003) (0.004) (0.004) (0.003) (0.002) (0.002) (0.002)
dZ_lagI -0.186 *** -0.188 *** -0.186 *** -0.186 *** -0.338 *** -0.340 *** -0.338 *** -0.338 ***
(0.009) (0.009) (0.009) (0.009) (0.010) (0.010) (0.010) (0.010)
dZ_lag2 -0.122 *** -0.124 *** -0.122 *** -0.122 *** -0.213 *** -0.215 *** -0.213 *** -0.213 ***
(0.009) (0.009) (0.009) (0.009) (0.011) (0.011) (0.011) (0.011)
dZ_lag3 -0.122 *** -0.123 *** -0.122 *** -0.122 *** -0.145 *** -0.147 *** -0.145 *** -0.145 ***
(0.009) (0.009) (0.009) (0.009) (0.010) (0.010) (0.010) (0.010)
SIZE 0.007 *** 0.007 *** 0.007 *** 0.007 *** -0.044 *** -0.044 *** -0.044 *** -0.044 ***
(0.002) (0.002) (0.002) (0.002) (0.009) (0.009) (0.009) (0.009)
REG 0.038 0.038 0.040 0.040 0.059 0.059 0.058 0.059
(0.032) (0.032) (0.032) (0.032) (0.044) (0.044) (0.044) (0.044)

R2 0.1748 0.1754 0.1743 0.1742 0.3355 0.3357 0.3355 0.3356
AR (dDD) 0.0010 0.0017 0.0006 0.0004 0.0001 0.0003 0.0001 0.0001













Table 2-14. Continued
Industry Fixed Effects Firm Fixed Effects
SIAV EIAV DIAV EDIAV SIAV EIAV DIAV EDIAV
Positive Z Score Changes
dDD_lagI -0.001 0.000 0.001 0.001 0.007 0.010 ** 0.005 0.008 *
(0.003) (0.003) (0.003) (0.004) (0.008) (0.005) (0.006) (0.005)
dDD_lag2 0.001 0.003 0.001 0.001 0.001 0.009 0.002 0.006
(0.003) (0.003) (0.003) (0.004) (0.009) (0.006) (0.007) (0.005)
dDD_lag3 0.003 0.004 -0.001 -0.001 0.001 0.011 ** 0.002 0.008 *
(0.003) (0.003) (0.003) (0.004) (0.008) (0.005) (0.006) (0.005)
dZlagI -0.047 *** -0.048 *** -0.048 *** -0.048 *** -0.272 *** -0.273 *** -0.272 *** -0.272 ***
(0.009) (0.009) (0.009) (0.009) (0.011) (0.011) (0.011) (0.011)
dZ_lag2 0.007 0.007 0.007 0.008 -0.142 *** -0.143 *** -0.142 *** -0.142 ***
(0.009) (0.009) (0.009) (0.009) (0.011) (0.011) (0.011) (0.011)
dZ_lag3 0.006 0.006 0.007 0.007 -0.143 *** -0.144 *** -0.143 *** -0.143 ***
(0.008) (0.008) (0.008) (0.008) (0.011) (0.011) (0.011) (0.011)
SIZE -0.011 *** -0.011 *** -0.011 *** -0.011 *** 0.041 *** 0.042 *** 0.041 *** 0.042 ***
(0.002) (0.002) (0.002) (0.002) (0.014) (0.014) (0.014) (0.014)
REG -0.010 -0.010 -0.009 -0.009 0.125 0.115 0.126 0.117
(0.029) (0.029) (0.029) (0.029) (0.149) (0.149) (0.149) (0.149)

R2 0.1107 0.1107 0.1105 0.1105 0.2281 0.2287 0.2281 0.2285


AR2 (dDD) 0.0002


AR (dDD) 0.0002 0.0002 0.0000 0.0000 0.000 1 0.0006 0.0001 0.0004


0.0002 0.0000 0.0000 0.0001


0.0006 0.0001 0.0004













Table 2-15. Sensitivity of summary statistics to alternative input assumptions. SIAV is the simple implied asset volatility calculated by
de-levering historical equity volatility. EIAV is the equity-implied asset volatility calculated from equity prices and
historical equity volatility. DIAV is the debt-implied asset volatility calculated from debt prices and historical equity
volatility. EDIAV is the equity-and-debt-implied asset volatility calculated from contemporaneous equity and debt prices.
Implied asset volatilities are reported in percent per year. VSIAV, VEIAV, VDIAV, and VEDIAV are the
corresponding estimates of the market value of assets in billion dollars. DD_SIAV, DDEIAV, DD_DIAV, and
DD EDIAV are the corresponding distance-to-default measures.


Time to Firm Resolution
Weighted Average Debt Weighted Average Debt
Duration Maturity
Median Mean Median Mean
2.92 8.35 2.91 8.31
2.21 6.55 1.79 5.57
2.20 6.66 1.88 6.03
2.22 6.59 1.81 5.63


14.7
20.0
21.1
22.8

3.18
1.68
1.29
1.31


Default Point


95% of Total Debt
Median Mean
2.90 8.16
2.74 7.69
2.20 6.28
2.74 7.69


16.8
28.2
26.0
26.6

3.86
1.29
1.45
1.27


16.9
18.1
23.0
31.7

5.09
4.32
2.07
2.15


99% of Total Debt
Median Mean
2.90 8.15
2.77 7.76
2.21 6.31
2.77 7.76


14.8
15.7
20.2
29.5

4.83
4.17
1.86
1.99


Issuer Yield
Weighted Averge Issue
Yields Largest Issue's Yield
Median Mean Median Mean
2.91 8.29 2.91 8.28
2.82 8.01 2.82 8.00
2.23 6.46 2.23 6.45
2.82 8.00 2.82 7.99


14.8
15.5
20.3
30.0

4.83
4.36
1.88
2.00


4.83
4.36
1.89
2.00


16.9
17.7
23.1
32.4

5.08
4.66
2.15
2.21


N 28236 28A13 27350 27354 27335 27317


V SIAV
V EIAV
V DIAV
V EDIAV

SIAV
EIAV
DIAV
EDIAV

DD SIAV
DD EIAV
DD DIAV
DD EDIAV


N 28.236 28.113


27.750 27.754


27.735 27.717













Table 2-15. Continued
Tax Adjustment Debt Priority
Senior (Junior) Bonds Credit Spreads
Moody's AAA-Rated All Debt Assumed Senior (Junior) to Calculated from Non-
None Yield Senior Remaining Debt Callable Bonds Only
Median Mean Median Mean Median Mean Median Mean Median Mean
V SIAV 2.91 8.32 5.32 12.09 2.88 8.23 1.71 4.17 5.76 13.75
V EIAV 2.83 8.06 5.18 11.64 2.75 7.83 1.52 3.89 5.64 13.30
V DIAV 2.18 6.35 4.83 11.26 2.03 5.88 1.07 2.75 4.34 10.86
V EDIAV 2.82 8.04 5.18 11.64 2.73 7.78 1.51 3.88 5.63 13.29

SIAV 14.8 16.9 14.8 16.2 14.8 17.0 25.1 27.1 13.9 15.3
EIAV 15.5 17.7 15.4 16.8 15.8 18.0 27.6 30.7 14.3 15.8
DIAV 20.9 23.6 16.7 18.1 23.8 27.0 43.3 43.1 18.9 21.2
EDIAV 31.5 33.8 20.3 21.8 38.6 40.8 49.5 49.6 28.9 30.7

DD SIAV 4.81 5.06 5.22 5.54 4.82 5.06 3.38 3.66 5.29 5.56
DD EIAV 4.36 4.66 4.78 5.09 4.15 4.42 2.76 2.99 4.90 5.20
DD DIAV 1.82 1.97 4.22 4.20 1.13 1.47 1.02 1.43 2.12 2.38
DD EDIAV 1.94 2.05 4.61 4.02 1.41 1.65 1.08 1.33 2.22 2.46

N 27,740 7,425 27,802 27,412 10,031











Table 2-16. Analysis of IAV and HAV forecasting properties under alternative
assumptions. We estimate RAV,,, = ,0 + 5,Voaltility Forecast,,, + ,,.

Volatility forecast is one of the five: SIAV, EIAV, DIAV, EDIAV, or HAV.
SIAV is the simple implied asset volatility calculated by de-levering historical
equity volatility. EIAV is the equity-implied asset volatility calculated from
equity prices and historical equity volatility. DIAV is the debt-implied asset
volatility calculated from debt prices and historical equity volatility. EDIAV
is the equity-and-debt-implied asset volatility calculated from
contemporaneous equity and debt prices. HAV is an estimate of annualized
historical asset volatility calculated over the year prior to the end of each
quarter. RAV is an estimate of annualized realized asset volatility over the
two years following each quarter-end. Standard errors are reported in
parenthesis. All coefficient estimates are statistically significant at the 1


Time to Resolution
Intercept

Slope

R 2
Default Point
Intercept

Slope

R 2
Issuer Yield
Intercept

Slope

R 2
Tax Adjustment
Intercept

Slope


percent level.
EDIAV EIAV DIAV SIAV HAV
Average Duration of Traded Debt
0.095 0.114 0.075 0.103 0.122
(0.002) (0.002) (0.002) (0.002) (0.001)
0.382 0.305 0.498 0.496 0.331
(0.010) (0.006) (0.010) (0.010) (0.005)
0.062 0.083 0.095 0.100 0.132
95% of Total Debt
0.109 0.106 0.097 0.104 0.123
(0.002) (0.002) (0.002) (0.002) (0.001)
0.242 0.447 0.395 0.491 0.329
(0.007) (0.009) (0.008) (0.010) (0.005)
0.052 0.096 0.093 0.097 0.131


Weighted Average Issue Yield
0.110 0.107 0.097 0.104 0.123
(0.002) (0.002) (0.002) (0.002) (0.001)
0.239 0.449 0.393 0.491 0.328
(0.007) (0.009) (0.008) (0.010) (0.005)
0.051 0.096 0.092 0.097 0.130
None
0.109 0.107 0.097 0.104 0.123
(0.002) (0.002) (0.002) (0.002) (0.001)
0.231 0.449 0.382 0.491 0.329
(0.007) (0.009) (0.008) (0.010) (0.005)
0.049 0.096 0.090 0.097 0.131


EDIAV EIAV DIAV SIAV HAV
Average Maturity of Traded Debt
0.106 0.116 0.090 0.104 0.112
(0.003) (0.002) (0.003) (0.002) (0.001)
0.298 0.244 0.369 0.490 0.391
(0.009) (0.006) (0.009) (0.010) (0.006)
0.044 0.066 0.064 0.098 0.157
99% of Total Debt
0.108 0.107 0.096 0.104 0.124
(0.002) (0.002) (0.002) (0.002) (0.001)
0.243 0.450 0.396 0.490 0.328
(0.007) (0.009) (0.008) (0.010) (0.005)
0.052 0.096 0.093 0.097 0.130


Largest Isssue Yield
0.109 0.107 0.097 0.104 0.123
(0.002) (0.002) (0.002) (0.002) (0.001)
0.240 0.449 0.395 0.491 0.328
(0.007) (0.009) (0.008) (0.010) (0.005)
0.051 0.096 0.092 0.097 0.130
Average Yield on Moody's AAA-rated Bonds
0.124 0.102 0.100 0.101 0.088
(0.004) (0.004) (0.004) (0.004) (0.003)
0.231 0.426 0.415 0.453 0.501
(0.017) (0.020) (0.022) (0.022) (0.012)
0.028 0.064 0.054 0.063 0.208


Debt Priority All Debt Assumed Senior Senior Bonds Assumed Senior to all other Debt
Intercept 0.094 0.107 0.089 0.104 0.123 0.107 0.107 0.099 0.101 0.123
(0.003) (0.002) (0.002) (0.002) (0.001) (0.003) (0.002) (0.003) (0.002) (0.001)
Slope 0.230 0.453 0.370 0.495 0.332 0.158 0.261 0.202 0.318 0.333
(0.006) (0.009) (0.007) (0.010) (0.006) (0.006) (0.006) (0.006) (0.007) (0.006)
R2 0.061 0.100 0.103 0.102 0.133 0.032 0.067 0.045 0.073 0.134
Non-callable Bonds Only
Intercept 0.107 0.092 0.094 0.091 0.092
(0.004) (0.003) (0.003) (0.003) (0.002)
Slope 0.200 0.477 0.349 0.504 0.451
(0.011) (0.017) (0.014) (0.018) (0.010)
R2 0.036 0.080 0.067 0.078 0.177


R











Table 2-17. Logit analysis of defaults under alternative assumptions. We estimate the
logistic regression DFLT,,, = ac + acDD,, + aControls,,, + ,,, on the sample of
all 1,795 observations and the subsample of 519 non-investment-grade
observations. The dependent variable DFLT equals 1 if the firm is delisted
due to liquidation or performance, or files for bankruptcy in the three years
following the fourth quarter of 1982, 1985, 1988, 1991, 1994, 1997, and 2000;
it equals 0 otherwise. DD_SIAV, DD_EIAV, DD_DIAV, and DD_EDIAV
are the distance-to-default measures calculated from the simple, equity-
implied, debt-implied, and equity-and-debt-implied asset volatilities
respectively. R2 is max-rescaled pseudo R2, which is an indicator of fit for
logit models. A R2 is the marginal contribution of each DD to R2, which is the
difference between R2 of a model including DD, and that of a base model
excluding it.
Investment and Non-investment Grade Non-investment Grade
Observations Observations
DD SIAV DD EIAV DD DIAV DD EDIAV DD SIAV DD EIAV DD DIAV DD EDIAV
Time to Resolution: Weighted Average Duration of Traded Debt


R2 0.227 0.168 0.156
AR2 (DD) 0.079 0.020 0.008
Time to Resolution: Weighted Average Maturity
R2 0.208 0.151 0.139
AR2 (DD) 0.077 0.020 0.007
Deafult Point: 95% of Total Debt
R2 0.212 0.197 0.189
AR2 (DD) 0.062 0.047 0.039
Deafult Point: 99% of Total Debt
R2 0.235 0.192 0.185
AR (DD) 0.085 0.043 0.036
Issuer Yield: Weighted Average Issue Yields
R2 0.223 0.196 0.191
AR (DD) 0.073 0.046 0.042
Issuer Yield: Largest Issue Yield
R2 0.223 0.196 0.190
AR (DD) 0.073 0.046 0.041


Tax Adjustment: None
R2 0.222
AR (DD) 0.073
Tax Adjustment: Average
R2 0.489
AR (DD) 0.011


0.196
0.047
Yield on
0.478
0.001


Debt Priority: All Debt Assumed S
R2 0.230 0.196
AR (DD) 0.075 0.041
Debt Priority: Senior (Junior) Bond
R2 0.244 0.241
AR (DD) 0.087 0.084


Non-callable Bonds Only
R2 0.344
AR (DD) 0.010


0.156
0.008
of Traded Debt
0.137
0.006

0.204
0.054

0.203
0.054

0.211
0.061

0.209
0.060


0.182 0.193
0.032 0.043
Moody's AAA-rated Bonds
0.511 0.514
0.034 0.037
senior
0.198 0.233
0.043 0.078
Is Assumed Senior (Junior) t(
0.197 0.215
0.040 0.057


0.335 0.425 0.411
0.000 0.090 0.077


0.158 0.143 0.131 0.134
0.034 0.018 0.006 0.009

0.136 0.128 0.112 0.113
0.033 0.024 0.008 0.009

0.149 0.134 0.137 0.143
0.022 0.007 0.010 0.016

0.165 0.134 0.139 0.148
0.038 0.007 0.012 0.021

0.156 0.134 0.138 0.146
0.029 0.007 0.011 0.019

0.156 0.134 0.139 0.146
0.029 0.007 0.012 0.019

0.156 0.134 0.138 0.145
0.029 0.007 0.011 0.019

0.590 0.576 0.598 0.586
0.039 0.025 0.046 0.034


0.164
0.032
Remaining
0.180
0.043


0.141
0.008
Debt
0.174
0.037


0.156 0.178
0.024 0.046

0.150 0.160
0.013 0.023


0.392 0.414 0.402 0.361
0.056 0.078 0.066 0.025










Table 2-18. Analysis of Moody's credit ratings under alternative assumptions. We

estimate RTG,n = +1 DDtn + k Controlsk, n +t, via OLS for

the sample of 25,701 observations over 1975-2001. Moody's rating of Aaa to
Caa is coded as 1 to 19 respectively, so that as ratings deteriorate, the
dependent variable increases. The dependent variable is not discrete since firm
rating is the average rating of its debt issues which does not have to be the
same. DD SIAV, DD EIAV, DD DIAV, and DD EDIAV are the distance-
to-default measures calculated from the simple, equity-implied, debt-implied,
and equity-and-debt-implied asset volatilities respectively. AR2 is the
contribution of DD to the R2 of a model including control variables only.
Standard errors are reported in parenthesis. Statistical significance at the 1, 5,
and 10 percent level is denoted by ***, **, and respectively.
All Observations
DD SIAV DD EIAV DD DIAV DD EDIAV
Time to Resolution: Weighted Average Duration of Traded Debt
R2 0.590 0.636 0.615 0.627
AR2 (DD) 0.000 0.047 0.026 0.038
Time to Resolution: Weighted Average Maturity of Traded Debt
R2 0.607 0.643 0.622 0.629
AR2 (DD) 0.000 0.035 0.015 0.022
Deafult Point: 95% of Total Debt
R2 0.638 0.662 0.618 0.629
AR2 (DD) 0.060 0.085 0.040 0.052
Deafult Point: 99% of Total Debt
R2 0.636 0.655 0.614 0.623
AR2 (DD) 0.060 0.079 0.038 0.047
Issuer Yield: Weighted Average Issue Yields
R2 0.633 0.645 0.616 0.616
AR2 (DD) 0.059 0.070 0.041 0.041
Issuer Yield: Largest Issue Yield
R2 0.633 0.645 0.609 0.611
AR2 (DD) 0.059 0.070 0.035 0.037
Tax Adjustment: None
R2 0.634 0.644 0.601 0.604
AR2 (DD) 0.060 0.070 0.027 0.030
Tax Adjustment: Average Yield on Moody's AAA-rated Bonds
R2 0.453 0.476 0.486 0.440
AR2 (DD) 0.063 0.086 0.096 0.050
Debt Priority: All Debt Assumed Senior
R2 0.636 0.659 0.622 0.630
AR2 (DD) 0.056 0.079 0.042 0.050
Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remaining Debt
R2 0.628 0.637 0.621 0.624
AR2 (DD) 0.016 0.025 0.010 0.012
Non-callable Bonds Only
R2 0.488 0.498 0.499 0.497
AR2 (DD) 0.073 0.083 0.083 0.082











Table 2-18. Continued
Investment-Grade Firms Non-Investment-Grade Firms
DD SIAV DD EIAV DD DIAV DD EDIAV DD SIAV DD EIAV DD DIAV DD EDIAV


Time to Resolution: Weighted Average Duration of Traded Debt
R2 0.376 0.408 0.400 0.406
AR2 (DD) 0.000 0.032 0.024 0.030
Time to Resolution: Weighted Average Maturity of Traded Debt
R2 0.391 0.415 0.406 0.409
AR2 (DD) 0.000 0.025 0.016 0.018
Deafult Point: 95% of Total Debt
R2 0.418 0.437 0.413 0.418
AR2 (DD) 0.044 0.063 0.039 0.044
Deafult Point: 99% of Total Debt
R2 0.417 0.430 0.409 0.413
AR2 (DD) 0.044 0.058 0.036 0.041
Issuer Yield: Weighted Average Issue Yields
R2 0.413 0.420 0.413 0.410
AR2 (DD) 0.043 0.050 0.043 0.039
Issuer Yield: Largest Issue Yield
R2 0.413 0.420 0.403 0.402
AR2 (DD) 0.042 0.050 0.033 0.031
Tax Adjustment: None
R2 0.412 0.418 0.389 0.389
AR2 (DD) 0.043 0.049 0.020 0.020
Tax Adjustment: Average Yield on Moody's AAA-rated Bonds
R2 0.402 0.425 0.410 0.385
AR2 (DD) 0.039 0.062 0.047 0.022
Debt Priority: All Debt Assumed Senior


0.412 0.429 0.415 0.419
0.041 0.058 0.044 0.048


Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remaini
R2 0.431 0.441 0.430 0.436
AR2 (DD) 0.019 0.029 0.018 0.024
Non-callable Bonds Only


0.442 0.451 0.464 0.458
0.034 0.044 0.057 0.050


AR (DD)


AR2 (DD)


0.318 0.358 0.342 0.363
0.000 0.040 0.024 0.045

0.337 0.369 0.352 0.364
0.000 0.032 0.015 0.027

0.340 0.367 0.348 0.383
0.032 0.060 0.040 0.075

0.339 0.362 0.346 0.376
0.031 0.054 0.039 0.069

0.337 0.351 0.339 0.362
0.031 0.045 0.033 0.056

0.337 0.351 0.335 0.355
0.031 0.045 0.029 0.049

0.338 0.351 0.344 0.365
0.032 0.045 0.038 0.059

0.533 0.531 0.541 0.546
0.007 0.006 0.016 0.020

0.344 0.368 0.350 0.386
0.031 0.055 0.037 0.073
ng Debt
0.315 0.320 0.312 0.311
0.004 0.009 0.001 0.000

0.506 0.503 0.494 0.498
0.023 0.020 0.011 0.015











Table 2-19. Analysis of credit rating changes under alternative assumptions. We estimate
the logit model
3 3
dRTG =i+ B-dt.DD I l 2 4, k Controls +
dRTGt,n o + l t dDDt -i,n 2DDt -4,n 3 l3dRTGt ,n +4RTGt 4,n kConrolst,n t,n
=1 =1 k
for the period 1975-2001. Moody's rating change, dRTG, equals -1 if a firm is
downgraded, 1 if it is upgraded, and 0 if its rating remains the same. When
rating change is the dependent variable, we further distinguish upgrades and
downgrades that cross the investment grade threshold from those that do not.
The model estimates the probability of the lower rating change values.
dDD_SIAV, dDD_EIAV, dDD_DIAV, and dDD EDIAV are quarterly
changes in the distance-to-default measures calculated from the simple,
equity-implied, debt-implied, and equity-and-debt-implied asset volatilities
respectively. Lags of variables are so indicated. The model's fit is measured
by the max re-scaled pseudo R2. AR2 is the contribution of all lags of DD and
dDD to the R2 of a model including all but these variables.
Credit Rating Downgrades Credit Rating Upgrades
DD SIAV DD EIAV DD DIAV DD EDIAV DD SIAV DD EIAV DD DIAV DD EDIAV
Time to Resolution: Weighted Average Duration of Traded Debt


R2 0.0919 0.0934 0.0854 0.0899
AR (DD) 0.0136 0.0151 0.0071 0.0116
Time to Resolution: Weighted Average Maturity of Traded Debt
R2 0.0916 0.0953 0.0866 0.0910
AR2 (DD) 0.0134 0.0171 0.0084 0.0128
Deafult Point: 95% of Total Debt
R2 0.0934 0.0988 0.0916 0.0888
AR (DD) 0.0104 0.0158 0.0086 0.0058
Deafult Point: 99% of Total Debt
R2 0.0991 0.0997 0.0939 0.0920
AR (DD) 0.0153 0.0159 0.0101 0.0082
Issuer Yield: Weighted Average Issue Yields
R2 0.0964 0.0995 0.0961 0.0948
AR (DD) 0.0130 0.0161 0.0127 0.0114
Issuer Yield: Largest Issue Yield
R2 0.0959 0.0990 0.0928 0.0906
AR (DD) 0.0129 0.0159 0.0098 0.0076
Tax Adjustment: None
R2 0.0953 0.0982 0.0924 0.0892
AR (DD) 0.0128 0.0157 0.0098 0.0066
Tax Adjustment: Average Yield on Moody's AAA-rated Bonds
R2 0.0874 0.0986 0.1097 0.1064
AR (DD) 0.0010 0.0122 0.0233 0.0200


Debt Priority: All Debt Assumed Senior
R2 0.0956 0.0983
AR (DD) 0.0129 0.0155


0.0926 0.0909
0.0098 0.0082


Debt Priority: Senior (Junior) Bonds Assumed Senior (Junior) to Remainin
R2 0.0935 0.1132 0.0857 0.0916
AR (DD) 0.0165 0.0362 0.0087 0.0146
Non-callable Bonds Only
R2 0.1387 0.1561 0.1262 0.1202
AR (DD) 0.0323 0.0496 0.0198 0.0137


0.1572 0.1591 0.1587 0.1607
0.0004 0.0023 0.0019 0.0038

0.1589 0.1589 0.1590 0.1595
0.0003 0.0003 0.0005 0.0009

0.1552 0.1561 0.1556 0.1552
0.0006 0.0014 0.0010 0.0005

0.1551 0.1564 0.1562 0.1555
0.0002 0.0015 0.0013 0.0006

0.1554 0.1565 0.1559 0.1557
0.0004 0.0015 0.0009 0.0007

0.1553 0.1564 0.1558 0.1554
0.0004 0.0015 0.0009 0.0005

0.1551 0.1562 0.1559 0.1554
0.0003 0.0014 0.0010 0.0006

0.1563 0.1539 0.1523 0.1542
0.0055 0.0031 0.0016 0.0034

0.1544 0.1555 0.1572 0.1561
0.0008 0.0019 0.0036 0.0025
g Debt
0.1628 0.1642 0.1639 0.1646
0.0006 0.0020 0.0017 0.0024


0.1643 0.1599 0.1619
0.0009 -0.0035 -0.0015


0.1732
0.0098









84






06




05




04




S03






01




0






Quarter

-*-SIAV --EIAV DIAV EDIAV



Figure 2-1. Median implied asset volatility over 1975-2001


















0.5

0.4E

0.4

0.35

0.23

IAV 0.2.

0.1

0.1$

01 EDIAV

0.0 DIAV


1 2 SIAV
3
Asset/Debt Ratio Quartiles




Figure 2-2. Median implied asset volatility by assets-to-debt ratio quartile

























3-

2-
2: -- I --





0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

ON ON
Quarter

--DDSIAV -- DDEIAV DDDIAV DD EDIAV

Figure 2-3. Median distance to default over 1975-2001














CHAPTER 3
BANK RISK REFLECTED IN SECURITY PRICES: EQUITY AND DEBT MARKET
INDICATORS OF BANK CONDITION

3.1. Introduction

The banking industry is one of the most heavily regulated industries in the U.S.

There are two commonly cited reasons for this extensive oversight. Banks play an

important role in the economy, which creates the concern that bank failures might have a

ripple effect and de-stabilize the financial system. In addition, bank claimholders are

thought to be unable or unwilling to curb a bank's appetite for risk. These widely held

beliefs have resulted in a complex set of government regulations that attempt to limit the

risk-taking activities of banking firms. It was not until recently that bank supervisors

warmed up to the idea that market discipline can aid them in this task:

The real pre-safety-net discipline was from the market, and we need to adopt
policies that promote private counterpart supervision as the first line of defense
for a safe and sound banking system. (Greenspan, 2001)

Regulators have started to view market discipline as a desirable and necessary

supplement to government oversight. Market discipline was proposed as one of the three

pillars discussed in the Basel II proposal, and the Gramm-Leach-Bliley legislation

required the study of mandatory subordinated debt proposals as a tool of improving

market discipline.

In order to determine whether market discipline can deliver the benefits ascribed to

it, researchers have examined whether the information in bank-issued securities is









accurate and timely, and whether it can improve supervisory assessments.1 The general

consensus is that bank risk is reflected in the valuation of all the securities that a bank

issues. Most studies focus on the information in uninsured liabilities. They document a

positive contemporaneous association between bank subordinated debt yields or large

deposit rates, and indicators of risk (Evanoff and Wall 2002, Hall et al. 2002, Jagtiani and

Lemieux 2000, Jagtiani and Lemieux 2001, Jagtiani et al. 2002, Krishnan et al. 2003,

Morgan and Stiroh 2001, Sironi 2002). Although there are fewer studies that investigate

the informational content of equity prices, they reach the same conclusion market prices

reflect a bank's current condition (Gropp et al. 2002, Krainer and Lopez 2002). Event

studies provide further evidence that the prices of publicly traded debt and equity respond

to relevant news in a rational manner (Allen et al. 2001, Berger and Davies 1998, Harvey

et al. 2003, Jordan et al. 2000).

Even if market information is timely and accurate, there is also the question of

whether it can add value to supervisory information. Numerous studies document that

equity-market and debt-market indicators can aid regulators in their monitoring of banks

by marginally increasing the explanatory power of regulatory-rating forecasting models.

Berger et al. (2000) find that supervisory assessments are less accurate than equity

market indicators in reflecting the bank's condition except when the supervisory

assessment is based on recent inspections. Gunther et al. (2001) show that equity data in

the form of expected default frequency adds value to BOPEC forecasting models. Elmer

and Fissel (2001) and Curry et al. (2001) find that simple equity-market indicators (price,

return, and dividend information) add explanatory power to CAMEL forecasting models


1 See Flannery (1998) for an overview of the literature on the market discipline of financial firms.









based on accounting information. Evanoff and Wall (2001) show that yield spreads are

slightly better than capital ratios in predicting bank condition. Krainer and Lopez (2003)

find that equity and debt-market indicators are in alignment with subsequent BOPEC

ratings and that including these in BOPEC off-site monitoring model helps identify

additional risky firms.

These studies suggest that regulators can benefit from explicitly or implicitly

including market information into supervisory models. However, they do not address the

question of which market information to include. Previous research has argued that using

debt prices is better suited for the purpose of oversight, since the incentives of debt

holders are more closely aligned with those of regulators in that neither group likes an

increase in asset risk.2 However, this advantage of debt market prices is balanced out by a

number of disadvantages. Debt prices are notoriously difficult to collect. While some

corporate bonds trade on NYSE and Amex, they account for no more than 2% of market

volume (Nunn et al. 1986). The accuracy of bond data is also problematic. Data quotes

on OTC trades tend to be diffuse, and based on matrix valuation rather than on actual

trades, and Warga and Welch (1993) document that there are large disparities between

matrix prices and dealer quotes. Hancock and Kwast (2001) compare bond-price data

from four sources, and find that the correlation among bond yields from the different

sources are only about 70-80%. Finally, Saunders et al. (2002) document that the





2 Gorton and Santomero (1990) are the first to point out that this statement is not necessarily true. The
payoff to subordinated debt-holders is a nonlinear function of risk. Thus, at low leverage levels,
subordinated debtholders have incentives similar to those of equityholders. However, the authors document
that none of the banks in their sample have low enough leverage for this to occur. Furthermore, this
describes an extreme situation that supervisors are likely to have already detected.