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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 INDUSTRIALFIRM 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. Calloption 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. DistancetoDefault 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. Calloption 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 22. Sim ple and rank correlations ............................................. ............................. 62 23. Simple and rank correlations of implied and historical asset volatility with realized asset v volatility ................................................................ .......... .... 63 24. Analysis of IAV and HAV forecasting properties..............................................64 25. Analysis of the relative informational content of IAV and HAV in forecasting R A V ............................................................................. 6 5 26. Average DD statistics by default status............................... ... .......... ................. 67 27. Logit analysis of defaults....... ................................................ .................... 68 28. Median distancetodefault estimates by Moody's credit rating .............................69 29. Median changes in distancetodefault estimates by Moody's credit rating change .............. ....... ........................................ .................. .. 70 210. Analysis of M oody's credit ratings ..................................................... ............... 71 211. Logit analysis of credit rating changes. .............. ......... ................... ............... 72 212. Average statistics by Zscore deciles................................. ......................... 73 213. A analysis of Zscore......... .......... ....................................................... .............. 74 214. A analysis of Zscore changes..................... ......... .......... ................. ............... 75 215. Sensitivity of summary statistics to alternative input assumptions ........................77 216. Analysis of IAV and HAV forecasting properties under alternative assume options ........................................... ............................ 79 217. Logit analysis of defaults under alternative assumptions................. ................80 218. Analysis of Moody's credit ratings under alternative assumptions........................81 219. Analysis of credit rating changes under alternative assumptions..........................83 31. Sum m ary statistics ......................................................... ........... ..... 131 32. Sim ple and rank correlations ....................................................... ............... 132 33. Average market indicators of risk by Moody's credit rating..................................133 34. Average market indicators of risk by asset quality deciles .................................... 134 35. Average market indicators of risk by SCORE deciles ............................................ 135 36. Analysis of M oody's credit ratings ..................................................... ............... 136 37. A analysis of asset quality m measures ................................................ ........ ....... 137 38. Analysis of financial health SCORE .............................................. .................. 139 39. Mean value tests of forecasting ability of market indicators.............. ..................... 140 310. Logit analysis of material changes in firm condition. .........................................141 311. Analysis of asset quality changes (LLAGL) ....................................................142 312. Analysis of asset quality changes (BADLOANS)................................................144 313. Logit analysis of SCORE changes...................................... ........................ 146 314. Sensitivity of summary statistics to alternative input assumptions ........................148 315. Analysis of asset quality measures under alternative assumptions ......................149 316. Analysis of asset quality changes ..................................... ........... ............... 150 317. Logit analysis of SCORE changes...................................... ........................ 152 LIST OF FIGURES Figure page 21. M edian implied asset volatility over 19752001 ................................... ...............84 22. Median implied asset volatility by assetstodebt ratio quartile ...............................85 23. Median distance to default over 19752001 .... ................................. 86 31. Median implied asset volatility (IAV) through time for 19861999 ....................153 32. Median implied asset volatility (IAV) by assettodebt ratio quartile...................154 33. Median distance to default (DD) through time 19861999 .................................... 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 equityonly or debtonly models. Risk measures constructed from both equity and debt prices are more closely related to bank credit ratings, assetportfolio 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 quartertoquarter changes in the firm's assetportfolio 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 equitycall and debtput 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, shortterm 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 bondprice data from four sources and find that correlation between bond yields from the different sources are in the 7080% 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 bondmarket 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 riskvaluation 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, creditrating changes, and assetreturn 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 industrialfirm 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 19861999. 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 INDUSTRIALFIRM 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 industrialfirm 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 19752001. 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 assetreturn 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 alternativemodel assumptions on the quality of the firm risk measures. Four estimates of asset volatility are analyzed in this chapter: * Asset volatility obtained by delevering equityreturn 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 riskvaluation 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 noninvestment grade firms, in an attempt to achieve a more balanced sample. For noninvestment 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 noninvestment grade firms, and by DD_DIAV when we limit ourselves to the subset of investmentgrade firms. We also examine the ability of changes in DD to predict creditrating 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 creditrating 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 lowZ (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 ratingchange results, we find that lagged changes in DD have more explanatory power for negative Zscore changes than for positive ones. The fit statistics of these models indicate that DD adds littletono 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 highfrequency and highquality 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 contingentclaimmodel assumptions does not. The informational content of risk measures is significantly affected by tax and calloption adjustments, as well as timetofirmresolution and debtpriority structure assumptions. This provides an important checklist of robustness tests for those conducting empirical research using contingentclaim 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 exchangetraded 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 zerocoupon 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) (21) 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 riskfree 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. Rearranging the formula used by Merton (1974) allows us to express the creditrisk premium as the spread between the yield on risky debt, R, and the yield on riskfree debt with otherwise the same characteristics: RR =In V eRf N( d)+N(d2) / r (22) 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 singleclass debt assumption is relaxed by Black and Cox (1976), who analyze the debtvaluation 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) (23') 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 BlackCox model most frequently appears in the literature as the spread between the yield on subordinated debt (R2 ) and the riskfree rate (R ) of the same maturity: R2 R, = In eRf [N(d,)N(d)] D N(d2) +D N(2) / (23) D2 D2 D2 2.1.2. Applications of Contingent Claim Valuation The above contingentclaim approach to pricing firm debt has many applications in the literature on creditrisk 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 contingentclaim 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 contingentclaim 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 (24') 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 contingentclaim 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. Contingentclaim valuation of equity has been used extensively in the literature on bank deposit insurance where the equitycall 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. 21 and Merton's boundary condition V = E E (24) 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 equityimplied 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 contingentclaim model to calculate the equity values of failed banks and find that these greatly exceed the negative networth estimates of the FDIC. They conclude that the equitycall 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 contingentclaim equitypricing model, the literature on market discipline of bank and bank holding companies makes use of the contingentclaim debtpricing 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 contingentclaim valuation techniques to calculate implied asset volatilities; and by Flannery and Sorescu (1996), who use it to obtain theoretical defaultrisk 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 19871988, 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 21 and 23 simultaneously for the market value of assets and the standard deviation of asset returns. We refer to this volatility estimate as the equity anddebt 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 morediverse sample. We obtain data on industrial firms for the period 19752001. 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 "horserace" 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 defaultrisk 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 (24') 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 riskfree, 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 marketvalueofassets estimate higher than those produced by the three simultaneousequation methodologies that follow. The equityimplied asset volatility (EIAV) is calculated by solving the system E = VN(d,) De Rf N(d2) (21) E (SV =p  = VN(d,) (24) 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 debtimplied 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) / (23) 1D2 D) 2 D(2 E Oy V~   V VN(d,) (24) 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 subordinateddebt valuation model, because we assume that publicly traded debt is likely to be last in a firm's debtpriority 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 moreaccurate EIAV. As in the calculation of equityimplied 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 equityanddebt implied asset volatility (EDIAV) is obtained by solving the system of nonlinear equations E = VN(d,) De R'fN(d2) (21) R, R, = ln e d)N(d )] N(d )+ + N(d2) /c (23) 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 CreditRisk 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 distancetodefault (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 contingentclaim 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 1year 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 resolutiontime 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 1yeartomaturity assumption. However, they offer no evidence as to which maturity assumption produces the better estimate of asset volatility. In the application of contingentclaim models to the valuation of industrial firms there is much less uniformity in the timetoexpiration 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 timetoexpiration 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 shortterm and longterm 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 9598% 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 defaultpoint 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 firmquarter observations for 19752001. 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 19752001. 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 fixedrate couponpaying debentures that are not convertible, putable, secured, or backed my mortgages/assets. We collect data on their monthend 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 firmspecific 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, nonconvertible, nonputable, 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 monthend 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 creditrisk spread, we need to subtract from each corporate yield the yield on a debt security that is riskfree 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 creditrisk 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 pretax return to yield the same aftertax 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 10year Arated 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 taxinduced 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 taxadjusted raw creditrisk 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 AAArated 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 creditrisk 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 nonAAArated bonds in our sample we use the difference between their yield and the average AAA yield as an alternative tax adjustment for the raw creditrisk 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. Calloption adjustment The taxadjusted yield spreads calculated above might still contain some noncredit 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 nonnegative, the spread over Treasuries whether adjusted for taxes or not, will exceed the creditrisk 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 optionadjusted credit spread. For each callable corporate bond in our sample, we use the maturitycorresponding "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 calloption parameters as the corporate bond but the same market price as the noncallable Treasury bond adjusted for taxes. The difference between the yield on the hypothetical callable and the actual noncallable Treasury bond is the value of the option to prepay. We subtract these option values from the taxadjusted spreads calculated earlier to obtain optionadjusted 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 shortterm 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 optionadjustment methodology produces higher option values. When combined with an initially low yield (highrated 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 samefirm 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 equityreturn observations in a quarter. These data filters attempt to reduce the effect of the bidask bounce on the estimate of equityreturn 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 19752001. 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 quarterend during 1975 2001. We use this as one estimate of the firm's face value of subordinated debt and input it into Eq. 23. 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. 22. 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. 22. If YS is instead that of a nonsenior 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. 23. 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 19752001 and retain those that are associated with bankruptcy, liquidation, and other financial difficulties (delisting codes greater than 400). We collect bankruptcyfiling dates from FISD for the period 19952001. 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 bankruptcyfiling 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 firmquarter 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 21 presents summary statistics on the sample of 27,723 firmquarters. The average market value of assets is in the range of $6.38.1 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 systemofequations 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 delevering equity volatility using the market value of equity and book value of debt. Once a systemofequations 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 21 plots median implied asset volatility for each quarter during 19752001, 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 threemonth period that includes the October 1987 crash. On the other hand, EDIAV is not affected by the crashinduced historical equity volatility and as a result is a more forwardlooking 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 assetstodebt ratio ranking to assign them to one of four quartiles. Figure 22 shows median implied asset volatilities from our four methodologies by assetstodebt 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 distancetodefault (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 21 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 23. 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 19801997 the DD calculated from EDIAV has fluctuated only in the range of 1.502.50 while the median DDEIAV has fluctuated in the range of 1.006.50. Once again, the medians of the four DD estimates seem to be converging towards the end of the sample period. Table 22 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 22 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 equityreturn 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 equityreturn 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 nontraded debt. The second estimate assumes that the yield on nontraded 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 23 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 25.131.2% and 42.556.7% 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 assettodebt ratio quartile and present these in Table 23. We find that as the amount of debt decreases (assetstodebt 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 assettodebt 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 quarterend t plus a zeromean 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, (25) 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 quarterend 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 quarterend 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 24 presents the results from the estimation of Eq. 25 for the whole sample of 21,570 firmquarter observations. All of the intercepts are statistically different from zero which implies that both forwardlooking 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 wholesample 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 assetstodebt ratio might affect the forecasting abilities of IAV is supported by the results from estimating Eq. 25 for each of the four assetstodebt 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 assetstodebt ratio quartiles. The IAV measures produce an R2 that is extremely low in the first quartile in the range of 0.73.5% 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 assetstodebtratio quartile is characterized by the highest explanatory power which implies that IAV estimates contain better information for lowdebt 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 24 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, (26) 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. 26 and that of Eq. 25 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. 26 for the whole sample of 21,570 firmquarters and then separately for each of the assettodebtratio quartiles. The wholesample results in Table 25 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 assetreturn 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 assetstodebt ratio quartiles in Table 25 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 assetsto debt ratio quartile. Along with the results in Table 24, 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 assetreturn volatility. 2.6. Default and Default Probability Tests To compare the relative defaultforecasting 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 defaultforecasting accuracy of the distancetodefault (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 threeyear period to its DD prior to the beginning of that threeyear period. We divide the data into eight subperiods: 198385, 198688, 198991, 199294, 199597, 19982000, 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 threeyear period is chosen to balance the need for a short window to capture the DDdefault 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 nonoverlapping threeyear periods defined earlier. This leaves us with 1,795 firmquarter 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 threeyear 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 firmquarters, 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 'lopsided' sample creates, we conduct the occurrenceofdefault tests not only on the whole sample but also on the subsample of noninvestment 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 26 provides summary statistics on the average distancetodefault 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 noninvestment 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 threeyear 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,, ) (27) 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 equityvalue 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 nonliquidation 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 27 presents the results from the estimation of Eq. 27. The wholesample 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 rescaled pseudo Rsquare, R2, is in the range of 19.0122.26%. 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 noninvestmentgrade 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 noninvestment 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 noninvestment grade firms. Table 28 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 29 investigates whether quarterly changes in firm DD over the period of 19752001 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 noninvestment 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 beginningofthequarter DD is higher than that of the previous quarter. This counterintuitive association between average DD and credit rating changes holds true for the firms downgraded from investment grade into noninvestment 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 noninvestment 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 (28) 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 nonregulated 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 nonregulated 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. 28 via OLS are presented in Table 210. 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 highernumber 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 wholesample 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 noninvestment 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 noninvestmentgrade 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 Grangercausality test. We examine whether credit rating upgrades and downgrades can be forecasted with information contained in lagged distancetodefault 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 ti,n 2 t4,n i 1 (29) 3 + ZE 3 .dRTG +4 RTG, + ElkControls n) 1 tj,n 4 t4,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 t1, 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 ti,n 2 t4,n (210) 3 + E y .3dRTG +7.RTG 4, + 7k Controls ) j 3 t !,n 4 t4,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 t1. 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 211 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 211 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 nochanges 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) Zmodel 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 Zmodel 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 Zmodel. 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 15). In contrast, when Z is high (portfolios 610) 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 Zscore at the end of each quarter and assign the firm to one often Zdecile portfolios. We start our analysis with simple univariate comparisons between ZScores and DD estimates. Each quarter we assign firms in our sample to one often Zscore deciles. Table 212 presents medians of the four DD estimates by ZScore 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 lowZ deciles, while the ones that incorporate information from equity prices are more consistent over the highZ deciles. We then estimate a model separately for lowZ (portfolios 15) and highZ (portfolios 610) firms. That is, Slow low low DD + low Controls + low t,n 0 t,n k k,t,n t,n (2 k (211) Z high = high + high D + high Controls + C high t,n 0 i tn k k t,n t,n Table 213 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 highZ 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 samedirection 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 t1 to quarterend t. The main independent variable is the change in one of the four distancetodefault 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 quarterend t 1 to quarterend 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 (212) 3 dZ =0 + C 0. dDD +O9, Controls t,n =0 + ti,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 defaultpoint differences across industries or firms respectively. In essence, this is identical to estimating a panel regression with industry or firm fixed effects.15 Table 214 presents the results from estimating Eq. 212. 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 Zscore 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 distancetodefault 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 alternativeassumption estimates of IAV and DD. We include a sample of our results below. 2.7.1. Summary Statistics Table 215 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 noncallable bonds only. In contrast, employing alternative timetoresolution, taxadjustment, or debtpriority 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 oneyear to resolution assumption the three systemof 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 215 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 AAArated bonds, the two IAV estimates significantly decrease. Finally, the sample summary statistics are most dramatically affected by changes in the debt priority assumption. Table 215 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 debtpriority 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 216 presents the results from reestimating Eq. 35. As suggested by the summary statistics in Table 215, 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 noncallable bonds we lose almost two thirds of our observations. These seem to be observations that contain highquality 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 reestimating the default forecasting model Eq. 27 are shown in Table 217. Increasing the time to resolution has the effect of decreasing the explanatory power of the DD estimates obtained through any of the systemofequations 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 AAArated bonds reduces explanatory power for the whole sample but produces some of the highest R2 for the subsample of noninvestment grade firms. The sensitivity results in Table 217 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 218 presents the results from reestimating the credit ratings model (Eq. 29). 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 investmentgrade 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 reestimating the downgrade/upgrade logit model (Eq. 210) can be seen in Table 219. As we already established, the market measures are statistically significant but improve the fit of forecasting models only marginally. Table 219 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 AAArated 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 delevering 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 impliedassetvolatility methodologies produces a default risk measure that consistently outperforms the others. When we examine whether the distancetodefault 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 impliedvolatility and distancetodefault 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 contingentclaim pricing models. It also provides researcher and practitioners with some guidance as to the model parameters most likely to influence results. Table 21. Summary statistics. Summary statistics are for the sample of 27,723 firm quarter observations over 19752001. SIAV is the simple implied asset volatility calculated by delevering historical equity volatility. EIAV is the equityimplied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equityanddebt 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 distancetodefault 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 22. Simple and rank correlations. Correlations are for the sample of 27,723 firmquarter observations over 19752001. SIAV is the simple implied asset volatility calculated by delevering historical equity volatility. EIAV is the equityimplied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equityanddebtimplied 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 distancetodefault 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 23. Simple and rank correlations of implied and historical asset volatility with realized asset volatility. Correlations are for the sample of 21,570 firmquarter observations over 19752001. SIAV is the simple implied asset volatility calculated by de levering historical equity volatility. EIAV is the equityimplied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equityanddebtimplied 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 quarterend. 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 nontraded 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 AssetstoDebt 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 AssetstoDebt 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 AssetstoDebt 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 AssetstoDebt 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 24. 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 delevering historical equity volatility. EIAV is the equityimplied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equityanddebt 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 AssetstoDebt 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 AssetstoDebt 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 AssetstoDebt 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 AssetstoDebt 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 25. 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 delevering historical equity volatility. EIAV is the equityimplied asset volatility obtained from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility obtained from debt prices and historical equity volatility. EDIAV is the equityanddebtimplied 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 quarterend. 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 AssetstoDebt 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 AssetstoDebt 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 25. Continued IAV Methodology Sample Used in Estimation E AssetstoDebt Ratio, Quartile 3, N=5,410 Intercept (i IAV (i HAV (i R2 AR2 (IAV) AssetstoDebt 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 26. 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 debtimplied asset volatility, and EDIAV is the equityandebtimplied 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 Noninvestment Grade Observations All 1,795 3.29 2.89 1.30 1.39 Nondefaulting 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 *** Noninvestment Grade Observations All 519 2.45 1.92 0.86 1.01 Nondefaulting 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 27. 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 noninvestmentgrade 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 distancetodefault measures calculated from the simple, equityimplied, debtimplied, and equityanddebtimplied asset volatilities respectively. P3P8 are period indicator variables. R2 is maxrescaled 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 Noninvestment Grade Observations Noninvestment 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 28. Median distancetodefault estimates by Moody's credit rating. Median statistics are on the sample of 20,298 firmquarters for the period 19752001. SIAV is the simple asset volatility, EIAV is the equityimplied asset volatility, DIAV is the debtimplied asset volatility, and EDIAV is the equityandebt 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 oneyear default rate over 19831999. 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 19831999 (%) 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 NonInvestment 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 29. Median changes in distancetodefault estimates by Moody's credit rating change. Median statistics are on the sample of 20,298 firmquarters for the period 19752001. SIAV is the simple asset volatility, EIAV is the equityimplied asset volatility, DIAV is the debtimplied asset volatility, and EDIAV is the equityandebtimplied asset volatility. dDD is the quarterly change in the distancetodefault 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 210. 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 firmquarters for the period 19752001. 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 distanceto default measures calculated from the simple, equityimplied, debtimplied, and equityanddebtimplied 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 NonInvestment 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 NonInvestment 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 211. 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 t4,n 3j t,n 4 t4,n tn tn i j=1 k for the sample of 20,298 firmquarters during the period 19752001. 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 distancetodefault measures calculated from the simple, equityimplied, debtimplied, and equityanddebt 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 212. Average statistics by Zscore deciles. Zscore 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 equityimplied asset volatility, DIAV is the debtimplied asset volatility, and EDIAV is the equityandebtimplied asset volatility. DD is the distance to default measure calculated from the corresponding asset values and volatilities. ZScore 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 213. Analysis of Zscore. 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 firmquarter observations for 19752001. The dependent variable is ZScore as calculated in Altman (1969) and is a measure of default probability based on accounting reports. A higher ZScore 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 distancetodefault measures calculated from the simple, equityimplied, debtimplied, and equityanddebtimplied asset volatilities and values respectively. Control variables (industry and yearquarter 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 ZScore 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 ZScore 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 214. Analysis of Zscore changes. We estimate via OLS d2 3 ,n 0 + E dDD +0 Controls, t,n = 0 0 1 ti, n k k, t, n i=1 k + E on the sample of 19,800 firmquarter observations for 19752001. The dependent variable is Altman's (1969) ZScore. A higher ZScore 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 distancetodefault measures calculated from the simple, equityimplied, debtimplied, and equityanddebtimplied 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 214. 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 215. Sensitivity of summary statistics to alternative input assumptions. SIAV is the simple implied asset volatility calculated by delevering historical equity volatility. EIAV is the equityimplied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equityanddebtimplied 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 distancetodefault 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 215. Continued Tax Adjustment Debt Priority Senior (Junior) Bonds Credit Spreads Moody's AAARated 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 216. 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 delevering historical equity volatility. EIAV is the equityimplied asset volatility calculated from equity prices and historical equity volatility. DIAV is the debtimplied asset volatility calculated from debt prices and historical equity volatility. EDIAV is the equityanddebtimplied 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 quarterend. 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 AAArated 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 Noncallable 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 217. 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 noninvestmentgrade 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 distancetodefault measures calculated from the simple, equity implied, debtimplied, and equityanddebtimplied asset volatilities respectively. R2 is maxrescaled 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 Noninvestment Grade Noninvestment 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 Noncallable 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 AAArated 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 218. 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 19752001. 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 todefault measures calculated from the simple, equityimplied, debtimplied, and equityanddebtimplied 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 AAArated 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 Noncallable Bonds Only R2 0.488 0.498 0.499 0.497 AR2 (DD) 0.073 0.083 0.083 0.082 Table 218. Continued InvestmentGrade Firms NonInvestmentGrade 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 AAArated 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 Noncallable 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 219. Analysis of credit rating changes under alternative assumptions. We estimate the logit model 3 3 dRTG =i+ Bdt.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 19752001. 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 distancetodefault measures calculated from the simple, equityimplied, debtimplied, and equityanddebtimplied asset volatilities respectively. Lags of variables are so indicated. The model's fit is measured by the max rescaled 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 AAArated 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 Noncallable 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 21. Median implied asset volatility over 19752001 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 22. Median implied asset volatility by assetstodebt 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 23. Median distance to default over 19752001 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 destabilize 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 risktaking 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 presafetynet 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 GrammLeachBliley 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 bankissued 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 equitymarket and debtmarket indicators can aid regulators in their monitoring of banks by marginally increasing the explanatory power of regulatoryrating 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 equitymarket 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 debtmarket indicators are in alignment with subsequent BOPEC ratings and that including these in BOPEC offsite 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 bondprice data from four sources, and find that the correlation among bond yields from the different sources are only about 7080%. 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 debtholders 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. 