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## Material Information- Title:
- Essays on fixed income securities
- Creator:
- Zhou, Lei, 1969-
- Publication Date:
- 2002
- Language:
- English
- Physical Description:
- vii, 118 leaves : ill. ; 29 cm.
## Subjects- Subjects / Keywords:
- Adverse selection ( jstor )
Bond rating ( jstor ) Covariance ( jstor ) Estimation methods ( jstor ) Financial bonds ( jstor ) Information asymmetry ( jstor ) Investors ( jstor ) Mathematical variables ( jstor ) Standard and Poors 500 Index ( jstor ) Yield ( jstor ) Dissertations, Academic -- Finance, Insurance, and Real Estate -- UF ( lcsh ) Finance, Insurance, and Real Estate thesis, Ph.D ( lcsh ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Thesis:
- Thesis (Ph.D.)--University of Florida, 2002.
- Bibliography:
- Includes bibliographical references (leaves 113-117).
- General Note:
- Printout.
- General Note:
- Vita.
- Statement of Responsibility:
- by Lei Zhou.
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51020623 ( OCLC )
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ESSAYS ON FIXED INCOME SECURITIES By LEI ZHOU 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 2002 To my wife, my son and my parents ACKNOWLEDGMENTS I first would like to thank Dr. Miles Livingston, the chairman of the committee, for his guidance, patience and support for my work. I am also grateful to Dr. Andy Naranjo, Dr. M. Nimalrendran and Dr. Carl Hackenbrack for their helpful comments and suggestions. I thank my wife, Lei, for her firm commitment and great sacrifices. She has been very supportive and patient, and I am fortunate to have her as my wife. Finally, I would like to thank my parents, Bojun and Yuming. Without their endless faith, support and encouragement, I will not be at this point in my life. iii TABLE OF CONTENTS page A CKN O W LED GM EN TS ................................................................................................. III AB STRA CT....................................................................................................................... vi CHAPTER I IN TRO DU CTION ...................................................................................................... 1 2 THE IMPACT OF RULE 144A DEBT OFFERINGS UPON BOND YIELDS AND UND ERW RITER FEES ............................................................................................. 3 In tro d u c tio n .................................................................................................................... 3 Background of Rule 144A ......................................................................................... 6 D ata and M ethodology.............................................................................................. 13 Em pirical Results ....................................................................................................... 19 Conclusion ................................................................................................................... 30 3 BOND RATINGS AND PRIVATE INFORAMTION ........................................... 44 Introduction.................................................................................................................. 44 Literature Review ..................................................................................................... 46 M ethodology ................................................................................................................ 51 D a ta .............................................................................................................................. 6 5 Em pirical Results .................................................................................................... 68 Conclusion ................................................................................................................... 77 4 CON CLU SION .............................................................................................................93 APPENDIX A CATEGORICAL VARIABLE METHOD (CVM) ............................................... 95 A ssum ptions and D efinitions.................................................................................. 96 First Stage Estim ation .............................................................................................. 97 Second Stage Estim ation......................................................................................... 99 Third Stage Estim ation ............................................................................................. 100 B MEASUREMENT OF INFORMATION ASYMMETRY........................................102 iv Proxies from Corporate Finance Literature .............................................................. 102 Proxy from Market Microstructure Literature .......................................................... 104 LIST OF REFERENCES.................................................................................................113 BIOGRAPHICAL SKETCH ...........................................................................................118 V 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 ESSAYS ON FIXED INCOME SECURITIES By Lei Zhou August 2002 Chair: Miles B. Livingston Department: Finance, Insurance, and Real Estate This dissertation consists of two essays on fixed income securities. The first essay investigates the impact of the Securities and Exchange Commission's [SEC] Rule 144A on corporate debt issues. The second essay studies the private information contents of bond ratings. Corporate bonds issued under Rule 144A are exempt from registration with the SEC. We find Rule 144A bond issues have higher yields than publicly issued bonds after adjusting for risk. Such yield premiums of Rule 144A issues may be due to lower liquidity, information uncertainty, and weaker legal protection for investors. Underwriter fees for Rule 144A issues are not significantly different from underwriter fees for publicly issued bonds. Bonds issued under Rule 144A may have registration rights, which require the issuer to exchange the bonds for public bonds within a stated period, or pay higher yields. While high-yield bonds usually have registration rights, we find that the majority of vi investment-grade bonds do not. Registration rights have a greater impact on yields for high-yield than for investment-grade bonds. The second essay investigates whether bond ratings contain private information that is not available to investors. We use the latent variable technique to link private information with bond ratings directly. We use three variables (firm size, analyst forecast errors and adverse selection component of bid-ask spread) to proxy for the private information and find that the information asymmetry leads to lower ratings and higher bond yields. However, private information content only accounts for less than 10% of the variations in bond ratings. vii CHAPTER 1 INTRODUCTION Fixed income securities are a very important part of the US financial market. This dissertation investigates two important topics on fixed income securities. First, we examine a new type of debt offering, called Rule 144A issues, and their impact upon the bond yields and underwriter fees. Second, we study whether bond ratings contain private information that is not available to investors. The SEC introduced a new Rule, called Rule 144A in April 1999. Securities issued under Rule 144A do not have to file a public registration statement with the SEC, but can be sold only to qualified financial institutions. Since its adoption, the Rule 144A market has been growing very fast. Annual issues of Rule 144A non-convertible debt have swelled from $3.39 billion in 1990 to $235.17 billion in 1998. Using a sample of 4,070 industrial and utility bonds, we find that Rule 144A issues are found to have higher yields than publicly issued bonds after adjusting for risk. Yield premiums are higher if the issuer does not file periodic financial statements with the SEC. The yield premiums of Rule 144A issues may be due to lower liquidity, information uncertainty, and weaker legal protection for investors. Bonds issued under Rule 144A may have registration rights, which require the issuer to exchange the bonds for public bonds within a stated period, or pay higher yields. While high-yield bonds usually have registration rights, we find that the majority of investment-grade bonds do not. Registration rights have a greater impact on yields for I 2 high-yield than for investment-grade bonds. Underwriter fees for Rule 144A issues are not significantly different from underwriter fees for publicly issued bonds. Another important topic in fixed income security research is whether bond ratings carry private information. Previous empirical studies try to relate bond ratings to bond yields and/or stock returns and provide indirect evidence on the information content of ratings. We use the latent variable technique to link private information with bond ratings directly. We use three variables (firm size, analyst forecast errors and adverse selection component of bid-ask spread) to proxy for the private information and find that information asymmetry leads to lower ratings and higher bond yields. Since firms with large information asymmetry problems are likely to share more private information with the rating agencies, this finding is consistent with the hypothesis that bond ratings do contain private information. However, the private information only accounts for a small percentage of variation in ratings and bond yields. We also find that bond issues that have split ratings from S&P and Moody's have more private information content in their ratings than bond issues that do not have split ratings. CHAPTER 2 THE IMPACT OF RULE 144A DEBT OFFERINGS UPON BOND YIELDS AND UNDERWRITER FEES Introduction Since 1990, the Securities and Exchange Commission has allowed firms to sell security issues to qualified institutional buyers under so-called Rule 144A. Rule 144A issues are not required to be registered with the SEC and may not be resold to individual investors, but may be traded between qualified institutional buyers. Rule 144A issues may have "registration rights," which require the issuer to exchange the original Rule 144A issue for a public bond issue within a stipulated period. If the exchange does not occur, the issuer must pay a higher interest rate. The basic justification for the waiver of advance registration is the belief that large institutional buyers are sophisticated investors and do not need the SEC to examine each offering of securities in depth. Public issues of securities are required to be registered before they are offered for sale to individual investors, however, who are presumed to be less sophisticated and informed than large institutional buyers. The Rule 144A market has been growing very fast. Annual issues of Rule 144A non-convertible debt have swelled from $3.39 billion in 1990 to $235.17 billion in 1998. In the meantime, the traditional private placement bond market has shrunk from $109.94 billion annually to $51.10 billion. Rule 144A issues have accounted for up to 80% of the high-yield bond market in recent years. 3 4 Despite its size, the Rule 144A market has drawn little attention from academics. Only one published article exclusively studies yields on high-yield bonds and focuses upon the information disclosure of Rule 144A issues. Fenn (2000) argues that expedience is the only motivation for Rule 144A issues. Unlike Fenn (2000), we find that yields for Rule 144A offerings are substantially higher than for public offerings for both investment-grade and high-yield bonds. In addition, we find that Rule 144A issues by private firms without any publicly traded securities, and consequently not required to file periodic financial statements with the SEC, have markedly higher yields. This finding is consistent with Bethel and Sirri's (1998) discussion of the importance of company reporting to the SEC. When we follow Fenn's methodology and reproduce his sample, we find that his findings seem to be sensitive to both time period and model specification. There are several possible explanations for why Rule 144A issues might have higher yields. First, Rule 144A issues are less liquid than public bond issues, since the universe of buyers in the primary and secondary market is restricted to qualified financial institutions. Second, the disclosure requirements for Rule 144A issues are less stringent, giving issuing firms greater latitude as to information disclosure. Buyers of Rule 144A offerings may thus require higher yields because of information uncertainty. The effect is greater for privately held firms that do not file periodic financial statements with the SEC. Third, public debt issuers bear more legal liability than Rule 144A issuers. For Rule 144A issues, the bond buyer bears considerably more risk about information accuracy. 5 We also find a dramatic difference in the use of registration rights (the requirement to exchange the Rule 144A issue for a public offering) for investment-grade and high-yield Rule 144A bonds. While most high-yield Rule 144A issues include registration rights, more than half of investment-grade Rule 144A issues do not. In addition, registration rights have a greater impact on the yields for high-yield Rule 144A issues than for investment-grade Rule 144A issues. There is no significant difference in gross underwriter spread between Rule 144A issues and public bonds. Our paper contributes to the literature in several ways. First, we provide new findings on the use and impact of registration rights in Rule 144A issues. There are conflicting reports on the use of registration rights, and no previous research studies the impact of registration rights on yields and underwriter fees. Second, we find that about a quarter of Rule 144A bonds are issued by privately held firms that are not required to report to the SEC. While Rule 144A bonds pay yield premiums over public bonds in general, the Rule 144A issues by non-reporting firms have remarkably higher yield premiums. This finding supports the importance of company reporting to the SEC. Third, we include both investment-grade and high-yield bonds in our sample, and we find differences between the two. Yield premiums on high-yield Rule 144A issues are considerably higher than those on investment-grade Rule 144A issues, for example. Other studies either ignore investment-grade Rule 144A issues or do not investigate the two types of Rule 144A issues separately. Fourth, we study the gross underwriter spread of Rule 144A issues as well as the yields. Gross underwriter spread, an important component of total issuing costs, sheds 6 light on the riskiness of an issue. No one has looked at the differences in gross underwriter spread between Rule 144A issues and public issues of debt. Finally, we investigate in more detail the institutional background of the Rule 144A market--it liquidity, potential investors, information disclosure, and legal protection for investors--and relate this information to the empirical findings. Previous research focuses only on the information disclosure of Rule 144A issues. The chapter is organized as follows. The next section details the background and the development of the Rule 144A market. We also analyze the institutional details of Rule 144A issues and their expected impact on bond yields and underwriter spread. The third section describes the data and methodology. Empirical results are presented in the fourth section, while section five concludes the chapter. Background of Rule 144A Origination of Rule 144A One of the basic rationales of the 1933 Securities Act is to protect unsophisticated individual investors, or so-called widow and orphan investors, from fraud. In recent years, however, the US capital market has become more "institutionalized." The SEC reports that the percentage of ownership of US equities by institutional investors increased from 29.3% in 1980 to 47.5% in 1990 (Securities and Exchange Commission, 1994). These large institutional investors have expertise and experience in investing their assets. A registration requirement for security issues may not add much value to such large institutional investors, while it imposes significant costs on the issuers. A public registration requirement may also hinder foreign participation in the US capital market 7 because it is costly for foreign issuers to maintain GAAP-compliant accounting information and/or to disclose information not usually disclosed in their home countries.' To address such concerns, the SEC adopted Rule 144A in 1990. Securities issued under Rule 144A do not require registration with the SEC, but can be traded without restriction in the secondary market among "qualified institutional buyers," or QIBs.2 Rule 144A issues, which are technically private placements, enjoy a much more liquid secondary market than traditional private issues.3 Registration Rights Although Rule 144A issues do not initially have a public registration statement, they may include so-called registration rights, which require the issuer to register the issue with the SEC or exchange it for a registered issue within a specified time. If the issuer fails to do this, the coupon on the bond is increased by a designated amount, usually 0.25% to 0.50%. For example, the registration rights agreement of the 6 5/8% debenture due 2038 of Boeing Corp issued under Rule 144A reads like this: Additional Interest shall accrue on the Initial Securities ... [if] any such Registration Default shall occur . .. at a rate of 0.25% per annum. Since 1990, the amount of foreign issues in the Rule 144A market has increased significantly, to over $50 billion in 1998. Almost half of all foreign issues in 1998 were offered in the Rule 144A market. Chaplinsky and Ramchand (2000) provides a detailed analysis of foreign Rule 144A debt issues. 2 QIBs are generally defined as institutions that own or have investment discretion over $100 million or more in assets. In addition to the $100 million requirement, banks and savings and loan associations must also have at least $25 million of net worth to quality as QIBs. For registered broker-dealers, $10 million investment in securities would meet the requirement. 3 Loss and Seligman (2001, pp. 391-396) discuss the legal details of Rule 144A and Rule 144. 8 Most Rule 144A issues with registration rights do get registered eventually. In our study, we find only three Rule 144A issues with registration rights whose issuers failed to register the issues within the designated period, and the coupon rates were increased. There are three published reports on the extent of the use of registration rights. Investment Dealer's Digest (1997) and Bethel and Sirri (1998) report that about one-third of Rule 144A debt issues have registration rights. Fenn (2000), on the other hand, reports that over 97% of high-yield Rule 144A bonds were subsequently registered with the SEC. Our study reconciles these seemingly contradictory reports. As we describe in detail later, we find that over 98% of high-yield bonds have registration rights, but only about 40% of investment-grade bonds do. Development of Rule 144A Non-Convertible Debt Market Although both equities and bonds can be issued under Rule 144A, the majority of Rule 144A issues are non-convertible bonds. For example, a total of $262 billion of Rule 144A securities was issued in 1997: $40.7 billion in equities and $11.2 billion in convertible bonds (Bethel and Sirri, 1998). The remaining $210.1 billion, or 80% of all Rule 144A securities, was non-convertible debt. We examine Rule 144A non-convertible debt issues only. Figure 2-1 compares the annual issues of Rule 144A debt to the traditional private placement and public debt. Since adoption of the rule, the Rule 144A non-convertible debt market has been growing very quickly. Total annual new issues in the Rule 144A market have grown from $3.39 billion in 1990 to $235 billion (in inflation adjusted 1990 dollars) in 1998. New public debt issues have also experienced significant growth, from $106 billion in 1990 to $975 billion in 1998. Although both markets have grown 9 significantly, the Rule 144A market has grown proportionally faster. The traditional private market has shrunk, from $110 billion in 1990 to $51 billion in 1998. The rapid growth of the Rule 144A market seems to have come partially at the expense of the private placement market. Figure 2-2 shows the average issue size in the three markets. Privately placed non-convertible bonds are much smaller on average than publicly placed bonds. Small issues by small firms are usually placed in the private market because small firms are more likely to be subject to agency problems (Blackwell and Kidwell, 1988). Strict covenants, renegotiation provisions, and a small number of investors in private placements help to alleviate the asset substitution and under-investment problems. Figure 2-2 also shows that the average size of Rule 144A issues increased continually from 1991 to 1998, while public issue size has been decreasing. In fact, Rule 144A issue size on average has surpassed public issue size since 1996. Obviously the Rule 144A market has attracted many large issues that would otherwise have been placed in the public market. Thus, the growth of Rule 144A issues may also come at the expense of the public market. Institutional Details of Rule 144A Issues Rule 144A offers several advantages to issuing firms. Less information needs to be disclosed, and the information disclosed does not need to meet certain criteria. For example, financial statements need not be GAAP-consistent for Rule 144A issues. A firm can issue the debt quickly. Timely issuance may let a firm sell debt under favorable market conditions, when interest rates are lower. For these benefits, the issuing firms may be willing to pay premium yields. Indeed, if issuing firms did not have to pay premiums for such advantages, we would expect Rule 144A issues to dominate the 10 market. While the Rule 144A market has been very successful, especially in attracting high-yield issues, it far from dominates the public debt market. Indeed, about 20% of high-yield bonds and over 80% of investment-grade bonds are still offered in the public debt market. Hence, there must be some costs to issue in the Rule 144A market, and the issuing firms must be balancing the costs and benefits. The yield premium and/or the higher gross underwriter spread may constitute the costs of issue in this market. For investors, Rule 144A issues may be riskier than public issues. First, Rule 144A issues are less liquid than public bond issues, since the universe of buyers in both the primary and the secondary market is restricted to qualified financial institutions. Indeed, Cox (1999) finds that the number of bond buyers more than doubled and the number of transactions increased by approximately one-third following the subsequent public registration of bonds issued originally as Rule 144A issues.4 The restricted potential investor universe is clearly an important factor. Furthermore, Rule 144A issues may be categorized as "restricted securities" by some institutional investors such as insurance companies, pension funds, or mutual funds. These institutional investors may be constrained in the percentage of their portfolios they may invest in restricted securities, or they may have to maintain larger capital reserves for investment in Rule 144A issues. Indeed, the American Bar Association argued in 1999 that the use of registration rights in Rule 144A issues 4 While the total trading volume of Rule 144A issues declines after the post-issue registration, this does not contradict the argument that public registration makes Rule 144A issues more liquid. A newly issued security is usually much more liquid than a seasoned security. Hence, the observed decline in trading volume may reflect just the lower liquidity of seasoned securities. I1 permits an investment institution to reclassify "restricted securities" held in its portfolio to unrestricted status upon the completion of the exchange offer, without the need to sell those securities to make capital available for additional investment in privately placed debt securities. Even though Rule 144A issues may be reclassified as unrestricted securities if registered later, the issues may have a limited pool of potential buyers at the initial sale if they are "restricted securities." Hence, the smaller base of potential buyers and the "restricted securities" status may together reduce the liquidity of Rule 144A issues, producing a yield premium over public debt. Second, disclosure requirements for Rule 144A issues are less stringent. Legally, a Rule 144A offering does not have to disclose the same information as required under the Securities Act of 1933; the issuing firm has greater latitude as to disclosure. Such lack of disclosure may be of greater concern to investors in offerings by less well-known issuers, especially issuers with no public securities that do not file periodic disclosures with the SEC. Even for public firms that file with the SEC, such periodic disclosures do not provide detailed issue-specific information required by the 1933 Securities Act, such as the intended use of the proceeds. Third, investors in Rule 144A issues have weaker legal protection than investors in public debt issues (Bethel and Sirri, 1998). Under Section 1I of the Securities Act, the issuers of registered public debt are held "strictly liable" for losses to investors if they provide misleading information or omit material information in the registration statement. In other words, if ever there is misleading information or omission of material information, the issuer of registered public debt will be held liable, whether or not it acted knowingly. Investors in Rule 144A issues do not have such strong legal protection. Even if a Rule 144A issue has registration rights and is registered later, Rule IOb-5 of the 12 Exchange Act provides less legal protection. Rule IOb-5 holds an issuer liable if the issuer knowingly provides misleading information and investors make their investment decision on such misleading information. Hence, investors in Rule 144A issues have much weaker legal protection and would have a harder time suing an issuer in the event of default. Such concerns about legal protection may be important to insurance companies that, by regulation, have to make "prudent" investments, especially when they are investing in high-yield bonds. Expected Impact of Rule 144A on Yields and Underwriter Fees Our discussion indicates that Rule 144A may have advantages for issuing firms but disadvantages for investors. Issuing firms may be willing to pay for such advantages of Rule 144A offerings, possibly in the form of higher yields and/or gross underwriter spread. Similarly, investors may demand a higher rate of return on Rule 144A issues because of the disadvantages for them. Hence, we expect Rule 144A issues to have a yield premium over public issues. The impact of Rule 144A on gross underwriter spread is less clear. First, fewer potential investors and information uncertainty make Rule 144A issues more difficult to sell than public debt, so an underwriter may require higher fees. Yet underwriting Rule 144A issues may be less risky in some ways and involve less work for underwriters. For example, weaker legal protection for investors in Rule 144A issues means less legal liability for underwriters. Also, it is estimated to take only half the time to issue debt under Rule 144A than to issue a registered offering (Investment Dealers Digest, 1997). For an underwriter, shorter and less burdensome marketing means lower costs. A short underwriting period reduces interest rate risks for underwriters too. 13 Furthermore, while in a traditional public offering, the underwriter devotes considerable time and staff to help an issuer prepare a registration statement and file with the SEC, these are not necessary for a Rule 144A issue. If investment bankers can underwrite Rule 144A issues more quickly and with less work, the underwriter may be willing to charge a lower fee for Rule 144A issues. The net impact of Rule 144A on the underwriter gross spread is therefore unclear and is an empirical question that we address later. Data and Methodology Construction and Description of the Sample The New Issues Database of the Securities Data Company (SDC) is used to collect data for all non-convertible, domestic bond issues with fixed coupon rates in the Rule144A and public market by industrial and utility firms from 1997 through 1999.5 Issues not rated by both Moody's and Standard & Poor's are excluded. A small number of issues with perpetual maturities have been excluded. To check the data integrity, the Bloomberg database is used. As it is impractical to check every observation manually, about 100 outliers are checked. Among them, about one-fourth have problems.6 Some of them are excluded. For example, issues of 5 We start the sample at 1997 because few Rule 144A issues before 1997 report gross underwriter spread in the SDC database. Since 1997, we can find gross underwriter spread for a significant number of Rule 144A issues, though still only about 30% of Rule 144A issues in our sample report gross underwriter spread. 6 Outliers are those with a residual outside three standard deviations in the regressions. Half of the problematic observations have major errors, such as misclassification and wrong decimal points. Another half has minor errors, such as a small difference in gross underwriter spread, or yield. After correcting for these errors, we reran the regressions and checked for the new outliers. We found no major errors, but a few minor errors. 14 preferred stocks mis-classified as bond offerings by SDC are excluded. Others are corrected. This leaves us a total of 4,070 observations: 1,418 Rule 144A issues and 2,652 7 public issues. Table 2-1 gives the descriptive statistics for the full sample. There are a total of 1,542 issuing firms in the sample. Among them, 663 issued in the public market, 944 issued in the Rule 144A market, and 65 issued in both markets. Firms issuing in the public market have an average of 4.0 issues, while firms issuing in the Rule 144A market have an average of only 1.5 issues for the sample period.8 The average size of a public offering is $129.04 million; the average size of a Rule 144A offering is $177.69 million. Ninety-one percent of the issues in the public market are investment-grade, and over 98% are senior debt. Only 32% of Rule 144A issues are investment-grade, and 68% are senior debt. Indeed, 74% of all high-yield bonds in 1997 were issued in the Rule 144A market (Bethel and Sirri, 1998). Figure 2-3 gives the distribution of ratings for the public and Rule 144A issues. For public issues, about 40% of issues are A-rated bonds and 30% are BBB-rated bonds. In total, about 90% of public issues are rated between AA and BBB. For Rule 144A 7 35.11% of public bonds and 26.94% of Rule 144A issues are issued by utility firms. We have studied the industrial issues and utility issues separately, and find the results are essentially identical. 8 The issue frequency for public debt seems to be high. One potential explanation for such high issue frequency is that there are more short-term near-money debt issues in the public debt market. Yet the average maturity for public debt is 12.17 years, significantly longer than the average maturity of Rule 144A issues. We eliminate issues with maturity less than or equal to 2 years from the sample, and find that the issue frequency for public debt is still much higher than issue frequency of Rule 144A issues: 3.70 times vs. 1.48 times. Hence, short maturity does not explain the high issue frequency in the public debt market. None of our results changes with the modified sample. 15 issues, about 50% are B-rated bonds. A, A/BBB and BBB bonds account for about 25% of Rule 144A issues. Interestingly, more than 3% of Rule 144A issues are AAA bonds. Gross underwriter spread is the compensation that the issuer pays to the underwriters. Original yield is the bond yield to maturity at original issuance. The yield on a comparable maturity Treasury is subtracted to arrive at the Treasury spread. Table 2-1 shows that the average gross underwriter spread and average Treasury spread are higher for Rule 144A issues than for public bond issues. Table 2-2 gives the average gross underwriter spread and Treasury spread across different ratings. The differences in gross underwriter spread between Rule 144A issues and public issues are usually small, although we find significantly higher gross underwriter spreads for Rule 144A issues in three rating categories (AA/A, BBB, and BB). Rule 144A issues have higher Treasury spreads than public issues in 11 out of the 12 rating categories. Although the differences in the yields are significant at the 1% or 5% level in only 4 of the 12 rating categories, these four rating categories (A, BBB, BB, and B) account for the majority of the observations. Hence, rating differences cannot explain all the large differences in Treasury spread between public issues and Rule 144A issues. Table 2-1 also shows that 97.70% of public debt offerings and 66.36% of Rule 144A offerings are issued by public firms.9 Another important difference between public 9 An issuing firm is defined as a public firm if the firm or its parent has public traded equity. We find this information on SDC. 16 debt and Rule 144A issues is that more than 50% of Rule 144A issues are first-time debt issues, compared to only 10% of public debt issues.'0 Firms with neither publicly traded equity nor public bonds are not required to file periodic disclosure with the SEC. These firms are usually called non-SEC-reporting firms, or simply non-reporting firms. We classify an issuing firm as non-reporting if 1) it is not a public firm and 2) it has not issued any public debt securities since 1970. " Table 2-1 shows that 23% of Rule 144A offerings are issued by non-reporting firms, while less than 1% of public offerings are issued by non-reporting firms. In total, 347 bonds are issued by non-reporting firms: 74% high-yield Rule 144A issues, 21% investment-grade Rule 144A issues, and only 5% public bond issues. This indicates that non-reporting firms have a strong preference for the Rule 144A market. Methodology The primary methodology in this study is simple ordinary least squared regressions. Later we use Heckman's (1979) treatment effect for potential self-selection bias. The dependent variables are the gross underwriter spread and the Treasury spread in basis points. The independent variables include proxies for risks of individual bond issues, proxies for market conditions, other control variables and test variables. A debt offering is classified as a first-time issue if the issuing firm has not sold any public fixed income security (straight or convertible debt, preferred stock) since 1970. " Two possible misclassifications may occur. If a non-public firm issued a public bond before 1970, but not since then, and the bond is still outstanding, then our method would misclassify it as a non-reporting firm, while in fact it is still required to file with the SEC. Or, if a non-public firm issued a public bond after 1970 which had been retired and no other public debt is outstanding, we would misclassify it as a reporting firm while in fact it is not. Although these two situations are possible, we see the chances as small, and they will not make a significant difference in our results. 17 Proxies for risks The rating dummy variables represent specific bond ratings: BBB = 1 if the issue is rated BBB by both Moody's and S&P and zero otherwise, BBB/BB = I if the issue is rated BBB by one rating agency but BB by another agency, and zero otherwise, and so on. The regression base case is AAA-rated bonds. Previous studies find that bond ratings are significant determinants of both bond yield and gross underwriter spread (Lee et al., 1996, and Jewell and Livingston, 1998). Log of Maturity is the natural log of years to maturity. The longer the maturity, the riskier the issue. Percentage of Years of Call Protection is the percentage of years that the call protection is in effect. Call protection reduces the reinvestment risk of investors and makes issues less risky. Senior Debt is a dummy variable equal to one if the issue is senior debt, and zero otherwise. Since senior debt is less risky, we expect the coefficients on Senior Debt to be negative in both regressions. Proxies for market conditions Bond default risk premium fluctuates with overall market conditions. To control for the fluctuation, we include in the regressions a Default Risk Premium variable, which is the difference between the Merrill Lynch BBB Corporate Bond Index and the 10-year US Treasury Index. Another two variables to control for market conditions are dummy variables for years 1998 and 1999. In regressions, the base case is AAA-rated bonds issued in 1997. 1 The relationship between maturity and gross underwriter spread and yields may not be linear. We have examined both years-to-maturity and log of maturity in the regressions. Log of maturity seems to have a better fit and is reported in the results, although the results are essentially the same if years-to-maturity is used. 18 Other control variables The First-Time Debt Issue dummy equals one if the issuer has not issued any fixed income securities since 1970 and zero otherwise. A first-time issue may have a higher yield, as the issuer does not have a reputation in the security market. Also, the underwriting cost may be higher, as an investment banker must devote more resources and time to obtain information about a new issuer and to find buyers. Fenn (2000) finds that yield premiums on first-time issues are about 30 basis points. Log of Issue Frequency is the natural log of the number of issues that each firm had over 1997 to 1999. Frequent issuers may have not only lower gross underwriter spread but also lower yield, since they are established players in the capital market and have a natural clientele. They may be regarded as less risky issuers. Frequent issues of debt, on the other hand, might convey a signal of financial trouble and add to a firm's debt level. That may increase the yields on frequent issuers. The net effect of issue frequency is therefore unclear. The Public Firm dummy equals one if the SDC database indicates that the issuer has publicly traded equity and zero otherwise. Because there is usually more information on public firms available to investors, the yield and gross underwriter spread of bonds issued by public firms are expected to be lower. Log of Proceeds is the natural log of total proceeds. Many empirical studies indicate that there are economies of scale in gross underwriter spread. That is, percentage gross underwriter spread falls as the size of an issue increases. (See, for example, Lee et al., 1990.) Altinkilic and Hansen (2000) argue that there are also diseconomies of scale in spreads; 30% of the bond issues in their sample are in a range of diseconomies of scale. 19 Hence, the sign of the coefficient on Log of Proceeds in the gross underwriter spread regression is not clear. Large issues of bonds are usually more liquid than small issues, and investors may require lower rates of return for more liquid issues. Hence, we expect the sign on the coefficient on Log of Proceeds in the Treasury yield regression to be negative. The Utility Finn dummy equals one if the issuer is a utility firm and zero otherwise. Test variables In the first set of regressions, the test variable is the Rule 144A dummy, which equals one for the Rule 144A issues and zero otherwise. The dummy variable is used to test whether the gross underwriter spread and Treasury spread are different for the Rule 144A issues and public bond issues. In another set of regressions, two dummy variables for Rule 144A issues are created, according to whether the issuing firms are required to file periodic disclosure with the SEC. If a Rule 144A offering is issued by a non-reporting firm, the dummy Rule 144A by Non-Reporting Firm equals one and zero otherwise. Similarly, if a Rule 144A offering is issued by a reporting firm, the dummy Rule 144A by Reporting Firm equals one and zero otherwise. Empirical Results Treasury Spread The impact of Rule 144A offerings upon Treasury spread is examined in Table 23. The Column A regression uses a single dummy variable for Rule 144A issues. The 20 coefficient is 18.97 and significant, indicating that Rule 144A issues have yields that are almost 19 basis points higher than public bond issues.13 The first-time debt issue dummy variable is positive 30 basis points, consistent with Fenn's finding. The public firm dummy is negative 28 basis points, indicating that public firms have a cost advantage in raising external debt. The logarithm of issue frequency is negative 8 basis points; more frequent issuers tend to have lower yields. The default risk premium is positive and significant. The logarithm of proceeds, a measure of issue size, is negative 3 basis points; that is, larger issues tend to be more liquid and hence have lower yields. The dummy variables for bond rating tend to increase as the rating gets lower. The risk premium rises at an increasing rate as ratings drop. The coefficient for the senior debt dummy is positive and almost 49 basis points, indicating that senior debt has higher yields, a counter-intuitive result that may be caused by the rating agencies' tendency to give senior debt unjustified higher ratings. Fenn (2000) and Fridson and Garman (1997) have similar findings. The log of maturity is positive 17 basis points, suggesting that longer maturities have higher risk. The utility firm dummy variable is negative, implying lower risk for utility bonds. Column B breaks the dummy variable for Rule 144A issues into two separate dummy variables: one for non-reporting firms, and the other for reporting firms. The " We also break the sample into two sub-samples: issues with maturity shorter than or equal to 5 years and issues with maturity longer than 5 years. The coefficients on the Rule 144A dummy in the sample are very similar, 18.16 and 19.17, respectively, both significant at the 1% level. 21 coefficient for Rule 144A issues by non-reporting firms is 54 basis points, and the coefficient for Rule 144A issues by reporting finns is 19 basis points; both are highly significant. The difference between the two coefficients is significant at the 1% level. The absolute size for the first-time debt issue dummy drops from 30 to 24 basis points, and the public firm dummy becomes insignificantly different from zero. All the other coefficients are very similar to Column A results. One possible explanation for the higher yields on Rule 144A issues is sample selection bias. The previous regressions implicitly assume that the Rule 144A dummy is exogenous, but issuers may not choose a public offering or a Rule 144A offering randomly. Perhaps riskier issuers (in a given rating category) may choose to issue in the Rule 144A market because less information needs to be disclosed. To examine whether a selection bias exists, we estimate the Heckman's treatment effect model (Greene 1993, pp. 713-714, and Maddala, 1983, p. 263). We use Heckman's two-stage regression methodology (Heckman, 1979). First, we estimate a probit model of the choice between Rule 144A and public debt and calculate the inverse Mills ratio. Next, we add the inverse Mills ratio to the regression as an additional explanatory variable. If its coefficient is not significantly differently from zero, we can conclude there is no evidence of selection bias. Column C in Table 2-3 presents the results of the first set of regressions after the Heckman's treatment. The coefficient on the inverse Mills ratio is not statistically different from zero. Nor does the coefficient on the Rule 144A dummy change significantly after Heckman's treatment. There is thus no evidence that the yield differences between Rule 144A issues and public issues are due to sample selection bias. 22 Table 2-4 differentiates the regressions by high-yield bonds and investment-grade bonds. In Column A, the coefficient for Rule 144A issues is much higher for high-yield bonds than for investment-grade bonds. In other words, the yield premium for high-yield Rule 144A bonds is much higher than the yield premium for investment-grade Rule 144A bonds. Similarly, in Column B, the regression coefficient for SEC-reporting issues is higher for high-yield bonds than for investment-grade bonds. For Rule 144A issues by non-reporting firms, the coefficient for high-yield bonds is slightly lower than the coefficient for investment-grade bonds, although the difference is not statistically significant.14 This is somewhat surprising, given that high-yield Rule 144A issues on average have considerably higher yield premiums than investment-grade Rule 144A issues. One possible explanation is that the information uncertainty of nonSEC-reporting firms is very severe and has a first-order impact on yields. The difference between high-yield and investment-grade Rule 144A is overshadowed by the severe information uncertainty of the non-SEC-reporting firms. 1 To test the statistical significance of the difference between the two coefficients, we run a pooled regression of high-yield and investment-grade bonds. In addition to the explanatory variables in the separate regressions, we create a 0-1dummy variable for high-yield bonds and interact it with all the other explanatory variables. The results of the pooled regression are identical to those of the separate regressions, and the coefficients on these interaction terms are the differences in the coefficients between the separate high-yield and investment-grade regressions. The coefficient on the interaction term between high-yield dummy and Rule 144A by non-reporting firm dummy is -10.64 but not significant. The coefficient on the interaction term between high-yield dummy and Rule 144A by reporting firm dummy is 22.22 and significant at the 1% level. 23 In summary, we have three basic findings about Treasury spread. First, Rule 144A issues have on average a yield premium of 19 basis points over public debts, everything else equal. This is consistent with the expected impact of Rule 144A on bond yields. Second, Rule 144A issues by non-SEC-reporting firms have considerably higher yield premiums, 54 basis points, than Rule 144A issues by SEC-reporting firms. This is consistent with the information uncertainty argument. Investors are concerned about the quantity and quality of disclosures for Rule 144A issues because they are not registered with the SEC. Firms that file periodic disclosure statements with the SEC already have made a considerable amount of firm-specific information available, so there is less information uncertainty. For issuers without periodic reports or disclosure statements, information uncertainty is of greater concern, and yield premiums are higher. Third, high-yield Rule 144A issues have higher yield premiums than investmentgrade Rule 144A issues. This finding is consistent with the weaker legal protection and liquidity arguments. Concerns about legal protection may be of greater importance to insurance companies, which are required by regulation to make prudent investments, especially when they are investing in high-yield bonds. High-yield Rule 144A issues are acceptable to a smaller pool of potential investors, and they are less liquid than investment-grade Rule 144A issues. It is not surprising that high-yield Rule 144A issues have higher yield premiums than investment-grade Rule 144A issues. Comparison to Fen's Study Our findings are different from those of Fenn (2000). Fenn finds that the yield premiums of Rule 144A over public debt issues have disappeared in recent years. We find the yield premiums of Rule 144A issues still exist. When we try to reproduce Fenn's 24 results using his methodology, we find that they are sensitive to 1) the regression model specification, and 2) the time period. First, we follow Fenn's methodology and create a sample of non-convertible highyield bond issues from 1993 to the first half of 1998. Our mimic sample is very close to Fenn's (1,566 observations compared to his 1,562). The distributions of the mimic sample over years, ratings, and industry categories are similar to Fenn's sample.'5 To control for the variation of corporate bond yields over the years, Fenn uses a year trend variable, set equal to issuing year minus 1993. To test whether the yield premium on Rule 144A has changed over the years, Fenn adds an interaction term between the Rule 144A dummy and the year trend variable in the regression. He finds that the yield premium on Rule 144A issues over public debt issues is about 41 basis points, but dropping by 8 basis points every year (as the interaction term shows). Hence, Fenn concludes that the yield premium disappears by 1998 (41 - 8(98-93) = 1). Fenn's results are provided in the first column of Table 2-5 (Fenn's Table 5, column 2, p. 396). We follow Fenn's methodology and run the same regression. Our results are reported in the second column of Table 2-5. Most of our coefficients are very close to Fenn's and have the same significance level, although our mimic regression has a slightly lower R-squared value. The mimic regression finds that the yield premium for Rule 144A is about 58 basis points, and declines by 12 basis points each year. Although the coefficients on the Rule 144A dummy and the interaction term are higher for our mimic 1 When we run the same baseline regression on our mimic sample set (with no Rule 144A dummies as in Fenn's paper), we find the coefficients are very close to Fenn's. The complete comparisons are available from the authors. 25 regression, the basic interpretation is the same as Fenn's; that is, the yield premium disappears by 1998 (58 - 12*5 = -2). The year trend variable, however, implicitly assumes a linear time trend for yields on high-yield bonds. The yields on high-yield bonds increased from 1993 to 1995 and decreased significantly in 1997 and 1998. The annual averages of the Merrill Lynch High Yield 175 Index are 10.38%, 10.71%, 11.05%, 10.40%, 9.76%, and 9.19% from 1993 to 1998, clearly not a linear trend.16 A negative coefficient on the linear year trend variable in Fenn's study erroneously estimates declining yields from 1993 through 1995 and underestimates the decline in yields in 1997 and 1998. This underestimation coincides with an increased percentage of Rule 144A issues in the high-yield bond market. Hence, the interaction term of the Rule 144A dummy and the year variable picks up some of the underestimation of the yield decreases of high-yield bonds in 1997 and 1998. When we change the year trend variable to 0-1 dummy variables for each year, we find that the coefficient on the interaction term drops significantly, from -12 to -9 basis points and the significance level declines from 1% to 5% (Table 2-5, Column 3). The coefficient on the Rule 144A dummy changes only slightly. Hence, we can no longer claim that the yield premium disappears completely in 1998 (55 - 9*5 = 10), although it still shows a declining trend. The coefficients on the year dummies confirm that yields do not drop significantly until 1997. 16 The Merrill Lynch High Yield 175 Index tracks the performance of the 175 most liquid below-investment-grade public US corporate bonds. 26 More important, when we expand the sample by including the second half of 1998 and 1999 (Table 2-5, Column 4), the interaction term becomes insignificant, while the yield premium for Rule 144A issues is 35 basis points and significant. Thus, the yield premium for Rule 144A issues does not disappear over time. In separate regressions for each year (unreported but available on request), we find that the yield premiums for Rule 144A issues are low for 1996 and 1997 (similar to Fenn's), but range from 40 to 80 basis points in the second half of 1998 and 1999. Hence, instead of disappearing yield premiums, we find fluctuating yield premiums on Rule 144A issues over the years: high in 1993 to 1995, low in 1996 to the first half of 1998, and high again in the second half of 1998 and 1999. Fenn's data end at the first half of 1998, while ours extend through 1999. This time period difference contributes to the different findings.'7 In summary, the evidence of declining yield premiums is not robust to changes in regression specification and time periods. Use of Registration Rights and Their Impact There have been conflicting claims about the use of registration rights. To investigate the question further, we search on the Bloomberg database for post-issue registration of every Rule 144A issue in our sample. For issues not in Bloomberg, we search the company name in the SEC's electronic database EDGAR for registration statements. We are able to find 1,326 of the 1,418 Rule 144A issues in either Bloomberg or EDGAR. Table 2-6 gives our findings. 17 We obtain similar results when we include first-time issuer dummy, private firm dummy, and their interaction terms with the Rule 144A dummy in the regression. Similar results are also obtained when only B-rated bonds are investigated. 27 Like Fenn, we find that virtually all high-yield Rule 144A bonds issued between 1997 and 1999 have registration rights. Only 44% of the investment-grade Rule 144A bonds, however, have registration rights.18 The impact of registration rights on the Treasury spread is examined in Table 2-7 for both investment-grade and high-yield bonds. The same regression as in Table 2.3. is run with two dummy variables for Rule 144A issues: those with registration rights and those without registration rights. Several results are noteworthy. First, the coefficients for high-yield bonds are larger in absolute value than for investment-grade bonds, consistent with the findings in Table 2.4. Second, the yield premium for high-yield Rule 144A issues without registration rights is 82 basis points, compared to 33 basis points for issues with registration rights. A chi-square test rejects the null hypothesis that these two coefficients are the same at the 10% level.'9 This finding indicates that registration rights help to reduce the yield premium for high-yield Rule 144A bonds over public debt. Note that this finding should be treated 18 While Rule 144A issues by non-reporting firms may choose not to have registration rights to remain private, the evidence does not support this argument. First, although more than a quarter of high-yield Rule 144A bonds are issued by non-reporting firms, 95% of them have registration rights. Second, for investment-grade Rule 144A issues, 39% of those by non-reporting firms have registration rights, while 44% of those by reporting firms have registration rights. Thus, there is no dramatic difference in the use of registration rights by reporting vs. non-reporting firms. 1 We also run a regression on Rule 144A issues only, with a registration right dummy variable (1 if with registration rights and zero otherwise). The coefficient on the registration rights is negative and significant at the 10% level, indicating that high-yield Rule 144A issues with registration rights have lower yields than similar Rule 144A issues without registration rights. 28 with caution, because there are only 17 high-yield Rule 144A issues without registration rights. The yield premium for investment-grade Rule 144A issues without registration rights is smaller than the yield premium on investment-grade issues with registration rights, but the difference between the two coefficients is not statistically significant.20 These findings together suggest that registration rights help to reduce yield premiums for high-yield Rule 144A issues, and hence most issuers of high-yield Rule 144A issues choose to have registration rights. Registration rights do not seem to make a difference in yield premiums for investment-grade bonds, and issuing firms are thus relatively indifferent with respect to registration rights. These findings are consistent with several explanations. First, because of the greater riskiness of high-yield bonds, agency costs and moral hazard problems tend to be higher (Jensen and Meckling, 1976, and Campbell and Kracaw, 1990). Hence, investors would want more information disclosure for high-yield bonds. With registration rights, the issuing firm promises to register in the near future and meet stricter disclosure requirements of the 1933 Securities Act, signaling investors that the issuer is not hiding unfavorable information. Second, there is a smaller pool of potential investors for high-yield bonds than investment-grade bonds because of legal restrictions on investments in high-yield bonds for some institutional investors. The number of potential investors in Rule 144A issues 20 A chi-square test fails to reject the null hypothesis that the two coefficients are the same. We also run a regression on Rule 144A issues only, with a registration right dummy variable (1 if with registration rights and 0 otherwise). The coefficient on the registration rights is not statistically different from zero, indicating that registration rights do not have an impact on yields for investment-grade Rule 144A issues. 29 increases after the issue becomes registered. Consequently, registration rights would help to reduce the illiquidity premium on high-yield Rule 144A issues, but would have less of an impact on investment-grade Rule 144A issues. Underwriter Spread The impact of Rule 144A upon gross underwriter spread is shown in Table 2-8 In Column A, the Rule 144A dummy variable includes all issues sold through Rule 144A. This coefficient is not significant. In Column B, Rule 144A issues are separated into non-reporting firms (with no publicly traded securities) and firms filing periodic financial statements with the SEC. Neither coefficient is significantly different from zero. The first-time debt issue dummy variable is positive and significant. Log of issue frequency is negative and significant. Percentage of Years of Call Protection is negative and significant. Senior debt has a negative and significant coefficient. Maturity has a positive and significant coefficient. The utility firm dummy has a negative and significant coefficient. Note that the coefficients for all the investment-grade rating dummy variables are not significantly different from zero. As ratings fall below investment grade, coefficients become significant and increase, indicating that gross underwriter fees are much higher for high-yield bonds because of the greater difficulties in selling these bonds. This is consistent with Livingston and Miller (2000). An unreported regression for gross underwriter spread for high-yield bonds and investment-grade bonds separately finds that the coefficient for investment-grade Rule 144A issues is 4 basis points and significant, but a coefficient of this magnitude is not economically meaningful. The coefficient for the high-yield Rule 144A issues is not significant. 30 In summary, we find that gross underwriter spreads are not statistically different for Rule 144A and public debt issues in general. There are offsetting impacts of Rule 144A on the spread. On the one hand, fewer potential investors and information uncertainty make underwriting Rule 144A issues harder than public debt. On the other hand, underwriting Rule 144A issues may be less risky in some ways and involve less work for underwriters. Our finding of similar underwriter spreads suggests that the two impacts offset each other. Conclusion Rule 144A bonds do not require a registration filing with the Securities and Exchange Commission. They may be purchased by qualified financial institutions and traded to other qualified financial institutions, but may not be purchased by individuals. Some Rule 144A bonds require the issuer to replace the bonds with publicly traded bonds within a stipulated period of time and are designated as having registration rights. Although high-yield bonds issued under Rule 144A usually have registration rights, we find that the majority of investment-grade bonds do not. Our empirical results indicate that Rule 144A bond issues have higher yields to maturity than publicly issued bonds. The effect is greater for Rule 144A bonds issued by private firms without publicly traded securities. The yield premiums of Rule 144A issues are likely due to lower liquidity, information uncertainty, and weaker legal protection for investors. Gross underwriter spreads for Rule 144A bond issues and publicly registered bond issues are essentially equivalent. 31 1200.00 1000.00 800.00 600.00 400.00 200.00 0.00 [ Rule 144a 0 Private Debt E Public Debt 1990 1991 1992 1993 1994 1995 1996 1997 1998 Figure 2-1 Annual Issues of Rule 144A, Private, and Public Non-Convertible Debt Market 160.00 140.00 a 120.00 1- 0 Rule 144a S80.00 80.N Private Debt 60.00 Public Debt 40.00 20.00 0.00 1990 1991 1992 1993 1994 1995 1996 1997 1998 Figure 2-2 Average Issue Size 32 60.00% 50.00% 40.00%/o 30.00% 20.00% 10.00% C00 OW ri-iFI n-FHFL o Rule 144A o Public F 2 sfR Figure 2-3 Distribution of Ratings rfl nFI - -1 p 33 Table 2-1 Descriptive Statistics for Full Sample, 1997 - 1999 Publ Number of Issues Number of Issuing Firms Average Number of Issues Per Issuing Firm Average Proceeds(in Millions) Percentage of Investment-Grade Issues Percentage of Senior Debt Avg. Gross Underwriter Spread (in Basis Points) Original Yield Avg. Basis Points of Treasury Spread Percentage of Industrial Percentage of Utility Firms Avg. Percentage of Years That are Call Protected Average Years to Maturity Percentage of Public Firms Percentage of First-Time Debt Issue Percentage of Issues by Non-Reporting Firms Significantly different from public issues at the 1% level(*) ic Issues 2652 663 4.0 $129.04 (2635) 91.48% 98.30% 72 (1985) 6.81% (2093) 115 (2093) 64.89% 35.11% 73.96% (2648) 12.17 97.70% 10.56% 0.68% Rule 144A Issues 1418 944 1.5 $177.69* (1406) 31.59% 67.70% 200* (444) 9.18%* (1317) 351* (1317) 73.06% 26.94% 57.75%* (1288) 10.24* 66.36% 51.20% 23.20% 34 Table 2-1 Continued Note: The sample is obtained from the New Issue Database of Securities Data Company (SDC) and consists of domestic Rule 144A and public non-convertible, fixed coupon rate bond issues by industrial and utility firms from January 1997 through the end of 1999. Issues that are not rated by both Moody's and S&P are excluded. Also, perpetual issues are excluded. The numbers in parentheses are numbers of observations used to calculate the averages. 35 Table 2-2 Comparison of Gross Underwriter Spread and Treasury Spread by Ratings Gross Underwriter Spread Treasury Spread Public Rule 144A Public Rule 144A Rating Issues Issues Issues Issues AAA 65 51 78 103 (13) (7) (25) (23) AAA/AA 53 N.A.a 81 208 (7) (0) (7) (2) AA 62 68 80 101 (144) (4) (142) (24) AA/A 57 88** 96 146*** (92) (3) (73) (4) A 55 54 80 118* (766) (28) (834) (92) A/BBB 67 59 116 111 (106) (19) (111) (55) BBB 61 67** 120 162* (647) (57) (684) (157) BBB/BB 81 91 169 181 (26) (12) (26) (29) BB 154 176** 217 276* (112) (43) (115) (106) BB/B 237 254 337 357 (10) (18) (10) (50) B 258 266 379 453* (56) (223) (60) (704) B/CCC 288 279 507 563 (4) (24) (4) (51) CCC and 335 321 661 687 Below (2) (6) (2) (20) a No Rule 144A issues with gross underwriter spread information fall into the AAA/AA category. Significantly different from public issues at the 1% level(*), 5% level (**) and 10% level Note: This table compares the mean gross underwriter spread and Treasury spread of Rule 144A and public issues of all rating categories. When an issue has either a Moody's or an S&P rating, that rating is used. If an issue is rated by both Moody's and S&P, and the two rating agencies agree on the rating, then that rating is used. If Moody's and S&P disagree on the rating, a split rating is assigned. For example, if Moody's rates an issue Aaa and S&P rates AA, then split rating AAA/AA is assigned to the issue. The numbers in parentheses are numbers of observations used to calculate the means. 36 Table 2-3 Treasury Spread Regression Column A Column B Column C (One Dummy (Two Dummies Independent Rule 144A for Rule 144A (Heckman's Variables Issues) Issues) Treatment) Intercept -108.07* -122.78* -108.58* Rule 144A Dummy 18.97* 19.99* Rule 144A by Non-Reporting Firm - 53.92* Rule 144A by Reporting Finn - 19.03* First-Time Debt Issue Dummy 30.14* 24.38* 30.13* Public Firm Dummy -27.94* -9.42 -27.97* Log of Issue Frequency -7.56* -7.78* -7.57* Year 1998 Dummy -10.66* -10.51* -10.77* Year 1999 Dummy 5.34 5.40 5.16 Default Risk Premium 1.00* 0.99* 0.99* Log of Proceeds -3.11* -3.19* -3.14* AA 9.73 9.12 9.82 AA/A 22.55 20.40 22.68 A 15.35 13.34 15.49 A/BBB 34.46* 33.65* 34.57* BBB 54.49* 52.62* 54.63* BBB/BB 93.50* 92.04* 93.14* BB 173.18* 171.58* 173.20* BB/B 286.43* 284.33* 286.16* B 370.58* 368.17* 370.53* B/CCC 483.48* 479.02* 480.61* CCC and Below 592.77* 588.43* 592.39* Percentage of Years of Call Protection 1.68 1.55 1.75 Senior Debt Dummy 48.95* 48.70* 49.34* Log of Maturity 17.27* 17.31* 17.31* Utility Firm Dummy -9.30* -8.87* -9.32* Inverse Mills Ratio - -0.58 3258 3258 3258 Number of Obs. 0.83 0.83 0.83 Adjusted R2 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*), 5% level (**) and 10% level (***). This table shows the regressions of Treasury spread on control variables for risks and test variables. The dependent variable is the Treasury spread. The base case is an AAA-rated bond issued in 1997. First-Time Debt Issue dummy equals one if the issuer has not issued any fixed income security (straight debt, convertible debt or preferred stocks) since 1970, 37 Table 2-3 Continued and zero otherwise. Public Firm dummy equals one if the issuer has publicly traded equity, zero otherwise. Log of Issue Frequency is the natural log of the number of the offerings each issuer had during the sample period. Year 1998 dummy equals one if the bond is issued in 1998 and zero otherwise. Year 1999 dummy equals one if the bond is issued in 1999 and zero otherwise. Default Risk Premium is the difference between the Merrill Lynch BBB Bond Index and the Merrill Lynch 10-Year Treasury Index. Percentage of Years of Call Protection is the percentage of years that the bond is call protected. Senior debt dummy equals one for senior debt issue, zero otherwise. Column A reports results when Rule 144A dummy is used. Rule 144A dummy equals one if the offering is issued under Rule 144A, and zero otherwise. The regression tests whether the Rule 144A issues have higher yields over public issues. Column B uses two dummy variables for Rule 144A issues: one for Non-Reporting Firms, and one for Reporting Firms. If the issuing firm of a Rule 144A offering has not issued any public fixed income security (straight debt, convertible debt or preferred stock) since 1970, and the issuing firm and its parent firm do not have public traded equity, we classify the firm as non-reporting. Rule 144A by Non-Reporting Firms dummy equals one if the issuing firm is a non-reporting firm, and zero otherwise. Rule 144A by Reporting Firms dummy equals one if the issuing firm is a reporting firm, and zero otherwise. Column C reports the regression results of Column A after correcting for selection bias. We first estimate a probit model on the choice of Rule 144A issue or public issue and then calculate the inverse Mills ratio. It is then added to the regression as an additional variable to detect and correct for possible selection bias. 38 Table 2-4 Separate Treasury Spread Regressions for High-Yield Bonds and InvestmentGrade Bonds Colun Regre High-Yield Bonds n A Column B ssion Regression Investment-Grade Bonds Column A Column B Regression Regression Rule 144A 35.39* - 13.94* Rule 144A by Non-reporting Firm - 47.73* - 58.37* Rule 144A by Reporting Firm - 34.71* - 12.49* First-Time Debt Issue 44.2 1* 40.94* 19.64* 15.97* Dummy No. of Obs. 1065 1065 2193 2193 R-square 0.59 0.59 0.54 0.54 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*). This table shows separate Treasury spread regressions for high-yield bonds and investment-grade bonds. Only coefficients on the Rule 144A dummies and first-time debt issue dummy are reported. The coefficients on other regressors are similar to those reported in Table 2-3. 39 Table 2-5 Comparison to Fenn (2000) Variables Rating Log Issue Size Log maturity Senior Zero coupon Merrill Lynch Index Year Fenn's -0.67* -0.12* -0.26* 0.81* 0.67* 0.58* -0.12* Mimic Sample -0.67* -0.22* -0.32* 0.83* 0.45* 0.58* -0.09* Mimic Sample with Modified Year Dummies -0.67* -0.22* -0.32* 0.83* 0.44* 0.58* Expanded Sample (1993-1999) -0.66* -0.09* -0.14** 0.70* 0.56* 0.70* Rule 144A 0.41* 0.58* 0.55* 0.35* 144A*Year -0.08** -0.12* -0.09** 0.03 Year 1993 - - 0.46* 0.18 Year 1994 - - 0.62* 0.47* Year 1995 - 0.49* 0.16 Year 1996 - - 0.30* -0.01 Year 1997 - 0.00 -0.38* Year 1998 - - - -0.36* Adjusted R-square 0.67 0.60 0.61 0.59 No. of obs. 1562 1566 1566 2088 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*) and 5% level (**). Note: The first column of this table reprints Fenn's results (column 2 of Table 5, p. 396 of Fenn's paper). The second column gives the regression coefficients for our mimic sample. The third column gives the regression coefficients after we change the year trend variable (issuing year-1993) to 0-1 dummy variables for each year. The fourth column reports the regression coefficients after we expand the sample by including the second half of 1998 and 1999 data. - - 40 Table 2-6 Use of Registration Rights by Rule 144A Issues High-yield Investment-grade All Rule 144A Issues Rule 144A Issues Rule 144A Issues No. of Issues with Registration Rights 936 163 1099 Percentage of Issues with Registration Rights 98.22% 43.70% 82.88% Total No. of Issues 953 373 1326 Note: This table gives information on the use of registration rights by Rule 144A issues. For every Rule 144A issue, we check Bloomberg and SEC's EDGAR for post-issue registration and exchange offer. If a Rule 144A has been exchanged for an identical publicly registered debt issue, or the Rule 144A has been registered with the SEC after the initial issue, we classify it as Rule 144A issue with Registration Rights. Of 1,418 Rule 144A issues in our sample, we find 1,326 on either Bloomberg or EDGAR. 41 Table 2-7 Treasury Spread on Rule 144A Issues with and without Registration Rights High-Yield Bonds Investment-Grade Bonds Rule 144A with Reg. Rights 32.57* 14.30* Rule 144A w/o Reg. Rights 81.52* 7.11* First-Time Debt Issue Dummy 44.68* 14.94* Public Firm Dummy -26.90* -5.81 No. ofobs 1054 2155 R-square 0.59 0.54 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*). Note: This table compares Treasury spreads on Rule 144A offerings with registration rights, Rule 144A without registration rights, and public debt. The sample includes both Rule 144A issues and public debt issues. Only coefficients on the Rule 144A dummies, first-time issuer, and public firm dummies are reported. Coefficients on other regressors are similar to those reported in table 2-3. The dummy Rule 144A with Reg. Rights equals I if the bond is a Rule 144A issue with registration right and zero otherwise. The dummy variable Rule 144A w/o Reg. Rights equals 1 if the bond is a Rule 144A issue without registration right and zero otherwise. The base case is public issues. Two separate regressions are run for high-yield bonds and investment-grade bonds respectively. 42 Table 2-8 Gross Underwriter Spread Regression Independent Variables Intercept Rule 144A Dummy Rule 144A by Non-Reporting Firm Rule 144A by Reporting Firm First-Time Debt Issue Dummy Public Firm Dummy Log of Issue Frequency Year 1998 Dummy Year 1999 Dummy Default Risk Premium Log of Proceeds AA AA/A A A/BBB BBB BBB/BB BB BB/B B Column A (One Dummy for Rule 144A Issues) 44.30* 4.36 Column B (Two Dummies for Rule 144A Issues) 42.37* 4.28** -3.12 -3.24* -1.35 -2.74 -0.01 -0.84 11.53 7.25 10.27 13.62 11.73 26.75* 110.66* 182.5 1* 194.81 * 8.15 4.08 4.02** -1.12 -3.25* -1.33 -2.72 -0.56 -0.83 11.57 7.23 10.30 13.68 11.73 26.74* 110.80* 182.5 1* 194.80* B/CCC 207.19* 206.61* CCC and Below 261.88* 261.93* Percentage of Years of Call Protection -6.09* -6.12* Senior Debt Dummy -14.21* -14.20* Log of Maturity 16.90* 16.89* Utility Firm Dummy -3.50* -3.47* Number of Obs. 2368 2368 Adjusted R2 0.83 0.83 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*) and 5 % level (**). Note: This table shows the results of the regressions of gross underwriter spread on control variables for risks and test variables. The dependent variable is the gross underwriter spread in basis points. The base case in the regression is an AAA-rated bond issued in 1997. First-Time Debt Issue dummy equals one if the issuer has not issued any fixed income security (straight debt, convertible debt or preferred stocks) since 1970, and zero otherwise. Public Firm dummy equals one if the issuer has publicly traded equity, zero otherwise. Log of Issue Frequency is the natural log of the number of the offerings 43 Table 2-8 Continued each issuer had during the sample period. Year 1998 dummy equals one if the bond is issued in 1998 and zero otherwise. Year 1999 dummy equals one if the bond is issued in 1999 and zero otherwise. Default Risk Premium is the difference between the Merrill Lynch BBB Bond Index and the Merrill Lynch 10-Year Treasury Index. Percentage of Years of Call Protection is the percentage of years that the bond is call protected. Senior debt dummy equals one for senior debt issue, zero otherwise. Column A reports the results of the regression where the Rule 144A dummy is used. Rule 144A dummy equals one if the offering is issued under Rule 144A, and zero otherwise. The regression tests if the Rule 144A issues have higher gross underwriter spread over public issues. Column B uses two dummy variables: Rule 144A by Non-Reporting Firms, and Rule 144A by Reporting Firms. If the issuing firm of a Rule 144A offering has not issued any public fixed income security (straight debt, convertible debt, or preferred stock) since 1970, and the issuing firm and its parent firm do not have public traded equity, we classify the firm as non-reporting. Rule 144A by Non-Reporting Firms dummy equals one if the issuing firm is a non-reporting firm, and zero otherwise. Rule 144A by Reporting Firms dummy equals one if the issuing firm is a reporting firm, and zero otherwise. CHAPTER 3 BOND RATINGS AND PRIVATE INFORAMTION Introduction Bond ratings are an important component of the US financial world: almost all large corporate bonds have ratings. Bond ratings are used extensively as a proxy for bond riskiness and investors rely heavily on bond ratings to determine bond yields. Financial regulators also use bond ratings as a regulatory tool. For example, the Savings and Loan Associations are prohibited from investing in below investment-grade bonds. Because of their importance, there are extensive academic studies on bond ratings. One important question concerns about their information content. Rating agencies claim that bond ratings contain information beyond what is publicly available. When deciding on bond ratings, rating agencies usually meet with the management of the issuing firm that shares information with the rating agencies. Some of the information may be private information that the management does not disclose to the general public. Previous research on the information content of ratings takes two approaches. The first line of research studies the relationship between bond ratings and yields. West (1973), Liu and Thakor (1984), Ederington, Yawitz and Roberts (1987) and Reiter and Ziebart (1991) fall into this category. Generally, these studies find that ratings and bond yields are negatively correlated after controlling for some important publicly available information, implying that highly rated firms tend to have favorable private information. The second line of research examines the impact of rating changes on the bond yields and stock price. The results of these studies are mixed. While Weinstein (1977), 44 45 and Pinches and Singleton (1978) do not find an impact of rating changes on bond yields, Katz (1974), Grier and Katz (1976), and Ingram, Brooks and Copeland (1983) find significant changes in bond yields in response to bond rating changes. More recently, Holthausen and Leftwich (1986), and Hand, Holthausen and Leftwich (1992) find stock price goes up (down) when the firm's bond rating is upgraded (downgraded) or likely to be upgraded (downgraded). On the other hand, Kliger and Sarig (2000) find that equity value decreases (increases) when the firm's bond receives a better (worse) than expected rating from Moody's. Though the previous research has found some evidence that bond ratings have additional explanatory power of bond yields after controlling for a few pieces of public information, they fail to answer the question whether the bond ratings contain private information or additional publicly available information not included in their models. This study attempts to link the additional explanatory power of bond ratings to the degree of information asymmetry of the issuing firm in a latent variable model. Specifically, we use the latent variable methodology to identify two risk factors contained in the bond ratings. The first risk factor is common among bond ratings and four observable accounting variables: interest coverage ratio, leverage ratio, firm size and ROA. The second risk factor is not observable from the four financial variables, but is a common risk factor among bond ratings and proxies for information asymmetry. This second risk factor intends to capture private information in ratings. The larger the information asymmetry problem, the more private information the management would share with the rating agencies. Hence, if bond ratings do contain private information, then the proxies for information asymmetry should be correlated with the second risk 46 factors. The three variables used to proxy information asymmetry are firm size, analysts' earning forecast errors, and the adverse selection components of the stock bid-ask spread. We find that the second risk factor is indeed related to the information asymmetry proxies. Furthermore, the second risk factor is priced by the bond market. This is consistent with the hypothesis that bond ratings contain private information and such private information can be conveyed to the bond market through bond ratings. The rest of the chapter is organized as follows. The next section reviews the previous literature on the information content of bond ratings. The third section briefly discusses some technical issues of the latent variable model. Next, we describe the data and define the variables. The fifth section gives the empirical results and final section concludes the paper. Literature Review Rating agencies play a very important role in the US financial market through assigning credit ratings to corporate bonds. Bond rating is a significant determinant of bond yields and underwriter fees (see, for example, Jewell and Livingston, 1998). Ratings are also used extensively as regulatory tools. One important question then is how rating agencies determine bond ratings. Rating agencies claim that they incorporate private information beyond publicly available financial data into bond ratings. Much academic research uses various statistical models to predict bond ratings by several observable economic and financial variables and finds that only 50% to 70% of bond ratings can be explained by a few public available variables (see Kaplan and Urwitz, 1979, for a review). These studies seem to be consistent with the rating agencies' claim that there is more in the bond ratings than several publicly available financial ratios. However, the statistical models used in the previous studies fail to incorporate all 47 publicly available information. Hence, the remaining 30% to 50% of the variations in bond ratings not explained in the statistical models may be due to other public information not controlled for in the models, rather than private information rating agencies may have. To investigate the private information content of bond ratings, previous research has taken two paths. The first line of research investigates the relationship between bond rating and bond yield. In a classic study, Fisher (1959) finds that about 75% of bond yields can be explained by four observable variables: earnings variability, period of solvency, equity/debt ratio and bonds outstanding. West (1973) extends the study and finds that the residuals in the Fisher's bond yield regression are negatively correlated with the bond ratings: the higher the bond rating, lower the residual and, hence, the lower the bond yields. Based on the finding, West argues that the bond ratings have an independent impact on bond yields. However, the argument is problematic. It implicitly assumes that bond ratings are independent of the observable financial characteristics. However, since the bond ratings are partially determined by financial characteristics, only the surprise component of the bond ratings would have an impact on yield above and beyond the financial characteristics if they have an independent impact at all. For example, if a bond has similar observable financial characters as AAA bonds but carries an AA rating, then it would have a positive residual, or higher bond yields, in Fisher's yield regression. It would have a negative residual only if it has AA rating but similar observable financial characters as A bond. Hence, if the bond ratings have an independent impact on yield, 48 West's evidence only suggests that higher rated bonds are systematically rated higher than their financial characteristics predict. Ederington, Yawitz and Roberts (1987) regress bond yields on bond ratings as well as four financial variables (total assets, interest coverage ratio, leverage ratio and deviations of coverage ratio from historical trend). They find that both bond ratings and financial variables have explanatory power and therefore argue that bond ratings have information content above and beyond the four publicly observable financial variables. However, the methodology of this study is problematic. As previous research (see Kaplan and Urwitz, 1979) shows that 50-70% of bond ratings can be explained by a few observable financial variables, it is not appropriate to include both ratings and observable financial variables in the same regression because of potential multicollinearity problem. Liu and Thakor (1984) adopt a different methodology to avoid the potential multicollinearity problem. In their study of municipal bonds, they first regress the bond ratings on four observable economic variables and retrieve the residuals. They then regress the bond yields on the same four observable variables and the rating regression residuals. The rating regression residuals are found to have explanatory power in addition to the four observable economic variables. More recently, Reiter and Ziebart (1991) use a simultaneous equation technique and find that both bond ratings and financial information have impact on bond yields. Though these studies consistently find that bond ratings have an impact on bond yields above and beyond several observable financial or economic variables, they fail to directly address the question of whether bond ratings contain information that is not publicly available. Three plausible explanations may be consistent with the findings. 49 First, bond ratings contain publicly available information not captured in the few selected variables in the studies. For example, a pharmaceutical company may have a miracle drug for cancer pending FDA approval. This information may not be captured in the common financial variables like firm size or leverage ratio, but is publicly available to both the investors and rating agencies. Such information has an impact on bond ratings and yields concurrently. Hence, the observed additional impact of bond ratings on yields may be due to important omitted public information. Second, bond ratings may have an impact on bond yields due to their role as regulatory tools even if they do not have private information. In recent years, financial regulators are increasingly relying on bond ratings to regulate financial institutions. These regulations either prohibit certain financial institutions from investing in lower rated bonds, or require them to make larger capital reserve for investment in lower rate bonds (see Cantor and Packer, 1995 for a list of such regulations). Such regulations may force the issuing firms of lower rated bonds to increase bond yields to overcome the regulatory bias against them. Hence, even if bond ratings do not contain any private information, they would have an impact on bond yields because of their role as regulatory tools. The third explanation is that bond ratings have private information. However, the previous research has not provided any direct evidence that the additional explanatory power of ratings on bond yields derives from private information in ratings. The second line of research studies bond yields and stock price changes before and after rating changes, effectively controlling for all publicly available information for each firm. The basic argument of these studies is that rating changes should have an 50 impact on the bond yields and/or stock prices if they contain private information. On the other hand, if bond ratings only reflect publicly available information, then bond rating changes should not have an impact on bond yields and/or stock returns. Rather, there should be abnormal returns on bonds and/or stocks before the rating changes as new information becomes public that have an impact on bond yields and/or stock prices and also eventually lead to rating changes. The results of these studies are mixed. Earlier studies like Pinches and Singleton (1978) and Weinstein (1977) find that there are no abnormal returns on common stocks and corporate bonds after bond rating changes, but there seem to be abnormal returns before the bond rating changes. Such evidence indicates that rating agencies are lagging behind the capital market in incorporating new information on the bond ratings. On the other hand, Grier and Katz (1976), Katz (1974), and Ingram, Brook and Copeland (1983) find that bond yields do change in response to rating reclassifications. More recently, Holthausen and Leftwich (1986), and Hand, Holthausen and Leftwich (1992) use daily bond and stock price to study the reaction of bond and stock prices to both actual and potential rating changes. They generally find stock price goes up (down) when the firm's bond rating is upgraded (downgraded) or likely to be upgraded (downgraded). On the other hand, Kliger and Sarig (2000) find that equity value decreases (increases) when the firm's bond issues receives a better (worse) than expected rating from Moody's. This line of research eliminates the difficulties of controlling for all public information, but it still fails to provide direct links between bond ratings and private information. As mentioned earlier, bond ratings may have an independent impact on bond yields because of their role as regulatory tools. Hence, evidence of impact of 51 ratings changes on bond yields and/or stock returns does not necessarily imply private information in bond ratings. Methodology This study tries to provide direct links between private information content and bond rating by using the latent-variable technique. By definition, private information is not observable and not available to the general public. Hence, it is impossible to relate private information to bond ratings directly in a traditional regression model. However, the latent-variable technique can estimate the impact of an unobservable independent variable on some dependent variable as long as there are proxies for the unobservable variable. The technique has been used extensively in social science studies, where many variables, such as a person's intelligence or social status, are not observable or measurable. The basic idea of the latent variable technique is to utilize several indicators or proxies for the unobservable variable. These indicator variables are related to the unobservable variable, or latent variable, in various aspects. For example, the default risk of a particular bond issue is an unobservable variable, but a firm's leverage ratio, interest coverage ratio, profitability and firm sizes are all related to the default risk. Each of these indicator variables itself is a poor proxy for the latent variable, but it is possible to get a better measurement of the latent variable if several indicator variables are utilized simultaneously. The basic idea of the latent variable technique is to use a set of linear equations, where there are some unobservable latent variables and multiple indicator variables for each latent variable. Provided all the parameters are identifiable, this technique can yield the estimates of the unknown coefficients in the model. 52 The latent variable technique is discussed in detail in Joreskog and Goldberger (1979), Bollen (1989), and other papers (see, for example, Zellner, 1970, Goldberger, 1972). A Simple Latent Variable Model Suppose that Y is an nxp matrix of observable indicator variables and Z is an nxq matrix of unobservable latent variables.' P is the number of indicator variables, q is the number of latent variables and n is the number of observations. M is an nxp matrix of the means of Y (M consists of n rows of p, ap-dimension row vector of the means of the indicator variables). For simplicity, let's assume that all the latent variables have means 2 of 0, variances of I and they are not correlated with each other. Assume that Y and Z are linearly related as in the following equation: Y =M +ZP+V (1) where p is an qxp parameter matrix and f is an nxp error terms. Z and E are assumed to be uncorrelated. Let I be the covariance matrix of Y. So we have: S= (Y-M)'(Y-M) = P,'Z'Zp + F'Zp + P'Z'f + F' As Z and E are assumed to be uncorrelated, Y = P'Z'Zp + C' Capital letter in bold font stands for a matrix, lower case letter in bold font stands for a vector, and lower case italic letter stands for a scalar throughout the paper unless noted otherwise. 2 Because the latent variables are not observed, we can scale it to zero means and unit variances. 53 Since the latent variables are assumed to have means of 0 and variances of 1, Z'Z is an identity matrix. So we have: Y = p'P +V' (2) If we assume that the error terms are not correlated with each other, then F'fc is a diagonal matrix. Since Y is observable, we can estimate Y from sample data. Let S, be the sample covariance matrix of Y. So, we have S =b' + ' (3) where J = E(PI Y) and g= E(EIY) The covariance matrix of Y, or Y, is a function of P and '- and needs to be estimated. Let 0 stands for P and 't, the model parameters. So, Y = E(0). S is the covariance matrix of the sample data and can be calculated as in the following formula: 1 1 Sz IZ(Yk -P)(Yk - P) where yk is a p-dimensional row vector, representing one observation in Y (one row of Y). Equation system (3) has (p+I)p/2 equations, each equation representing one unique sample variance or covariance, and pxq + p unknown parameters. Among the unknown parameters, pxq parameters are coefficients on the q latent variables to be estimated andp parameters are error term variances. If (p+l )p/2 >pxq +p, several methods can be used to estimate the model parameters. Notice that it has been assumed for simplicity that the error terms are uncorrelated with each other. However, it is possible to allow for correlation among some error terms, as long as the number of equations in (3) is greater than the number of unknowns. The 54 maximum number of correlations between error terms is p(p-1-2q)/2. The difference in the number of equations (or the number of unique sample variance and covariance) and the number of parameters to be estimated is called the model degree of freedom. Estimation Techniques The latent variable technique allows us to estimate the coefficients on the unobservable latent variables, even if these variables cannot be measured. Several techniques can be used to estimate the model. Maximum likelihood (ML) and weighted least squares techniques are the most common methods of estimation when the indicator variables are continuous and categorical variable method (CVM) is appropriate when some or all of the indicator variables are categorical variables. Maximum likelihood method (ML) Maximum likelihood (ML) estimation assumes that Y, or indicator variables, follow a multivariate normal distribution with mean vector P. The joint probability of observing yk, or one particular observation of the p indicator variables, is then: f (Yk) =(27cY-P2 1 E 112 exp (Y' - P)Y--,('( - t =(27c)-p2 E 1-2 exp lr-i'(yk --'(Yk -P) The log-likelihood function for a sample size of n is then: 1 1 1 L= --nplog2w--nlog I--ntr--iS 2 2 2 The pxq + p unknown parameters can then be estimated by maximizing the loglikelihood function. How well the estimated model parameters fit the sample covariance matrix can be measured by ML fit function and tested by the likelihood ratio statistic. 55 Let i = J' + ' be estimated Y. The null hypothesis in the likelihood ratio test is that i = E (Ho), or the estimated covariance matrix equals the true covariance matrix. An alternative hypothesis is that S = I (HI), or the sample covariance matrix equals the true covariance. The alternative hypothesis is chosen because it does not have any constraint on the model parameters and it has the maximum value of log likelihood of observing the sample covariance. The difference in the log-likelihood of the model under the null hypothesis and alternative hypothesis is: FAIL 2 {L(HOl)-L(H1)}= log[i+tr'S-logJS-p (4) nI Equation (4) is also called the ML fit function. The fit function provides a way to measure the difference between the log likelihood of observing the sample covariance under HO and the log likelihood of observation sample covariance under the HI. Since the log likelihood is at the maximum value under HI, smaller value of the fit function indicates that the log likelihood under HO is fairly close to the maximum likelihood and the estimated model fits the sample data well. However, the fit function does not take into consideration the sample size. A better measure of the goodness of fit is the likelihood ratio statistic, which is obtained by multiplying the fit function by (n - 1). The likelihood ratio statistic is asymptotically distributed as chi-squared distribution. If the statistic is small and insignificant, the difference between the log likelihood under HO is not statistically different from the maximum likelihood, and therefore we cannot reject HO, which suggests that the model fit well. 56 Weighted least square method (WLS) The maximum likelihood estimation imposes a multivariate normal assumption on the indicator variables. In many cases, the indicator variables may not follow multivariate normal distributions. To get over the problem, Browne (1982, 1984) proposes the weighted least square estimation (WLS), which does not require the multivariate normal assumption. Even without the normality assumption, equation (2), Y = p's + E'E, still holds. One criterion for estimation is that the estimated Y be as close to S, the sample covariance matrix, as possible. Since both E and S are in matrix form, we need to minimize some scalar measure of distance between Z and S. One scalar measure is the sum of the squared differences between each distinctive element of the two matrices as follows: Fs = (s - T)(s - F)' where s is a row vector of p(p + 1)/2 elements, consisting of the non-duplicated elements of sample covariance matrix S, c is also a row vector of p(p + 1) / 2 elements, consisting of the corresponding terms in E. This distance measure, called simple unweighted least squares (ULS fit function), treats each squared difference equally. Browne proposes a weighted least squared distance measure as follows: I = (s -() W (s -()' where W, a p(p + 1)/ 2 by p(p + 1)/ 2 positive definite matrix, is the weights on the squared differences between each distinctive element of the two matrices. Browne shows that minimizing this sum of weighted squared fit function leads to robust estimation of the model parameters under a range of distributional assumptions if W is chosen be a 57 consistent estimator of the asymptotic covariance matrix of s with s. He further shows that the weighted least square estimator produces asymptotically unbiased estimates of the chi-square goodness of fit test and standard errors. Categorical variable method (CVM) Both ML and WLS methods implicitly assume that the indicator variables are continuous. When some or all of observable indicator variables are categorical variables, some of the model assumptions are violated. In many cases, some or all of the continuous indicator variables, Y, in equation (1) is not observable. Instead, another set of indicator variables, Y*, an nxp matrix, are observable. Among the p observable indicator variables, p; of them are continuous and (p -p1) of them are categorical. For continuous indicator variables, y = y, for all i = 1 to p;, where y* and y, are (nx 1) vectors. For categorical indicator variables, C, if T1,C yi <00 Ci-1 if riC y2 y,, 2 if T11 YJk < T12 I if -o where y* is the k's observation inj's categorical indicator variables, and yj~k is the k's element in the i's unobservable underlying indicator variable, for all k = I to n andj =p, top. 'ri,,2 ..., r , _ are thresholds for the categorical variablej. In this case, several assumptions of the latent variable models are violated. First of all, since Y* w Y for (p -P2) variables, Y*wM+Zp+F 58 In other words, the statistical model for Y in equation (1) does not hold for Y*. Also, the covariance matrix of the categorical indicator variables of Y* differs from the true covariance matrix of the underlying indicator variables of Y. The parameter estimators based on S*, the estimated covariance matrix of Y*, is likely to be inconsistent estimator of P. To solve this problem, Muthen (1984) proposes a three-stage estimation technique, called CVM method (Categorical Variable Method). In the three-stage estimation procedure, the thresholds for each categorical variables and means of continuous indicator variables are first estimated with limited information ML method. Then, given the first stage estimators, sample variance and covariance (for continuous variables), polychoric correlation (correlation between two categorical variables) and polyserial correlation (correlation between a categorical variables and a continuous variables) are estimated with limited information ML method. Finally, in the third stage, the model parameters will be consistently estimated by the WLS method, using the consistent estimators generated by the previous two stages. Appendix A gives a brief overview of the three-stage estimation procedure. Goodness-of-Fit of the Model In addition to the fit function and likelihood ratio test, Goodness of Fit Index (GFI) is another indication of model fitness of the latent variable model. For ML method, GFI is calculated as follows: GFI =1- [tr(i-'S - 1)2 / tr(i-S)2 For WLS and CVM methods, GFI is defined as follows: GFI = I - [(s - a)W-'(s -u)'/ sW-s'] 59 GFI is similar to the R-square of OLS in the sense that it is a measure of the amount of variance and covariance in the observed S that are accounted for by the estimated model i. When S = i (or equivalently s = a in WLS and CVM) GFI has the maximum value of 1. GFI greater than 0.9 generally indicates a well specified latent variable model. Potential Problems with Latent Variable Model While the latent variable technique is superior to OLS regression when the independent variables are not observable or measured with error, it has some potential problems that researchers need to be aware of A theory-based a priori model specification in latent variable technique is very important. Unlike OLS, the latent variable technique gives researchers greater freedom in model specification. A sample covariance matrix may be consistent with several different model specifications in that the sample data may fit different models equally well. Different model specifications, however, may lead to different substantive interpretations (MacCallum, 1995). Hence, it is important to specify an a priori model based on theories and findings from previous research. In addition, without examining all possible model specifications, researchers need to be careful when interpreting results from a particular model fit. A particular model, even when it fits the sample data very well, can only mean that it is one plausible structure of the underlying variables that produce the observed data. When there are competing theories of potential model structure, it is necessary to build alternative model specifications and compare the different models. 60 A related issue of model specification concerns about the degrees of freedom of latent variable models. As discussed before, the model degrees of freedom is the difference between the number of unique sample variance and covariance and the number of parameters to be estimated. When the latent variable model has zero degree of freedom, parameters in the model can be calculated exactly and the model will have perfect fit. However, such a model is not very interesting because it is sample data specific. On the other hand, if a model has a large number of degrees of freedom, it is hard to find a good fit. Thus, if a model with large degrees of freedom is found to fit the sample data well, we will be more confident in its results. Researchers should be cautious when interpreting results of models with very low degrees of freedom because it is likely that such results are sample data specific and cannot represent the true structure underlying the sample data (MacCallum, 1995). A common problem in model estimation is that the sample covariance matrix is not positive definite, that is, some variables are linearly dependent on others. If this is the case, we cannot estimate the model because it is not possible to invert the sample covariance matrix during estimation procedure. The solution to this problem is to increase sample size to avoid perfect linear dependency and choose observable variables carefully to eliminate redundancy. Simple Bond Rating Latent Variable Model First, we build a simple bond rating latent variable model with only one unobservable variable: default risk, or DR. This unobservable default risk has four proxy variables: interest coverage ratio, leverage ratio, firm size and return on assets (ROA). In other words, the DR is the default risk that is reflected in the four publicly available accounting variables. The following is a simple latent-variable bond rating model: 61 Interest Coverage Ratio = a/ + J1DR + Ei (5a) Leverage Ratio = a2 + /2DR + 62 (5b) Firm Size = a3 + /3DR + E3 (5c) ROA =a4 + /4DR + F4 (5d) Bond Rating = as + /)5DR + E5 (5e) These four observable variables are chosen to proxy for default risk because previous literature shows they can explain a significant amount of variation in bond ratings. Table 3-1 summarizes previous studies of determinants of bond ratings. Regardless of different statistical methodologies used, these studies generally find leverage ratio (measured by long-term debt/total asset, debt/total capital, equity/debt ratio, etc), interest coverage ratio, firm size (measured by total assets) and profitability (measured by ROA) are among the most common significant determinants of the bond ratings. These four variables have been shown to be significant determinants of ratings in at least two studies.3 Private Information Model Next, a latent variable for private information, PI, is added to the model. The difficulty is to find proxies for private information that issuing firms may share with rating agencies. Fortunately, there is large literature on the information asymmetry and many proxies have been developed to measure the degree of information asymmetry between firms and investors. If an issuing firm has a large problem of information asymmetry, it would have more private information to share with the rating agencies. 62 Thus, proxies for information asymmetry can also serve as good proxies for private information. There are two classes of proxy variables for information asymmetry: corporate finance based and market microstructure based proxies. Appendix B gives a brief literature review on the two classes of information asymmetry proxies. In corporate finance literature, analysts' earning forecast errors have often been used as a proxy for information asymmetry as well because it is hard for analysts to forecast earnings of firms with large private information. For example, Thomas (2002) uses analysts' earnings forecast errors as a measurement of information asymmetry of diversified firms. Firm size is another proxy used in corporate literature to proxy information asymmetry. Large firms are often followed by more stock analysts and under more scrutiny of the financial media and its asymmetry information problem is generally less due to the greater awareness of investors of larger firms (Merton, 1987). Also, large firms generally access the capital markets more frequently and reveal more information to investors to lower their cost of capital. In market microstructure literature, information asymmetry is often measured by the adverse selection component of the bid-ask spread of a firm's stock. The bid-ask spread can generally be decomposed into three components: order processing, inventory costs, and adverse selection. The first two components compensate the market maker for 3 Another common variable is bond subordination. Since I am only interested in the information content of bond ratings in this study, the impact of bond features on credit ratings is beyond the scope of this study. Therefore, bond subordination is not used to proxy for default risk and subordinated debts are excluded from sample data. 63 the cost of handling the orders and holding an inventory. The third component, adverse selection, is a compensation to the market maker for trading with informed traders who take advantage of their private information on the value of the stock to make a profit. For firms with large asymmetric information problem, the market maker will widen the bidask spread to compensate for their potential losses from trading with informed traders. Holding the other two components constant, a wider bid-ask spread means a large adverse selection component for firms with large information asymmetry. Therefore, the adverse selection component has been recently used as a measurement of asymmetric information in corporate finance literature. For example, Flannery, Kwan and Nimalendran (2000) uses the adverse selection component of banks' bid-ask spread to measure the relative 'opaqueness' of the assets of banking firms. Appendix B briefly explains several methodologies to estimate the adverse selection component. Although there are other proxies for information asymmetry, such as market to book ratio and number of institutional investors, we choose the three proxies discussed above to build a parsimonious model. Fewer proxies for private information will bias against finding any private information content in bond ratings. The private information model is therefore as follows: Interest Coverage Ratio = a/ + #,DR + El (6a) Leverage Ratio = a2 + /2DR + E2 (6b) Firm Size = a3 + P3DR + y3 PI + C3 (6c) ROA = 6( + #4DR + E4 (6d) Bond Rating = a5 + /sDR + Ys PI + Es (6e) Adverse Selection = a6 + P6DR + Y6 PI + E6 (6f) 64 Forecast Error = a7 + /7DR + y7 PI + E7 (6g) If bond ratings do contain private information, then ys, and ys through Y7 will be significant. Also, we will compare the results of this model with those of the simple model. If bond rating do contain private information, then the private information model should explain a larger proportion of the variation of bond rating than the simple model because it incorporates more information. Complete Model Finally, it will be interesting to see if the default risk and private information, if any, carried by the bond ratings are priced by the bond market. To test that, we add the bond yields in the previous model. However, bond yields vary over time and maturity. Hence, to control for the difference in the maturity and issuing time, we subtract the yields on US treasuries of similar maturity on the issuing date from the original yields to maturity to get the treasury spread. The final model is as follows: Interest Coverage Ratio = ai + /JDR + 6 (7a) Leverage Ratio = a) + /2DR + E2 (7b) Firm Size = a3 + /3DR + '3 PI + 63 (7c) ROA = a4 + /4DR + E4 (7d) Bond Rating = a5 + /sDR + Ys PI + Es (7e) Adverse Selection = a6 + /6DR + Y6 PI + E6 (7f) Forecast Error = a7 + #7DR + y7 PI + E7 (7g) Treasury Spread = a8 + /sDR + y'8 PI + E8 (7h) Notice that in the last two models, we include DR in both analysts' forecast errors and adverse selection equations, even though these two variables are intended to capture private information. Since these two variables are publicly available, it might be possible 65 for investors to derive private information from them directly instead of through the rating agencies. To control for this, we include DR in these two equations. Data Data Collection The initial data on corporate bonds come from the Fixed Investment Securities Database (FISD) by the Global Information Services Inc. FISD has all new bond issues with 9-digit CUSIP number since April 1995 to early 2000. We collect all domestic new issues of industrial bonds from April 1,1995 to the end of 1999 with both Moody's and S&P ratings. Convertible bonds and bond issues with floating or zero coupons are excluded. Rule 144A issues have also been excluded because they are not registered with SEC. The initial dataset has 2,068 corporate bonds. Previous research finds that bond ratings are also partially determined by bond features, such as seniority. Since we are only interested in the information content of bond ratings in this study, the impact of bond features on credit ratings is beyond the scope of this study. Therefore, to create a more homogeneous sample, we exclude subordinated debt from the initial sample.4 This reduces the sample to 1,775 bonds. Bonds with credit enhancement features, such as loan guarantee or insurance, are also excluded. This eliminates another 118 issues. Furthermore, many firms issue multiple bonds, usually with different maturity, on the same date. These bonds often have the same credit ratings. To avoid multiple observations for a single issuer on the same date, we eliminate multiple issues by the same firms on the same date with the same bond ratings from both Moody's and S&P. This reduces the sample to 1,285 observations. 4 Inclusion of subordinated debt does not change my results. 66 Next, we match the bond issues with the issuing firms' financial data from COMPUSTAT, using the 6-digit CUSIP number. 266 observations fail to get a match and 88 observations have missing financial information. To get analysts' earning forecast errors, we match the sample with analysts earning forecasts from I/B/E/S. This further reduces the sample to 840 observations. Finally, another 59 issues are excluded because of lack of information on the stock bid-ask spread of the issuing firms. This leave 781 observations. A check of the 781 observations shows that several outliers have extreme values on accounting ratios and other variables that produce large kurtosis. Nine outliers are eliminated.5 The final sample has 772 observations. Variable Definitions Bond rating in the latent variable models is a numerical variable ranging from 1 (for issues rated CCC or below) to 7 (for issues rated AAA).6 Both Moody's and S&P's ratings are used to estimate the models and, as shown later, the results are essentially the same. Four accounting variables, interest coverage ratio, leverage ratio, firm size and ROA, are used to proxy public information in bond rating. COMPUSTAT annual data are used to calculate the four variables.7 Interest coverage ratio is the ratio of earnings 5 Inclusion of the nine outliers does not change the model estimation, though the model goodness of fit index tends to be lower. 6 A numerical rating variable ranging from I (CCC and below) to 17 (AAA) that takes bond ratings at the notch level have been used as well. The results are essentially the same in the WLS estimation. Because the compute software, Mplus, that we use for the CVM estimation can handle only up to 10 categories for rating variables, the notch level rating variables are not used in CVM estimation. 7 I have also used quarterly data to calculate the four variables and the results do not change. 67 before interest, tax, depreciation and amortization (EBITDA) over Interest Expenses ((data item 18 + data item 14 + data item 16 + data item 15)/data item 15). Leverage ratio is the long-term debt divided by total assets (data item 9/data item 44). Firm size is the market value of the firm's equity. It is calculated by multiplying the issuing firm's stock price (average of the preceding year high and low, or (data item 197 + data item 198)/2) by the number of shares (data item 25)). ROA is the net income divided by total assets (data item 172/data item 44). All the financial variables are for the year prior to the bond offering date. Analyst earning forecast errors are defined as follows: FE = abs(Average Analysts Annual EPS Forecast - Actual Annual EPS) Stock Price The analysts' forecasts are made nine months before the end of the fiscal year.' The forecast errors are scaled by the issuing firms' stock prices. Since both positive and negative earning surprises are indications of information asymmetry, we take the absolute value of the earning forecast errors as proxy for information asymmetry. For adverse selection component of bid-ask spread, we use the method proposed by George, Kaul and Nimalendran (1991). Appendix B gives the technical details of the GKN method of spread decomposition. Specifically, we use the last trading prices and quotes of the issuing firm's stock each day in the six months period before the bond issuing date to calculate the GKN adverse selection component. It is defined as the dollar adverse selection component as a percentage of the stock price. 8 Three months and six months forecasts are also used and there are no differences in results. 68 Descriptive Statistics Table 3-2 reports the summary statistics and correlation among variables. Note that some of the variables have very large kurtosis. Excess kurtosis makes maximum likelihood estimation method undesirable because it assumes that the model variables are multivariate normal. As a result, we use the weighted least square (WLS) method to estimate the model when bond ratings are treated as continuous variables because it does not assume multivariate normal distribution for the model indicator variable. 9 The correlation matrix indicates that the model variables are significantly correlated with each other. This is not surprising because these variables are proxies for the same underlying unobservable latent variables. Interest coverage ratio, leverage ratio, ROA and firm sizes are strongly correlated as they proxy for the unobservable default risk reflected in public information. In the meantime, firm size, analysts' earnings forecast errors and the adverse selection components are also correlated as they proxy for potential private information content in bond ratings. An interesting finding is that the proxies for private information and public information are also correlated. This makes the inclusion of DR in the last two equations in the private information model and complete model necessary. Empirical Results Model Estimation Results on simple model Tables 3-3 and 3-4 report the results of the simple bond rating latent variable model using S&P and Moody's ratings respectively. The results from the two tables are 9 Maximum likelihood method is also used to estimate the model as a robust check. The results are basically the same. 69 very similar. This is consistent with findings by Ederington (1986) that Moody's and S&P put similar weights or importance to the major financial accounting ratios when deciding on bond ratings. Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). The WLS estimation method assumes that all indicator variables are continuous. However, bond ratings are ordered categorical variables and not continuous. As discussed in the previous section, violation of the continuous variable assumption may lead to inconsistent estimators of the model parameters. To overcome the problem, we use Muthen's CVM method and treat bond rating as an ordered categorical variable. One basic assumption of CVM is that there is an underlying, unobservable continuous rating variable behind the observed categorical rating variable, and certain value of the observable categorical rating variable corresponds to a certain range of values of the underlying continuous rating variable. The model seems to be well specified in both WLS and CVM estimations as the fit function and chi-squared values indicate. The main findings are consistent with previous research. Basically, higher interest coverage ratio, lower leverage ratio, higher ROA and larger firm size are associated with lower default risks that lead to higher bond ratings. The R2 on the bond rating in WLS estimation is about 55%. A simple OLS regression of bond ratings on the four accounting variables (not reported) gives an Rsquare of 43%. Hence, the latent variable model seems to be superior to OLS in explaining the variations in bond rating. 70 A comparison of WLS and CVM estimation shows that the latter is more efficient as the t-statistics are much higher in CVM estimation though coefficient estimates are almost identical when the variables are continuous. The coefficients on the bond rating are bigger and more significant in CVM estimation. The R2 for the rating equations in CVM estimation measures the variations of the underlying, unobservable continuous rating variable that can be explained by the two latent variables. Not surprisingly, the R2 in CVM estimation is much higher than the R2 in WLS estimation. Results on private information model Tables 3-5 and 3-6 report the results of the private information model using S&P and Moody's ratings respectively. Again, the results of the two tables are very similar. The coefficients on DR remain largely unchanged from tables 3-3 and 3-4, suggesting that the latent variable, PI or private information, is orthogonal to DR or default risk reflected in public information. Interestingly, analysts' forecast errors and adverse selection components are also related to the default risk, or DR. This controls for the potential problem that the two variables only capture public information already reflected in the four accounting variables. The coefficients on PI are all significant. The three proxies for information asymmetry, firm size, analysts forecast errors and adverse selection components, are shown to be related to the unobservable private information. Specifically, large firms tend to have less private information, while firms with large forecast errors and adverse selection components have more private information. Does the private information variable have an impact on bond rating? Indeed it has. The coefficients on PI in WLS estimation (CVM estimation) are -0.177 (-0.247) and -0.199 (-0.295) for S&P and Moody's ratings respectively and significant. This suggests that large information 71 asymmetry has a negative impact on bond ratings, both Moody's and S&P. Similarly, in CVM estimation, the t-statistics are higher and the coefficients on PI are bigger and more significant in the bond rating equations. The significance of private information can be seen from the changes in R2 on the bond rating equations. Notice that the R2 on the bond ratings in WLS estimation (CVM estimation) has increase from about 55% (64%) in the simple model to 61% (72%) in the private information model, indicating that the additional private information latent variable has significant additional explanatory power on bond ratings. Since the two latent variables are assumed to have unit variance, it is easy to find out how much variation in the bond rating can be explained by each latent variable. Specifically, it can be shown from equation (6a) that Var (Bond Rating) = 5< Var( DR) + y, Var(PI) + Var(5) or Var (Bond Rating) = + + Var(e ,). By definition, R 2 = 51 /Var( Bond Rating) + y,2/ Var(Bond Rating). Given the 22 estimated /L, y; and R2, we can calculate /j /Var( Bond Rating) and y5/ Var(Bond Rating), or the contributions of the two latent variables to the R2. For the S&P regression in WLS (CVM) estimation, the DR reflected in the public information accounts for 56% (66%) of the variation of the rating and the private information reflected in the three information asymmetry proxies account for 5% (6%). For the Moody's regression in WLS (CVM) estimation, the two latent variables account for 54% (67%) and 8% (9%) of the rating variations respectively. Hence, it seems that the private information plays a relatively smaller role in bond ratings. As a result, it is 72 not surprising that some of the previous studies fail to find evidence that bond ratings have impact on yields after controlling for public information. Results on complete model The last question remains unanswered is whether the private information contained in the bond ratings is priced by the bond market. The results on the complete model with bond yields reported in tables 3-7 and 3-8 can help to answer this question. Again, the results are very similar when we use either Moody's or S&P ratings. First, notice that the default risk, or DR, has a very significant impact on bond yields. It is not surprising that higher default risk leads to higher bond yields. Secondly, the private information also has a significant impact on bond yields, though the coefficients and t-statistics are much smaller. Larger the private information, the higher the bond yields. This indicates that the bond market prices the private information conveyed in the bond rating. The R2 on the bond yields in both WLS estimation and CVM estimation is around 40%. In a separate OLS regression (not reported) of bond yields on the same 7 variables, the R2 is only about 30%. Hence, the latent variable technique performs better than simple OLS in explaining the variation in bond yields. To find out the relative importance of the two latent variables in explaining the bond yields, we calculate each variables contribution to the R2. For the model with S&P rating estimated by WLS (CVM) method, the DR accounts for 33% (30%) and PI accounts for another 8% (8%) of the variation in bond yields. For the model with Moody's rating estimated by WLS (CVM) method, the two variables account for 32% (28%) and 8% (7%) of the bond yields 73 Specification Tests One of the assumptions in the latent variable models is that the error terms are not correlated with each other. If, however, there is omission of relevant variables in the model, then the assumption of non-correlated error terms will be violated, leading to an ill-specified latent variable model. This potential problem can be detected by the modification indexes of the model. The modification index measures the decrease in the model chi-square that would result from changes in constrained parameters (Sorbom, 1989). For example, if the model assumption of zero correlation among error terms is violated, then the modification index will be big, indicating that the model specification will improve (or chi-square will decrease) by removing the zero correlation constraint. The modification index is significant at the 5% level when it is equal to or greater than 3.84. There are two ways to fix this potential missing variable problem. Ideally, we would like to find and build all missing latent variables into the models. However, this is generally not possible nor efficient because the goal of this paper is not to build a 'perfect and all-inclusive' rating model. Another simple way to solve the problem is to allow some error terms to be correlated in estimation. From the discussion on the technical issues on the latent variable models, we know that as many as p(p-1-2q)/2 covariances among error terms can be estimated, where p is the number of observable indicator variables and q is the number of unobservable latent variables. By estimating the covariances among some error terms, the latent variable model can control for the missing variable problem and focus on the latent variables of interest. 74 Since there is no ex-ante indication as to which error terms are likely to be correlated, we first estimate all the three models with the constraint that the correlation between all error terms be zero and then check for potential correlation from the modification indexes. With the constraint of zero correlation among error terms, the fitfunction and model chi-square all indicate that the models are not well-specified. Next, we relax the constraint on the pair of errors that have the largest modification index by estimating the covariance of the two error terms and re-estimate the model. we repeat the process until there is no obvious correlation in the remaining error terms. From table 3-3 through table 3-8, we report the pairs of error terms that have significant non-zero covariance. For example, for the simple bond rating latent variable models, the error terns between interest coverage ratio equation and leverage ratio (cov(ei, e2)), between interest coverage ratio equation and ROA equation (cov(ei, e4)), between leverage ratio equation and firm size equation (cov(e2, ej)), and firm size equation and ratings equation (cov(e3, e5)), are not constrained to be zero and the estimated covariance is statistically significant. Another potential problem of the latent variable bond rating model assumes that the PI variable, or private information, is not reflected in the other three publicly available accounting variables. This assumption may be problematic because the simple correlation matrix shows that the two proxies for information asymmetry used in the model are also correlated with the three accounting variables. The good news is that the modification index provides a good diagnosis for this potential problem. When we leave PI out of the equations of interest coverage ratio, leverage ratio ROA, we basically impose zero coefficients on the variable PI in these three equations. From the discussion 75 on modification index above, if the P1 is also reflected in the other three accounting variables or, in other words, the zero coefficient assumption is violated, then the modification indexes will be large and significant. Table 3-9 presents the modification indexes for the complete model with S&P rating estimated by WLS method. Modification indexes for other models with Moody's rating have similar results. Panel A of the table reports the indexes for the loading on the P1 latent variable on the three accounting variable equations. All three indexes are less than 1, suggesting that these three accounting variables are not related to the PI latent variable. Panel B gives the modification indexes of the error term covariance. Except for the seven pairs of error terms on which no constraint has been imposed as shown in table 3-7, none of the error term modification indexes is greater than the 3.84 critical value. Split Rating and Private Information The two rating agencies, S&P and Moody's, do not always give identical ratings to bond issues. About 13% to 18% of new bond issues receive different letter ratings from the two rating agencies (Ederington, 1986, Jewell and Livingston, 1998) and about 50% receive split ratings at the notch level (Jewell and Livingston, 1999).1o Ederington (1986) argues that split ratings occur due to random difference of opinion on the creditworthiness of bond issues. Jewell and Livingston (1998) shows that split ratings convey valuable information and are priced by the bond market. If an issuing firm has large information asymmetry problem, it is more likely to receive a split rating because it is harder for rating agencies to evaluate and agree on its creditworthiness. The implication is that the private information will play a larger role in 76 the determination of ratings if the bond issue receives a split rating. To test this, we form a sub-sample of 333 observations that have split ratings at the notch level and estimate the complete model. Table 3-10 and 3-11 report the results of the complete model on the split rating sub-sample with S&P and Moody's ratings respectively. A comparison of tables 3-7 and 3-10 for S&P rating (3.8. and 3.11. for Moody's rating) shows that the coefficients on PI, or private information, are much higher for the rating equations, suggesting that large information asymmetry makes it harder for rating agencies to agree upon the issuing firm's creditworthiness. In the same time, the coefficients on DR remain largely unchanged, consistent with Ederington's (1986) finding that split ratings are not caused by different interpretation of financial ratios by different rating agencies. Table 3-12 compares the relative contributions of the two risk factors to the variation of bond ratings for the whole sample and split rating sub-sample, based on the estimated coefficients in tables 3-7, 3-8, 3-10, and 3-11. For the whole sample, PI only explains 5%-9% of the variations in ratings, while DR accounts for almost 58% to 70% of the variations. For the split rating sub-sample, PI accounts for a much larger proportion of the rating variations, ranging from 11% to 17%, than the whole sample. Tables 3-10, 3-11, and 3-12, though suggesting strongly that private information plays a larger role in bond ratings for issues with split rating, do not test directly the statistical significance in the difference in the bond issues with split rating. To do that, we create a split rating dummy variable, equal to 1 if S&P and Moody's ratings split at 10 If one rating agency gives an issue an AA rating, while another gives a rating of A, the ratings are split at letter lever. If one rating agency gives an AA+ rating while another gives an AA rating, the rating are split at the notch lever. 77 the notch level and 0 otherwise. The dummy variable is then added to the complete bond rating model as an additional equation. Tables 3-13 and 3-14 report the estimated split rating model for the two ratings separately. The coefficients on PI in the split dummy variable equation are positive and significant, suggesting that larger information asymmetry makes it more likely to have split ratings. The coefficients on DR in the split dummy variable equation is not significant, suggesting that split ratings are not caused by different interpretation of public available accounting information which is consistent with the findings of Ederington (1986). Conclusion This paper uses the latent variable technique to investigate the information content of bond ratings. Previous studies on bond ratings only provide indirect evidence on the potential private information in bond ratings. Since private information is not observable by definition, it is impossible to link such information with bond ratings directly in traditional statistical models. The latent variable technique, however, provides us a way to directly link potential private information with bond ratings, using three observable proxies for information asymmetry. We find that bond ratings do contain private information. Generally speaking, if a firm has higher degree of information asymmetry, its bond ratings tend to be lower. However, private information does not seem to account for a very significant amount of variation in bond ratings. Less than 10% of bond variation can be explained by private information, compared to about 60% of variation explained by publicly available information. Furthermore, investors seem to be able to infer the private information from the bond ratings and require a higher bond yields for firms with greater private information. About 8% of bond yields can be 78 explained by the private information, while more than 30% is explained by the public information reflected in the bond ratings. For bond issues that receive split ratings from the rating agencies, private information is more important in explaining the variation in bond rating. 79 Table 3-1 Comparison of Rating Determinants Studies Significant Percentage of STUDY Methodology Determinants of Ratings Rating Predicted Subordination Regression Regression Total Assets SALES/NET WORTH Net Worth/Total Debt Working Capital/Sales Debt/Total Capital Equity/Debt Ratio Bonds Outstanding Period of Solvency 50% -60% NA Pinches and Mingo (1973, 1975) Altman and Katz (1974) Discriminant Function Discriminant Function Kaplan and Urwitz Ordered Probit (1979) Regression Ederington (1986) Ordered Probit Regression ROA Issue Size Subordination Interest Coverage Ratio Long-termn Debt/Total Asset Years of Consecutive Dividend Cash Flow Coverage Ratio Std. Error of Coverage Ratio Subordination Total Assets Long-Term Debt/Total Assets ROA Total Assets Subordination Coverage Ratio Variation in ROA Long-term Debt/Total Capital 60%-75% 77% 50-60% 72% to 76% Horrigan (1966) Pogue and Soldofsky (1969) 80 Table 3-2 Summary Statistics Standard Variable Mean Median Deviation Skewness Kurtosis Interest Coverage Ratio 9.242 7.239 7.677 2.901 12.151 Leverage 0.247 0.239 0.114 0.621 1.498 Firm Size (in Billions) $18.994 $6.319 33.556 3.402 12.665 Log (Firm Size, in 8.905 8.751 1.316 0.295 -0.372 millions) ROA 5.407% 5.238% 3.953% 0.330 2.775 Analysts Earning Forecast Error 0.965% 0.366% 1.519% 2.839 10.241 Adverse Selection Component 0.095% 0.090% 0.080% 2.204 9.452 Correlation Matrix Interest Analysts Coverage Log of Forecast Adverse Ratio Leverage Firm Size ROA Errors Selection Interest Coverage Ratio 1.000 Leverage -0.580*** 1.000 Log of Firm Size 0.274*** -0.152*** 1.000 ROA 0.605*** -0.302*** 0.262*** 1.000 Analysts Forecast Error -0.089** 0.078** -0.212*** -0.124*** 1.000 Adverse Selection -0.142*** 0.161*** -0.501*** -0.186*** 0.077** 1.000 The correlation is significant at the 1% level (***) or 50% level (**) 81 Table 3-3 Simple Model for S&P Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR R2 DR R Interest Coverage -4.700 -4.709 Ratio (V1) (-8.11) 0.37 (-21.50) 0.38 Leverage Ratio 0.058 0.058 (V2) (11.40) 0.26 (20.36) 0.26 Firm Size -0.603 -0.602 (V3) (-8.29) 0.20 (-11.48) 0.20 ROA -2.330 -2.329 (V4) (-10.55) 0.35 (-19.29) 0.35 S&P Rating -0.569 -0.799 (V5) (-11.38) 0.55 (-20.72) 0.64 Model Fit Fit Function 0.000 0.000 GFI 1.000 1.000 Chi-Square (d.f) 0.010(1) 0.004(1) Pr > Chi-Square 0.923 0.949 Non-Zero Error cov(ei,e2), cov(el,e4) cov(el,e2), cov(e,e4) Covariance cov(e2,e3), cov(ej,e5) cov(e2,e3), cov(e3,e5) Note: This table gives the estimated simple bond rating latent variable model with S&P rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=1; cov(ej,ej)=62 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=0 (ij=1,...5). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from I (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 82 Table 3-4 Simple Model for Moody's Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR R DR R2 Interest Coverage -4.410 -4.393 Ratio (VI) (-7.87) 0.33 (-21.08) 0.33 Leverage Ratio 0.061 0.060 (V2) (11.38) 0.28 (21.18) 0.28 Firm Size -0.636 -0.635 (V3) (-8.47) 0.22 (-11.63) 0.22 ROA -2.230 -2.251 (V4) (-9.61) 0.32 (-19.52) 0.33 Moody's Rating -0.546 -0.814 (V5) (-11.79) 0.56 (-23.56) 0.66 Model Fit Fit Function 0.000 0.000 GFI 1.000 1.000 Chi-Square (d.f) 0.1498 (1) 0.201(1) Pr > Chi-Square 0.699 0.654 Non-Zero Error cov(eie2), cov(ei,e4) cov(ei,e2), cov(ei,e4) Covariance cov(e2,e3), cov(e3,e5) cov(e2,e3), cov(e3,e5) Note: This table gives the estimated simple bond rating latent variable model with Moody's rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=1; cov(ei,ej)=S62 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=0 (ij=1,...5). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 83 Table 3-5 Private Information Model with S&P Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical VARIABLE Variable DR PI R2 DR PI R2 Interest Coverage -4.563 -4.711 Ratio (V1) (-8.16) - 0.37 (-22.21) - 0.37 Leverage Ratio 0.057 0.058 (V2) (11.60) - 0.26 (20.74) - 0.27 Firm Size -0.620 -1.004 -0.636 -1.065 (V3) (-8.63) (-7.64) 0.77 (-12.72) (-9.00) 0.83 ROA -2.300 -2.308 (V4) (-10.77) - 0.34 (-19.82) - 0.34 S&P Rating -0.570 -0.177 -0.814 -0.247 (V5) (-12.12) (-3.47) 0.61 (-21.63) (-4.93) 0.72 Adverse Selection 0.018 0.041 0.020 0.039 (V6) (4.15) (5.43) 0.34 (5.94) (6.71) 0.31 Forecast Error 0.309 0.170 0.315 0.161 (V7) (5.72) (2.89) 0.06 (6.50) (2.44) 0.05 Model Fit Fit Function 0.006 0.009 GFI 0.997 0.999 Chi-Square (d.f) 4.687(6) 6.844(6) Pr > Chi-Square 0.585 0.335 Non-Zero Error cov(ei,e2), cov(ei,e4) cov(el,e2), cov(el,e4) Covariance cov(e2,e3), cov(e4,e6) cov(e2,e3), cov(e4,e6) Note: This table gives the estimated private information bond rating model with S&P rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(e,,e,)=6,2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, e,)=cov(PI, ei)=0 (ij=1,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 84 Table 3-6 Private Infonnation Model with Moody's Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR PI R2 DR PI R2 Interest Coverage -4.448 -4.422 Ratio (V 1) (-7.93) - 0.34 (-21.59) - 0.33 Leverage Ratio 0.061 0.061 (V2) (11.77) - 0.29 (21.61) - 0.29 Firm Size -0.638 -0.920 -0.662 -0.941 (V3) (-8.74) (-8.85) 0.69 (-12.96) (-10.64) 0.71 ROA -2.210 -2.230 (V4) (-9.71) - 0.32 (-19.78) - 0.32 Moody's Rating -0.530 -0.199 -0.820 -0.295 (V5) (-11.95) (-4.14) 0.62 (-23.92) (-5.77) 0.76 Adverse Selection 0.019 0.043 0.021 0.043 (V6) (4.23) (6.29) 0.38 (6.01) (8.17) 0.36 Forecast Error 0.301 0.192 0.319 0.163 (V7) (5.58) (3.16) 0.06 (6.56) (2.44) 0.06 Model Fit Fit Function 0.007 0.008 GFI 0.997 0.999 Chi-Square (d.f) 5.539 (6) 6.010 (6) Pr > Chi-Square 0.477 0.422 Non-Zero Error cov(ei,e2), cov(el,e4) cov(ei,e2), cov(e,e4) Covariance cov(e2,e3), cov(e4,e6) cov(e2,e3), cov(e4,e6) Note: This table gives the estimated private information bond rating model with Moody's rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(e1,ej)=6j2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (ij=1,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from I (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 85 Table 3-7 Complete Model with S&P Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR PI R 2 DR PI R2 Interest Coverage -4.477 -4.633 Ratio (V1) (-8.24) - 0.35 (-23.08) - 0.36 Leverage Ratio 0.057 0.058 (V2) (11.85) - 0.25 (20.81) - 0.27 Firm Size -0.628 -0.972 -0.640 -1.045 (V3) (-8.68) (-7.51) 0.74 (-12.63) (-8.88) 0.81 ROA -2.256 -2.261 (V4) (-11.07) - 0.32 (-20.77) - 0.33 S&P Rating -0.585 -0.170 -0.835 -0.247 (V5) (-14.09) (-3.39) 0.64 (-23.87) (-4.82) 0.76 Adverse Selection 0.019 0.043 0.020 0.040 (V6) (4.20) (5.42) 0.35 (5.85) (6.66) 0.32 Forecast Error 0.307 0.169 0.322 0.158 (V7) (5.70) (2.88) 0.06 (6.64) (2.38) 0.06 Yield Spread 31.359 15.693 31.091 16.377 (V8) (10.26) (5.42) 0.41 (16.87) (6.24) 0.38 Model Fit Fit Function 0.010 0.011 GFI 0.996 0.999 Chi-Square (d.f) 7.608 (8) 8.754 (7) Pr > Chi-Square 0.473 0.271 Non-Zero Error cov(e1,e2), cov(ei,e4), cov(ei,es) cov(ei,e2), cov(el,e4), cov(e],es) Covariance cov(e2,e3), cov(e3,e8), cov(e4,e6) cov(e2,e3), cov(e3,es), cov(e4.e6) cov(e4,e8) cov(e4,es), cov(e7,e8) Note: This table gives the estimated complete bond rating model with S&P rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(ei,ej)=6i2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (i,j=l,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from I (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 86 Table 3-8 Complete Model with Moody's Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR PI R2 DR PI R2 Interest Coverage -4.300 -4.338 Ratio (V1) (-7.91) - 0.32 (-22.36) - 0.32 Leverage Ratio 0.060 0.060 (V2) (11.83) - 0.28 (21.64) - 0.29 Firm Size -0.652 -0.868 -0.661 -0.932 (V3) (-8.82) (-8.39) 0.65 (-12.76) (-10.42) 0.71 ROA -2.161 -2.187 (V4) (-9.78) - 0.30 (-20.41) - 0.31 Moody's Rating -0.551 -0.194 -0.837 -0.294 (V5) (-13.48) (-3.97) 0.65 (-25.41) (-5.67) 0.79 Adverse Selection 0.020 0.047 0.021 0.044 (V6) (4.30) (6.45) 0.42 (5.91) (8.11) 0.37 Forecast Error 0.303 0.178 0.324 0.162 (V7) (5.66) (2.96) 0.06 (6.64) (2.43) 0.06 Yield Spread 30.917 14.543 30.380 14.815 (V8) (10.78) (2.74) 0.39 (16.50) (6.18) 0.35 Model Fit Fit Function 0.014 0.011 GFI 0.995 0.999 Chi-Square 10.520(8) 8.276(7) Pr > Chi-Square 0.230 0.308 Non-Zero Error cov(ei,e2), cov(ei,e4, cov(ei,eg) cov(ei,e2), cov(ele4), cov(el,e8) Covariance cov(e2,e3), cov(e3,e8), cov(e4,e6) cov(e2,e3), cov(e3,es), cov(e4,e6) cov(e4,es) cov(e4,es), cov(e7,e8) Note: This table gives the estimated complete bond rating model with Moody's rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(ei,ej)=6,2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (ij=1,.. .8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from I (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 87 Table 3-9 Modification Indexes Complete Model with S&P Rating This table gives the modification indexes of the estimated complete bond rating model with S&P rating. The modification index measures the decrease in the model chi-square when a constrained parameter is allowed to vary (Sorbom, 1989). It basically measures the improvement in the model specification if the constraint on one parameter is removed. The modification index is significant at 5% level when it is equal to or greater than 3.84. NC: no constraint has been imposed on the parameter. Panel A: Modification Indexes for Latent Variable PI Equation PI Interest Coverage Ratio (V1) 0.00 Leverage Ratio (V2) 0.66 Firm Size (V3) ROA (V4) 0.20 S&P Rating (V5) Adverse Selection (V6) Forecast Error (V7) Yield Spread (V8) - Panel B: Modification Indexed for the Error Covariance el e2 e3 e4 e5 e6 e7 es el e2 NC e3 0.55 NC e4 NC 0.58 0.15 e5 0.01 0.06 1.42 0.01 e6 1.54 1.46 1.76 NC 1.08 e7 0.65 0.45 0.26 0.18 0.32 0.85 e8 NC 1.69 NC NC 0.81 2.60 1.26 - 88 Table 3-10 Complete Model with S&P Rating on Split Rating Sub-sample WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR PI R2 DR P1 R2 Interest Coverage -4.407 -4.819 Ratio (V1) ( -5.98) - 0.30 (-12.81) - 0.34 Leverage Ratio 0.045 0.051 (V2) (5.35) - 0.14 (11.21) - 0.19 Firm Size -0.244 -1.120 -0.4000 -1.074 (V3) (-2.13) (-10.53) 0.85 (-4.63) (-9.51) 0.86 ROA -2.199 -2.203 (V4) (-6.88) - 0.29 (-12.41) - 0.29 S&P Rating -0.609 -0.311 -0.800 -0.331 (V5) (-8.30) (-4.90) 0.69 (-13.27) (-4.79) 0.75 Adverse Selection 0.001 0.043 0.011 0.046 (V6) (0.17) (6.42) 0.29 (1.69) (6.54) 0.30 Forecast Error 0.272 0.400 0.310 0.368 (V7) (3.17) (4.72) 0.13 (4.54) (4.70) 0.12 Yield Spread 27.995 30.730 32.328 33.450 (V8) (6.61) (7.93) 0.49 (11.30) (7.87) 0.56 Model Fit Fit Function 0.023 0.030 GFI 0.992 0.998 Chi-Square 7.500 (8) 9.903 (9) Pr > Chi-Square 0.484 0.358 cov(ei,e2), cov(ei,e4), cov(e2,e3) cov(ei,e2), cov(ei,e4), cov(e2,e3) Non-Zero Error cov(e2,e8), cov(e3,e4), cov(e3,es) cov(e2,es), cov(e3,e8), cov(e4,e6) Covariance cov(e4,e6) Note: This table gives the estimated complete bond rating model with S&P rating on a split rating sub-sample. To be included in the sub-sample, the observation has different S&P rating and Moody's rating at the notch level. There are 333 observations in the split rating sub-sample. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(ei,e)=6,2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, e,)=0 (ij=l,...,8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging fror 1 (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 89 Table 3-11 Complete Model with Moody's Rating on Split Rating Sub-sample WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR PI R2 DR PI R2 Interest Coverage -4.301 -4.618 Ratio (V1) (-5.80) - 0.27 (-11.45) - 0.31 Leverage Ratio 0.060 0.058 (V2) (6.55) - 0.23 (14.03) - 0.23 Firm Size -0.354 -0.915 -0.447 -0.877 (V3) (-3.28) (-9.14) 0.63 (-5.07) (-8.87) 0.63 ROA -1.960 -2.016 (V4) (-6.27) - 0.22 (-11.83) - 0.24 Moody's Rating -0.541 -0.310 -0.825 -0.386 (V5) (-8.61) (-5.57) 0.69 (-15.60) (-5.72) 0.83 Adverse Selection 0.010 0.053 0.013 0.054 (V6) (1.25) (6.15) 0.39 (1.91) (6.93) 0.39 Forecast Error 0.149 0.559 0.250 0.509 (V7) (1.71) (5.02) 0.17 (3.38) (5.48) 0.17 Yield Spread 32.730 27.05 33.190 26.371 (V8) (8.35) (7.04) 0.47 (12.03) (7.45) 0.47 Model Fit Fit Function 0.028 0.028 GFI 0.990 0.9980. Chi-Square 9.281 (8) 9.163 (9) Pr > Chi-Square 0.319 0.422 Non-Zero Error cov(ei,e2), cov(ei,e4), cov(ei e8) cov(e,e2), cov(ele4), cov(e2,e3) Covariance cov(e2,e3), cov(e3,es), cov(e4,e6) cov(ej,es), cov(e4,e6), cov(e6,e7) cov(e6,e7) Note: This table gives the estimated complete bond rating model with Moody's rating on a split rating sub-sample. To be included in the sub-sample, the observation has different S&P rating and Moody's rating at the notch level. There are 333 observations in the split rating sub-sample. Var(DR)=Var(PI)=1; cov(e,,ej)=6i2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (i,j=I,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 90 Table 3-12 Relative Importance of DR and PI S&P Rating Moody's Rating Split Rating Split Rating Whole Sample Sub-sample Whole Sample Sub-sample WLS (CVM) WLS (CVM) WLS (CVM) WLS (CVM) % of Rating Variation Explained by DR 59% (70%) 55% (64%) 58% (70%) 52% (68%) % of Rating Variation Explained by PI 5% (6%) 14% (11%) 7% (9%) 17% (15%) Total (R2) 64% (76%) 69% (75%) 65% (79%) 69% (83%) 91 Table 3-13 Split Rating Model with S&P Rating WLS Estimation CVM Estimation RATING AS CONTINUOUS Rating as Categorical Variable Variable DR PI R 2 DR PI R2 Interest Coverage -4.553 -4.648 Ratio (V1) (-8.27) - 0.36 (-23.21) - 0.37 Leverage Ratio 0.058 0.059 (V2) (11.74) - 0.26 (21.39) - 0.27 Firm Size -0.635 -0.971 -0.647 -0.970 (V3) (-9.60) (-9.79) 0.74 (-13.38) (-11.93) 0.73 ROA -2.309 -2.316 (V4) (-11.23) - 0.34 (-21.50) - 0.35 S&P Rating -0.571 -0.175 -0.840 -0.251 (V5) (-12.96) (-3.55) 0.61 (-24.25) (-5.26) 0.77 Adverse Selection 0.018 0.043 0.019 0.045 (V6) (4.35) (7.13) 0.37 (6.05) (9.88) 0.37 Forecast Error 0.308 0.180 0.333 0.251 (V7) (5.94) (3.38) 0.06 (7.04) (4.46) 0.08 Yield Spread 27.038 36.788 27.28 30.48 (V8) (7.53) (4.55) 0.67 (13.39) (5.33) 0.51 Split Dummy (=I -0.045 0.098 -0.111 0.263 if split rating) (V9) (-1.73) (4.34) 0.05 (-1.79) (4.62) 0.08 Model Fit Fit Function 0.008 0.022 GFI 1.000 0.999 Chi-Square 5.839 (11) 17.339 (12) Pr > Chi-Square 0.884 0.137 Non-Zero Error cov(ei,e2), cov(ei,e4), cov(e2,e3) cov(eke2), cov(e,e4), cov(e2,e3) Covariance cov(ei, e8), cov(e3,es), cov(e4,e6) cov(el, e8), cov(e3,es), cov(e4,e6) cov(e4, e8), cov(e6,eg), cov(e2,eg) cov(e6,es), cov(e2,e9), cov(e5,e9) cov(e5,eo) Note: This table gives the estimated split bond rating model with S&P rating. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(ei,ej)=6,2 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (ij=1,...9). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from I (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. 92 Table 3-14 Split Rating Model with Moody's Rating WLS Estimation CVM Estimation Rating as Continuous Rating as Categorical Variable Variable DR PI R2 DR PI R2 Interest Coverage -4.393 -4.387 Ratio (VI) (-8.01) - 0.34 (-23.04) - 0.33 Leverage Ratio 0.061 0.061 (V2) (11.81) - 0.29 (22.20) - 0.29 Firm Size -0.648 -0.921 -0.679 -0.911 (V3) (-9.59) (-10.14) 0.70 (-13.98) (-12.15) 0.69 ROA -2.219 -2.254 (V4) (-10.20) - 0.32 (-21.06) - 0.32 Moody's Rating -0.530 -0.190 -0.833 -0.285 (V5) (-12.61) (-4.05) 0.61 (-25.40) (-5.75) 0.78 Adverse Selection 0.019 0.043 0.022 0.045 (V6) (4.42) (7.39) 0.38 (6.61) (10.19) 0.39 Forecast Error 0.293 0.205 0.334 0.257 (V7) (5.66) (3.67) 0.06 (7.03) (4.61) 0.08 Yield Spread 25.376 34.83 26.82 30.635 (V8) (7.22) (7.35) 0.61 (13.01) (5.71) 0.51 Split Dummy (=1 -0.045 0.099 -0.105 0.262 if split rating) (V9) (-1.63) (4.11) 0.05 (-1.59) (4.24) 0.08 Model Fit Fit Function 0.009 0.018 GFI 0.999 0.999 Chi-Square 7.070 (11) 13.760 (12) Pr > Chi-Square 0.793 0.316 Non-Zero Error cov(ei,e2), cov(el,e4), cov(e2,e3) cov(ei,e2), cov(e,e4), cov(e2,e3) Covariance cov(ei,es), cov(e3,es), cov(e4,e6) cov(ei, eg), cov(e3,es), cov(e4,e6) cov(e4,es), cov(e6,es), cov(e2,eg) cov(e6,eg), cov(e2,e9), cov(e5,e9) cov(e5,eg) Note: This table gives the estimated split bond rating model with Mooy's rating. Estimation constraints are as follows: Var(DR)=Var(PI)=1; cov(ei,ej)=62 if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ej)=0 (ij=1,...9). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from I (CCC and below) to 7 (AAA). Muthen's categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. CHAPTER 4 CONCLUSION Rule 144A bonds do not require a registration filing with the Securities and Exchange Commission. They may be purchased by qualified financial institutions and traded to other qualified financial institutions, but may not be purchased by individuals. Some Rule 144A bonds require the issuer to replace the bonds with publicly traded bonds within a stipulated period of time and are designated as having registration rights. Although high-yield bonds issued under Rule 144A usually have registration rights, we find that the majority of investment-grade bonds do not. Our empirical results indicate that Rule 144A bond issues have higher yields to maturity than publicly issued bonds. The effect is greater for Rule 144A bonds issued by private firms without publicly traded securities. The yield premiums of Rule 144A issues are likely due to lower liquidity, information uncertainty, and weaker legal protection for investors. Gross underwriter spreads for Rule 144A bond issues and publicly registered bond issues are essentially equivalent. The second essay uses the latent variable technique to investigate the information content of bond ratings. Previous studies on bond ratings only provide indirect evidence on the potential private information in bond ratings. Since private information is not observable by definition, it is impossible to link such information with bond ratings directly in traditional statistical models. The latent variable technique, however, provides us a way to directly link potential private information with bond ratings, using three observable proxies for information asymmetry. We find that bond ratings do contain 93 |

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PAGE 1 ESSAYS ON FIXED INCOME SECURITIES By LEI ZHOU 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 2002 PAGE 2 To my wife, my son and my parents PAGE 3 ACKNOWLEDGMENTS I first would like to thank Dr. Miles Livingston, the chairman of the committee, for his guidance, patience and support for my work. I am also grateful to Dr. Andy Naranjo, Dr. M. Nimalrendran and Dr. Carl Hackenbrack for their helpful comments and suggestions. I thank my wife. Lei, for her firm commitment and great sacrifices. She has been very supportive and patient, and I am fortunate to have her as my wife. Finally, I would like to thank my parents, Bojun and Yuming. Without their endless faith, support and encouragement, I will not be at this point in my life. iii PAGE 4 TABLE OF CONTENTS page ACKNOWLEDGMENTS iii ABSTRACT vi CHAPTER 1 INTRODUCTION I 2 THE IMPACT OF RULE 144A DEBT OFFERINGS UPON BOND YIELDS AND UNDERWRITER FEES 3 Introduction 3 Background of Rule I44A 6 Data and Methodology 13 Empirical Results 19 Conclusion 30 3 BOND RATINGS AND PRIVATE INFORAMTION 44 Introduction 44 Literature Review 46 Methodology 51 Data 65 Empirical Results 68 Conclusion 77 4 CONCLUSION 93 APPENDIX A CATEGORICAL VARIABLE METHOD (CVM) 95 Assumptions and Definitions 96 First Stage Estimation 97 Second Stage Estimation 99 Third Stage Estimation 100 B MEASUREMENT OF INFORMATION ASYMMETRY 102 IV PAGE 5 Proxies from Corporate Finance Literature 102 Proxy from Market Microstructure Literature 104 LIST OF REFERENCES 113 BIOGRAPHICAL SKETCH 118 V PAGE 6 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 ESSAYS ON FIXED INCOME SECURITIES By Lei Zhou August 2002 Chair: Miles B. Livingston Department: Finance, Insurance, and Real Estate This dissertation consists of two essays on fixed income securities. The first essay investigates the impact of the Securities and Exchange CommissionÂ’s [SEC] Rule 144A on corporate debt issues. The second essay studies the private information contents of bond ratings. Corporate bonds issued under Rule 144A are exempt from registration with the SEC. We find Rule 144A bond issues have higher yields than publicly issued bonds after adjusting for risk. Such yield premiums of Rule 144A issues may be due to lower liquidity, information uncertainty, and weaker legal protection for investors. Underwriter fees for Rule 144A issues are not significantly different from underwriter fees for publicly issued bonds. Bonds issued under Rule 144A may have registration rights, which require the issuer to exchange the bonds for public bonds within a stated period, or pay higher yields. While high-yield bonds usually have registration rights, we find that the majority of VI PAGE 7 investment-grade bonds do not. Registration rights have a greater impact on yields for high-yield than for investment-grade bonds. The second essay investigates whether bond ratings contain private information that is not available to investors. We use the latent variable technique to link private information with bond ratings directly. We use three variables (firm size, analyst forecast errors and adverse selection component of bid-ask spread) to proxy for the private information and find that the information asymmetry leads to lower ratings and higher bond yields. However, private information content only accounts for less than 10% of the variations in bond ratings. vii PAGE 8 CHAPTER 1 INTRODUCTION Fixed income securities are a very important part of the US financial market. This dissertation investigates two important topics on fixed income securities. First, we examine a new type of debt offering, called Rule I44A issues, and their impact upon the bond yields and underwriter fees. Second, we study whether bond ratings contain private information that is not available to investors. o The SEC introduced a new Rule, called Rule 144A in April 1999. Securities issued under Rule I44A do not have to file a public registration statement with the SEC, but can be sold only to qualified financial institutions. Since its adoption, the Rule 144A market has been growing very fast. Annual issues of Rule 144A non-convertible debt have swelled from $3.39 billion in 1990 to $235.17 billion in 1998. Using a sample of 4,070 industrial and utility bonds, we find that Rule 144A issues are found to have higher yields than publicly issued bonds after adjusting for risk. Yield premiums are higher if the issuer does not file periodic financial statements with the SEC. The yield premiums of Rule 144A issues may be due to lower liquidity, information uncertainty, and weaker legal protection for investors. Bonds issued under Rule 144A may have registration rights, which require the issuer to exchange the bonds for public bonds within a stated period, or pay higher yields. While high-yield bonds usually have registration rights, we find that the majority of investment-grade bonds do not. Registration rights have a greater impact on yields for 1 PAGE 9 2 high-yield than for investment-grade bonds. Underwriter fees for Rule 144A issues are not significantly different from underwriter fees for publicly issued bonds. Another important topic in fixed income security research is whether bond ratings carry private information. Previous empirical studies try to relate bond ratings to bond yields and/or stock returns and provide indirect evidence on the information content of ratings. We use the latent variable technique to link private information with bond ratings directly. We use three variables (firm size, analyst forecast errors and adverse selection component of bid-ask spread) to proxy for the private information and find that information asymmetry leads to lower ratings and higher bond yields. Since firms with large information asymmetry problems are likely to share more private information with the rating agencies, this finding is consistent with the hypothesis that bond ratings do contain private information. However, the private information only accounts for a small percentage of variation in ratings and bond yields. We also find that bond issues that have split ratings from S&P and MoodyÂ’s have more private information content in their ratings than bond issues that do not have split ratings. PAGE 10 CHAPTER 2 THE IMPACT OF RULE 144A DEBT OFFERINGS UPON BOND YIELDS AND UNDERWRITER FEES Introduction Since 1990, the Securities and Exchange Commission has allowed firms to sell security issues to qualified institutional buyers under so-called Rule 144A. Rule 144A issues are not required to be registered with the SEC and may not be resold to individual investors, but may be traded between qualified institutional buyers. Rule 144A issues may have Â“registration rights,Â” which require the issuer to exchange the original Rule 144A issue for a public bond issue within a stipulated period. If the exchange does not occur, the issuer must pay a higher interest rate. The basic justification for the waiver of advance registration is the belief that large institutional buyers are sophisticated investors and do not need the SEC to examine each offering of securities in depth. Public issues of securities are required to be registered before they are offered for sale to individual investors, however, who are presumed to be less sophisticated and informed than large institutional buyers. The Rule 144A market has been growing very fast. Annual issues of Rule 144A non-convertible debt have swelled from $3.39 billion in 1990 to $235.17 billion in 1998. In the meantime, the traditional private placement bond market has shrunk from $109.94 billion annually to $51.10 billion. Rule 144A issues have accounted for up to 80% of the high-yield bond market in recent years. 3 PAGE 11 4 Despite its size, the Rule 144A market has drawn little attention from academics. Only one published article exclusively studies yields on high-yield bonds and focuses upon the information disclosure of Rule 144A issues. Fenn (2000) argues that expedience is the only motivation for Rule 144A issues. Unlike Fenn (2000), we find that yields for Rule 144A offerings are substantially higher than for public offerings for both investment-grade and high-yield bonds. In addition, we find that Rule 144A issues by private firms without any publicly traded securities, and consequently not required to file periodic financial statements with the SEC, have markedly higher yields. This finding is consistent with Bethel and SirriÂ’s (1998) discussion of the importance of company reporting to the SEC. When we follow FennÂ’s methodology and reproduce his sample, we find that his findings seem to be sensitive to both time period and model specification. There are several possible explanations for why Rule 144 A issues might have higher yields. First, Rule 144A issues are less liquid than public bond issues, since the universe of buyers in the primary and secondary market is restricted to qualified financial institutions. Second, the disclosure requirements for Rule 144A issues are less stringent, giving issuing firms greater latitude as to information disclosure. Buyers of Rule 144A offerings may thus require higher yields because of information uncertainty. The effect is greater for privately held firms that do not file periodic financial statements with the SEC. Third, public debt issuers bear more legal liability than Rule 144A issuers. For Rule 144A issues, the bond buyer bears considerably more risk about information accuracy. PAGE 12 5 We also find a dramatic difference in the use of registration rights (the requirement to exchange the Rule 144A issue for a public offering) for investment-grade and high-yield Rule 144A bonds. While most high-yield Rule 144A issues include registration rights, more than half of investment-grade Rule 144A issues do not. In addition, registration rights have a greater impact on the yields for high-yield Rule 144A issues than for investment-grade Rule 144A issues. There is no significant difference in gross underwriter spread between Rule 144 A issues and public bonds. Our paper contributes to the literature in several ways. First, we provide new findings on the use and impact of registration rights in Rule 144A issues. There are conflicting reports on the use of registration rights, and no previous research studies the impact of registration rights on yields and underwriter fees. Second, we find that about a quarter of Rule 144A bonds are issued by privately held firms that are not required to report to the SEC. While Rule 144A bonds pay yield premiums over public bonds in general, the Rule 144A issues by non-reporting firms have remarkably higher yield premiums. This finding supports the importance of company reporting to the SEC. Third, we include both investment-grade and high-yield bonds in our sample, and we find differences between the two. Yield premiums on high-yield Rule 144A issues are considerably higher than those on investment-grade Rule 144A issues, for example. Other studies either ignore investment-grade Rule 144A issues or do not investigate the two types of Rule 144A issues separately. Fourth, we study the gross underwriter spread of Rule 144A issues as well as the yields. Gross underwriter spread, an important component of total issuing costs, sheds PAGE 13 6 light on the riskiness of an issue. No one has looked at the differences in gross underwriter spread between Rule 144A issues and public issues of debt. Finally, we investigate in more detail the institutional background of the Rule 144 A marketÂ— it liquidity, potential investors, information disclosure, and legal protection for investorsÂ— and relate this information to the empirical findings. Previous research focuses only on the information disclosure of Rule 144A issues. The chapter is organized as follows. The next section details the background and the development of the Rule 144A market. We also analyze the institutional details of Rule 144A issues and their expected impact on bond yields and underwriter spread. The third section describes the data and methodology. Empirical results are presented in the fourth section, while section five concludes the chapter. Background of Rule 144A Origination of Rule 144A One of the basic rationales of the 1933 Securities Act is to protect unsophisticated individual investors, or so-called widow and orphan investors, from fraud. In recent years, however, the US capital market has become more Â“institutionalized.Â” The SEC reports that the percentage of ownership of US equities by institutional investors increased from 29.3% in 1980 to 47.5% in 1990 (Securities and Exchange Commission, 1994). These large institutional investors have expertise and experience in investing their assets. A registration requirement for security issues may not add much value to such large institutional investors, while it imposes significant costs on the issuers. A public registration requirement may also hinder foreign participation in the US capital market PAGE 14 7 because it is costly for foreign issuers to maintain GAAP-compliant accounting information and/or to disclose information not usually disclosed in their home countries.' To address such concerns, the SEC adopted Rule 144A in 1990. Securities issued under Rule 144A do not require registration with the SEC, but can be traded without 2 restriction in the secondary market among Â“qualified institutional buyers,Â” or QIBs. Rule 144A issues, which are technically private placements, enjoy a much more liquid secondary market than traditional private issues.^ Registration Rights Although Rule 144A issues do not initially have a public registration statement, they may include so-called registration rights, which require the issuer to register the issue with the SEC or exchange it for a registered issue within a specified time. If the issuer fails to do this, the coupon on the bond is increased by a designated amount, usually 0.25% to 0.50%. For example, the registration rights agreement of the 6 5/8% debenture due 2038 of Boeing Corp issued under Rule 144A reads like this: Additional Interest shall accrue on the Initial Securities . . .[if] any such Registration Default shall occur ... at a rate of 0.25% per annum. ' Since 1990, the amount of foreign issues in the Rule 144A market has increased significantly, to over $50 billion in 1998. Almost half of all foreign issues in 1998 were offered in the Rule 144A market. Chaplinsky and Ramchand (2000) provides a detailed analysis of foreign Rule 144A debt issues. 2 QIBs are generally defined as institutions that own or have investment discretion over $100 million or more in assets. In addition to the $100 million requirement, banks and savings and loan associations must also have at least $25 million of net worth to quality as QIBs. For registered broker-dealers, $10 million investment in securities would meet the requirement. ^ Loss and Seligman (2001, pp. 391-396) discuss the legal details of Rule 144A and Rule 144. PAGE 15 8 Most Rule 144A issues with registration rights do get registered eventually. In our study, we find only three Rule 144 A issues with registration rights whose issuers failed to register the issues within the designated period, and the coupon rates were increased. There are three published reports on the extent of the use of registration rights. Investment DealerÂ’s Digest (1997) and Bethel and Sirri (1998) report that about one-third of Rule 144A debt issues have registration rights. Fenn (2000), on the other hand, reports that over 97% of high-yield Rule 144A bonds were subsequently registered with the SEC. Our study reconciles these seemingly contradictory reports. As we describe in detail later, we find that over 98% of high-yield bonds have registration rights, but only about 40% of investment-grade bonds do. Development of Rule 144A Non-Convertible Debt Market Although both equities and bonds can be issued under Rule 144A, the majority of Rule 144A issues are non-convertible bonds. For example, a total of $262 billion of Rule 144A securities was issued in 1997: $40.7 billion in equities and $1 1.2 billion in convertible bonds (Bethel and Sirri, 1998). The remaining $210.1 billion, or 80% of all Rule 144A securities, was non-convertible debt. We examine Rule 144A non-convertible debt issues only. Figure 2-1 compares the annual issues of Rule 144A debt to the traditional private placement and public debt. Since adoption of the rule, the Rule 144A non-convertible debt market has been growing very quickly. Total annual new issues in the Rule 144A market have grown from $3.39 billion in 1990 to $235 billion (in inflation adjusted 1990 dollars) in 1998. New public debt issues have also experienced significant growth, from $106 billion in 1990 to $975 billion in 1998. Although both markets have grown PAGE 16 9 significantly, the Rule 144A market has grown proportionally faster. The traditional private market has shrunk, from $110 billion in 1990 to $51 billion in 1998. The rapid growth of the Rule 144 A market seems to have come partially at the expense of the private placement market. Figure 2-2 shows the average issue size in the three markets. Privately placed non-convertible bonds are much smaller on average than publicly placed bonds. Small issues by small firms are usually placed in the private market because small firms are more likely to be subject to agency problems (Blackwell and Kidwell, 1988). Strict covenants, renegotiation provisions, and a small number of investors in private placements help to alleviate the asset substitution and under-investment problems. Figure 2-2 also shows that the average size of Rule 144A issues increased continually from 1991 to 1998, while public issue size has been decreasing. In fact. Rule 144A issue size on average has surpassed public issue size since 1996. Obviously the Rule 144A market has attracted many large issues that would otherwise have been placed in the public market. Thus, the growth of Rule 144A issues may also come at the expense of the public market. Institutional Details of Rule 144A Issues Rule 144A offers several advantages to issuing firms. Less information needs to be disclosed, and the information disclosed does not need to meet certain criteria. For example, financial statements need not be GAAP-consistent for Rule 144A issues. A firm can issue the debt quickly. Timely issuance may let a firm sell debt under favorable market conditions, when interest rates are lower. For these benefits, the issuing firms may be willing to pay premium yields. Indeed, if issuing firms did not have to pay premiums for such advantages, we would expect Rule 144A issues to dominate the PAGE 17 10 market. While the Rule 144A market has been very successful, especially in attracting high-yield issues, it far from dominates the public debt market. Indeed, about 20% of high-yield bonds and over 80% of investment-grade bonds are still offered in the public debt market. Hence, there must be some costs to issue in the Rule 144A market, and the issuing firms must be balancing the costs and benefits. The yield premium and/or the higher gross underwriter spread may constitute the costs of issue in this market. For investors. Rule 144A issues may be riskier than public issues. First, Rule 1 44 A issues are less liquid than public bond issues, since the universe of buyers in both the primary and the secondary market is restricted to qualified financial institutions. Indeed, Cox (1999) finds that the number of bond buyers more than doubled and the number of transactions increased by approximately one-third following the subsequent public registration of bonds issued originally as Rule 144A issues. The restricted potential investor universe is clearly an important factor. Furthermore, Rule 144A issues may be categorized as Â“restricted securitiesÂ” by some institutional investors such as insurance companies, pension funds, or mutual funds. These institutional investors may be constrained in the percentage of their portfolios they may invest in restricted securities, or they may have to maintain larger capital reserves for investment in Rule 144A issues. Indeed, the American Bar Association argued in 1999 that the use of registration rights in Rule 144A issues While the total trading volume of Rule 144A issues declines after the post-issue registration, this does not contradict the argument that public registration makes Rule 144A issues more liquid. A newly issued security is usually much more liquid than a seasoned security. Hence, the observed decline in trading volume may reflect just the lower liquidity of seasoned securities. PAGE 18 permits an investment institution to reclassify Â“restricted securitiesÂ” held in its portfolio to unrestricted status upon the completion of the exchange offer, without the need to sell those securities to make capital available for additional investment in privately placed debt securities. Even though Rule 144A issues may be reclassified as unrestricted securities if registered later, the issues may have a limited pool of potential buyers at the initial sale if they are Â“restricted securities.Â” Hence, the smaller base of potential buyers and the Â“restricted securitiesÂ” status may together reduce the liquidity of Rule 144A issues, producing a yield premium over public debt. Second, disclosure requirements for Rule 144A issues are less stringent. Legally, a Rule 144A offering does not have to disclose the same information as required under the Securities Act of 1933; the issuing firm has greater latitude as to disclosure. Such lack of disclosure may be of greater concern to investors in offerings by less well-known issuers, especially issuers with no public securities that do not file periodic disclosures with the SEC. Even for public firms that file with the SEC, such periodic disclosures do not provide detailed issue-specific information required by the 1933 Securities Act, such as the intended use of the proceeds. Third, investors in Rule 144A issues have weaker legal protection than investors in public debt issues (Bethel and Sirri, 1998). Under Section 1 1 of the Securities Act, the issuers of registered public debt are held Â“strictly liableÂ” for losses to investors if they provide misleading information or omit material information in the registration statement. In other words, if ever there is misleading information or omission of material information, the issuer of registered public debt will be held liable, whether or not it acted knowingly. Investors in Rule 144A issues do not have such strong legal protection. Even if a Rule 144A issue has registration rights and is registered later. Rule lOb-5 of the PAGE 19 12 Exchange Act provides less legal protection. Rule lOb-5 holds an issuer liable if the issuer knowingly provides misleading information and investors make their investment decision on such misleading information. Hence, investors in Rule 144A issues have much weaker legal protection and would have a harder time suing an issuer in the event of default. Such concerns about legal protection may be important to insurance companies that, by regulation, have to make Â“prudentÂ” investments, especially when they are investing in high-yield bonds. Expected Impact of Rule 144A on Yields and Underwriter Fees Our discussion indicates that Rule 144A may have advantages for issuing firms but disadvantages for investors. Issuing firms may be willing to pay for such advantages of Rule 144A offerings, possibly in the form of higher yields and/or gross underwriter spread. Similarly, investors may demand a higher rate of return on Rule 144A issues because of the disadvantages for them. Hence, we expect Rule 144A issues to have a yield premium over public issues. The impact of Rule 144A on gross underwriter spread is less clear. First, fewer potential investors and information uncertainty make Rule 144A issues more difficult to sell than public debt, so an underwriter may require higher fees. Yet underwriting Rule 144A issues may be less risky in some ways and involve less work for underwriters. For example, weaker legal protection for investors in Rule 144A issues means less legal liability for underwriters. Also, it is estimated to take only half the time to issue debt under Rule 144A than to issue a registered offering {Investment Dealers Digest, 1997). For an underwriter, shorter and less burdensome marketing means lower costs. A short underwriting period reduces interest rate risks for underwriters too. PAGE 20 13 Furthermore, while in a traditional public offering, the underwriter devotes considerable time and staff to help an issuer prepare a registration statement and file with the SEC, these are not necessary for a Rule 144A issue. If investment bankers can underwrite Rule 144A issues more quickly and with less work, the underwriter may be willing to charge a lower fee for Rule 144A issues. The net impact of Rule 144A on the underwriter gross spread is therefore unclear and is an empirical question that we address later. Data and Methodology Construction and Description of the Sample The New Issues Database of the Securities Data Company (SDC) is used to collect data for all non-convertible, domestic bond issues with fixed coupon rates in the Rulel44A and public market by industrial and utility firms from 1997 through 1999.^ Issues not rated by both MoodyÂ’s and Standard & PoorÂ’s are excluded. A small number of issues with perpetual maturities have been excluded. To check the data integrity, the Bloomberg database is used. As it is impractical to check every observation manually, about 100 outliers are checked. Among them, about one-fourth have problems.^ Some of them are excluded. For example, issues of ^ We start the sample at 1997 because few Rule 144A issues before 1997 report gross underwriter spread in the SDC database. Since 1997, we can find gross underwriter spread for a significant number of Rule 144A issues, though still only about 30% of Rule 144A issues in our sample report gross underwriter spread. ^ Outliers are those with a residual outside three standard deviations in the regressions. Half of the problematic observations have major errors, such as misclassification and wrong decimal points. Another half has minor errors, such as a small difference in gross underwriter spread, or yield. After correcting for these errors, we reran the regressions and checked for the new outliers. We found no major errors, but a few minor errors. PAGE 21 14 preferred stocks mis-classified as bond offerings by SDC are excluded. Others are corrected. This leaves us a total of 4,070 observations: 1,418 Rule 144A issues and 2,652 public issues.^ Table 2-1 gives the descriptive statistics for the full sample. There are a total of 1 ,542 issuing firms in the sample. Among them, 663 issued in the public market, 944 issued in the Rule 144A market, and 65 issued in both markets. Firms issuing in the public market have an average of 4.0 issues, while firms issuing in the Rule 144A market have an average of only 1 .5 issues for the sample period.* The average size of a public offering is $129.04 million; the average size of a Rule 144A offering is $177.69 million. Ninety-one percent of the issues in the public market are investment-grade, and over 98% are senior debt. Only 32% of Rule 144A issues are investment-grade, and 68% are senior debt. Indeed, 74% of all high-yield bonds in 1997 were issued in the Rule 144A market (Bethel and Sirri, 1998). Figure 2-3 gives the distribution of ratings for the public and Rule 144A issues. For public issues, about 40% of issues are A-rated bonds and 30% are BBB-rated bonds. In total, about 90% of public issues are rated between AA and BBB. For Rule 144A 7 35.1 1% of public bonds and 26.94% of Rule 144A issues are issued by utility firms. We have studied the industrial issues and utility issues separately, and find the results are essentially identical. 8 The issue frequency for public debt seems to be high. One potential explanation for such high issue frequency is that there are more short-term near-money debt issues in the public debt market. Yet the average maturity for public debt is 12.17 years, significantly longer than the average maturity of Rule 144A issues. We eliminate issues with maturity less than or equal to 2 years from the sample, and find that the issue frequency for public debt is still much higher than issue frequency of Rule 144A issues: 3.70 times vs. 1.48 times. Hence, short maturity does not explain the high issue frequency in the public debt market. None of our results changes with the modified sample. PAGE 22 15 issues, about 50% are B-rated bonds. A, A/BBB and BBB bonds account for about 25% of Rule 144A issues. Interestingly, more than 3% of Rule 144A issues are AAA bonds. Gross underwriter spread is the compensation that the issuer pays to the underwriters. Original yield is the bond yield to maturity at original issuance. The yield on a comparable maturity Treasury is subtracted to arrive at the Treasury spread. Table 2-1 shows that the average gross underwriter spread and average Treasury spread are higher for Rule 144A issues than for public bond issues. Table 2-2 gives the average gross underwriter spread and Treasury spread across different ratings. The differences in gross underwriter spread between Rule 144A issues and public issues are usually small, although we find significantly higher gross underwriter spreads for Rule 144A issues in three rating categories (AA/A, BBB, and BB). Rule 144A issues have higher Treasury spreads than public issues in 1 1 out of the 12 rating categories. Although the differences in the yields are significant at the 1% or 5% level in only 4 of the 12 rating categories, these four rating categories (A, BBB, BB, and B) account for the majority of the observations. Hence, rating differences cannot explain all the large differences in Treasury spread between public issues and Rule 144A issues. Table 2-1 also shows that 97.70% of public debt offerings and 66.36% of Rule 144A offerings are issued by public firms. ^ Another important difference between public ^ An issuing firm is defined as a public firm if the firm or its parent has public traded equity. We find this information on SDC. PAGE 23 16 debt and Rule 144A issues is that more than 50% of Rule 144A issues are first-time debt issues, compared to only 10% of public debt issues. Firms with neither publicly traded equity nor public bonds are not required to file periodic disclosure with the SEC. These firms are usually called non-SEC-reporting firms, or simply non-reporting firms. We classify an issuing firm as non-reporting if 1) it is not a public firm and 2) it has not issued any public debt securities since 1970." Table 2-1 shows that 23% of Rule 144A offerings are issued by non-reporting firms, while less than 1% of public offerings are issued by non-reporting firms. In total, 347 bonds are issued by non-reporting firms: 74% high-yield Rule 144A issues, 21% investment-grade Rule 144A issues, and only 5% public bond issues. This indicates that non-reporting firms have a strong preference for the Rule 144A market. Methodology The primary methodology in this study is simple ordinary least squared regressions. Later we use HeckmanÂ’s (1979) treatment effect for potential self-selection bias. The dependent variables are the gross underwriter spread and the Treasury spread in basis points. The independent variables include proxies for risks of individual bond issues, proxies for market conditions, other control variables and test variables. A debt offering is classified as a first-time issue if the issuing firm has not sold any public fixed income security (straight or convertible debt, preferred stock) since 1970. ' ' Two possible misclassifications may occur. If a non-public firm issued a public bond before 1970, but not since then, and the bond is still outstanding, then our method would misclassify it as a non-reporting firm, while in fact it is still required to file with the SEC. Or, if a non-public firm issued a public bond after 1970 which had been retired and no other public debt is outstanding, we would misclassify it as a reporting firm while in fact it is not. Although these two situations are possible, we see the chances as small, and they will not make a significant difference in our results. PAGE 24 17 Proxies for risks The rating dummy variables represent specific bond ratings: BBB = 1 if the issue is rated BBB by both MoodyÂ’s and S&P and zero otherwise, BBB/BB = 1 if the issue is rated BBB by one rating agency but BB by another agency, and zero otherwise, and so on. The regression base case is AAA-rated bonds. Previous studies find that bond ratings are significant determinants of both bond yield and gross underwriter spread (Lee et al., 1996, and Jewell and Livingston, 1998). Log of Maturity is the natural log of years to maturity. The longer the maturity, the riskier the issue. Percentage of Years of Call Protection is the percentage of years that the call protection is in effect. Call protection reduces the reinvestment risk of investors and makes issues less risky. Senior Debt is a dummy variable equal to one if the issue is senior debt, and zero otherwise. Since senior debt is less risky, we expect the coefficients on Senior Debt to be negative in both regressions. Proxies for market conditions Bond default risk premium fluctuates with overall market conditions. To control for the fluctuation, we include in the regressions a Default Risk Premium variable, which is the difference between the Merrill Lynch BBB Corporate Bond Index and the 10-year US Treasury Index. Another two variables to control for market conditions are dummy variables for years 1998 and 1999. In regressions, the base case is AAA-rated bonds issued in 1997. 12 The relationship between maturity and gross underwriter spread and yields may not be linear. We have examined both years-to-maturity and log of maturity in the regressions. Log of maturity seems to have a better fit and is reported in the results, although the results are essentially the same if years-to-maturity is used. PAGE 25 18 Other control variables The First-Time Debt Issue dummy equals one if the issuer has not issued any fixed income securities since 1970 and zero otherwise. A first-time issue may have a higher yield, as the issuer does not have a reputation in the security market. Also, the underwriting cost may be higher, as an investment banker must devote more resources and time to obtain information about a new issuer and to find buyers. Fenn (2000) finds that yield premiums on first-time issues are about 30 basis points. Log of Issue Frequency is the natural log of the number of issues that each firm had over 1997 to 1999. Frequent issuers may have not only lower gross underwriter spread but also lower yield, since they are established players in the capital market and have a natural clientele. They may be regarded as less risky issuers. Frequent issues of debt, on the other hand, might convey a signal of financial trouble and add to a firmÂ’s debt level. That may increase the yields on frequent issuers. The net effect of issue frequency is therefore unclear. The Public Firm dummy equals one if the SDC database indicates that the issuer has publicly traded equity and zero otherwise. Because there is usually more information on public firms available to investors, the yield and gross underwriter spread of bonds issued by public firms are expected to be lower. Log of Proceeds is the natural log of total proceeds. Many empirical studies indicate that there are economies of scale in gross underwriter spread. That is, percentage gross underwriter spread falls as the size of an issue increases. (See, for example, Lee et al., 1990.) Altinkilic and Hansen (2000) argue that there are also diseconomies of scale in spreads; 30% of the bond issues in their sample are in a range of diseconomies of scale. PAGE 26 19 Hence, the sign of the coefficient on Log of Proceeds in the gross underwriter spread regression is not clear. Large issues of bonds are usually more liquid than small issues, and investors may require lower rates of return for more liquid issues. Hence, we expect the sign on the coefficient on Log of Proceeds in the Treasury yield regression to be negative. The Utility Firm dummy equals one if the issuer is a utility firm and zero otherwise. Test variables In the first set of regressions, the test variable is the Rule 144A dummy, which equals one for the Rule 144A issues and zero otherwise. The dummy variable is used to test whether the gross underwriter spread and Treasury spread are different for the Rule 144A issues and public bond issues. In another set of regressions, two dummy variables for Rule 144A issues are created, according to whether the issuing firms are required to file periodic disclosure with the SEC. If a Rule 144A offering is issued by a non-reporting firm, the dummy Rule 144A by Non-Reporting Firm equals one and zero otherwise. Similarly, if a Rule 144A offering is issued by a reporting firm, the dummy Rule 144A by Reporting Firm equals one and zero otherwise. Empirical Results Treasury Spread The impact of Rule 144A offerings upon Treasury spread is examined in Table 23. The Column A regression uses a single dummy variable for Rule 144A issues. The PAGE 27 20 coefficient is 18.97 and significant, indicating that Rule 144A issues have yields that are almost 19 basis points higher than public bond issues.'^ The first-time debt issue dummy variable is positive 30 basis points, consistent with FennÂ’s finding. The public firm dummy is negative 28 basis points, indicating that public firms have a cost advantage in raising external debt. The logarithm of issue frequency is negative 8 basis points; more frequent issuers tend to have lower yields. The default risk premium is positive and significant. The logarithm of proceeds, a measure of issue size, is negative 3 basis points; that is, larger issues tend to be more liquid and hence have lower yields. The dummy variables for bond rating tend to increase as the rating gets lower. The risk premium rises at an increasing rate as ratings drop. The coefficient for the senior debt dummy is positive and almost 49 basis points, indicating that senior debt has higher yields, a counter-intuitive result that may be caused by the rating ageneiesÂ’ tendency to give senior debt unjustified higher ratings. Fenn (2000) and Fridson and Garman (1997) have similar findings. The log of maturity is positive 1 7 basis points, suggesting that longer maturities have higher risk. The utility firm dummy variable is negative, implying lower risk for utility bonds. Column B breaks the dummy variable for Rule 144A issues into two separate dummy variables: one for non-reporting firms, and the other for reporting firms. The We also break the sample into two sub-samples: issues with maturity shorter than or equal to 5 years and issues with maturity longer than 5 years. The coefficients on the Rule 144A dummy in the sample are very similar, 18.16 and 19.17, respectively, both significant at the 1% level. PAGE 28 21 coefficient for Rule 144A issues by non-reporting firms is 54 basis points, and the coefficient for Rule 144A issues by reporting firms is 19 basis points; both are highly significant. The difference between the two coefficients is significant at the 1% level. The absolute size for the first-time debt issue dummy drops from 30 to 24 basis points, and the public firm dummy becomes insignificantly different from zero. All the other eoefficients are very similar to Column A results. One possible explanation for the higher yields on Rule 144A issues is sample selection bias. The previous regressions implicitly assume that the Rule 144A dummy is exogenous, but issuers may not choose a publie offering or a Rule 144A offering randomly. Perhaps riskier issuers (in a given rating category) may choose to issue in the Rule 144A market because less information needs to be disclosed. To examine whether a selection bias exists, we estimate the HeckmanÂ’s treatment effect model (Greene 1993, pp. 713-714, and Maddala, 1983, p. 263). We use HeckmanÂ’s two-stage regression methodology (Heckman, 1979). First, we estimate a probit model of the choice between Rule 144A and public debt and caleulate the inverse Mills ratio. Next, we add the inverse Mills ratio to the regression as an additional explanatory variable. If its coefficient is not significantly differently from zero, we can conclude there is no evidenee of selection bias. Column C in Table 2-3 presents the results of the first set of regressions after the HeckmanÂ’s treatment. The coefficient on the inverse Mills ratio is not statistically different from zero. Nor does the coefficient on the Rule 144A dummy ehange significantly after HeckmanÂ’s treatment. There is thus no evidence that the yield differences between Rule 144A issues and public issues are due to sample selection bias. PAGE 29 22 Table 2-4 differentiates the regressions by high-yield bonds and investment-grade bonds. In Column A, the coefficient for Rule 144A issues is much higher for high-yield bonds than for investment-grade bonds. In other words, the yield premium for high-yield Rule 144A bonds is much higher than the yield premium for investment-grade Rule 144A bonds. Similarly, in Column B, the regression coefficient for SEC-reporting issues is higher for high-yield bonds than for investment-grade bonds. For Rule 144A issues by non-reporting firms, the coefficient for high-yield bonds is slightly lower than the coefficient for investment-grade bonds, although the difference is not statistically significant.'"' This is somewhat surprising, given that high-yield Rule 144A issues on average have considerably higher yield premiums than investment-grade Rule 144A issues. One possible explanation is that the information uncertainty of nonSEC-reporting firms is very severe and has a first-order impact on yields. The difference between high-yield and investment-grade Rule 1 44A is overshadowed by the severe information uncertainty of the non-SEC-reporting firms. To test the statistical significance of the difference between the two coefficients, we run a pooled regression of high-yield and investment-grade bonds. In addition to the explanatory variables in the separate regressions, we create a 0-1 dummy variable for high-yield bonds and interact it with all the other explanatory variables. The results of the pooled regression are identical to those of the separate regressions, and the coefficients on these interaction terms are the differences in the coefficients between the separate high-yield and investment-grade regressions. The coefficient on the interaction term between high-yield dummy and Rule 144A by non-reporting firm dummy is -10.64 but not significant. The coefficient on the interaction term between high-yield dummy and Rule 144A by reporting firm dummy is 22.22 and significant at the 1% level. PAGE 30 23 In summary, we have three basic findings about Treasury spread. First, Rule 144A issues have on average a yield premium of 19 basis points over public debts, everything else equal. This is consistent with the expected impact of Rule 144A on bond yields. Second, Rule 144A issues by non-SEC-reporting firms have considerably higher yield premiums, 54 basis points, than Rule 144A issues by SEC-reporting firms. This is consistent with the information uncertainty argument. Investors are concerned about the quantity and quality of disclosures for Rule 144A issues because they are not registered with the SEC. Firms that file periodic disclosure statements with the SEC already have made a considerable amount of firm-specific information available, so there is less information uncertainty. For issuers without periodic reports or disclosure statements, information uncertainty is of greater concern, and yield premiums are higher. Third, high-yield Rule 144 A issues have higher yield premiums than investmentgrade Rule 144A issues. This finding is consistent with the weaker legal protection and liquidity arguments. Concerns about legal protection may be of greater importance to insurance companies, which are required by regulation to make prudent investments, especially when they are investing in high-yield bonds. High-yield Rule 144A issues are acceptable to a smaller pool of potential investors, and they are less liquid than investment-grade Rule 144A issues. It is not surprising that high-yield Rule 144A issues have higher yield premiums than investment-grade Rule 144A issues. Comparison to FenÂ’s Study Our findings are different from those of Fenn (2000). Fenn finds that the yield premiums of Rule 144A over public debt issues have disappeared in recent years. We find the yield premiums of Rule 144A issues still exist. When we try to reproduce FennÂ’s PAGE 31 24 results using his methodology, we find that they are sensitive to 1 ) the regression model specification, and 2) the time period. First, we follow FennÂ’s methodology and create a sample of non-convertible highyield bond issues from 1993 to the first half of 1998. Our mimic sample is very close to FennÂ’s (1,566 observations compared to his 1,562). The distributions of the mimic sample over years, ratings, and industry categories are similar to FennÂ’s sample.Â’^ To control for the variation of corporate bond yields over the years, Fenn uses a year trend variable, set equal to issuing year minus 1993. To test whether the yield premium on Rule 144 A has changed over the years, Fenn adds an interaction term between the Rule 144A dummy and the year trend variable in the regression. He finds that the yield premium on Rule 144A issues over public debt issues is about 41 basis points, but dropping by 8 basis points every year (as the interaction term shows). Hence, Fenn concludes that the yield premium disappears by 1998 (41 8(98-93) = 1). FennÂ’s results are provided in the first column of Table 2-5 (FennÂ’s Table 5, column 2, p. 396). We follow FennÂ’s methodology and run the same regression. Our results are reported in the second column of Table 2-5. Most of our coefficients are very close to FennÂ’s and have the same significance level, although our mimic regression has a slightly lower R-squared value. The mimic regression finds that the yield premium for Rule 144A is about 58 basis points, and declines by 12 basis points each year. Although the coefficients on the Rule 144A dummy and the interaction term are higher for our mimic When we run the same baseline regression on our mimic sample set (with no Rule 144A dummies as in FennÂ’s paper), we find the coefficients are very close to FennÂ’s. The complete comparisons are available from the authors. PAGE 32 25 regression, the basic interpretation is the same as FennÂ’s; that is, the yield premium disappears by 1998 (58 12*5 = -2). The year trend variable, however, implicitly assumes a linear time trend for yields on high-yield bonds. The yields on high-yield bonds increased from 1993 to 1995 and decreased significantly in 1997 and 1998. The annual averages of the Merrill Lynch High Yield 175 Index are 10.38%, 10.71%, 11.05%, 10.40%, 9.76%, and 9.19% from 1993 to 1998, clearly not a linear trend. A negative coefficient on the linear year trend variable in FennÂ’s study erroneously estimates declining yields from 1993 through 1995 and underestimates the decline in yields in 1997 and 1998. This underestimation coincides with an increased percentage of Rule 144A issues in the high-yield bond market. Hence, the interaction term of the Rule 144A dummy and the year variable picks up some of the underestimation of the yield decreases of high-yield bonds in 1997 and 1998. When we change the year trend variable to 0-1 dummy variables for each year, we find that the coefficient on the interaction term drops significantly, from -12 to -9 basis points and the significance level declines from 1% to 5% (Table 2-5, Column 3). The coefficient on the Rule 144A dummy changes only slightly. Hence, we can no longer claim that the yield premium disappears completely in 1998 (55 9*5 = 10), although it still shows a declining trend. The coefficients on the year dummies confirm that yields do not drop significantly until 1997. The Merrill Lynch High Yield 175 Index tracks the performance of the 175 most liquid below-investment-grade public US corporate bonds. PAGE 33 26 More important, when we expand the sample by including the second half of 1998 and 1999 (Table 2-5, Column 4), the interaction term becomes insignificant, while the yield premium for Rule 144A issues is 35 basis points and significant. Thus, the yield premium for Rule 144A issues does not disappear over time. In separate regressions for each year (unreported but available on request), we find that the yield premiums for Rule 144A issues are low for 1996 and 1997 (similar to FennÂ’s), but range from 40 to 80 basis points in the second half of 1998 and 1999. Hence, instead of disappearing yield premiums, we find fluctuating yield premiums on Rule 144A issues over the years; high in 1993 to 1995, low in 1996 to the first half of 1998, and high again in the second half of 1998 and 1999. PermÂ’s data end at the first half of 1998, while ours extend through 1999. This time period difference Â• Â’17 contributes to the different findings. In summary, the evidence of declining yield premiums is not robust to changes in regression specification and time periods. Use of Registration Rights and Their Impact There have been conflicting claims about the use of registration rights. To investigate the question further, we search on the Bloomberg database for post-issue registration of every Rule 144A issue in our sample. For issues not in Bloomberg, we search the company name in the SECÂ’s electronic database EDGAR for registration statements. We are able to find 1,326 of the 1,418 Rule 144A issues in either Bloomberg or EDGAR. Table 2-6 gives our findings. Â’Â’ We obtain similar results when we include first-time issuer dummy, private firm dummy, and their interaction terms with the Rule 144A dummy in the regression. Similar results are also obtained when only B-rated bonds are investigated. PAGE 34 27 Like Fenn, we find that virtually all high-yield Rule 144A bonds issued between 1997 and 1999 have registration rights. Only 44% of the investment-grade Rule 144A bonds, however, have registration rights.Â’* The impact of registration rights on the Treasury spread is examined in Table 2-7 for both investment-grade and high-yield bonds. The same regression as in Table 2.3. is run with two dummy variables for Rule 144A issues: those with registration rights and those without registration rights. Several results are noteworthy. First, the coefficients for high-yield bonds are larger in absolute value than for investment-grade bonds, consistent with the findings in Table 2.4. Second, the yield premium for high-yield Rule 144A issues without registration rights is 82 basis points, compared to 33 basis points for issues with registration rights. A chi-square test rejects the null hypothesis that these two coefficients are the same at the 10% level. This finding indicates that registration rights help to reduce the yield premium for high-yield Rule 144A bonds over public debt. Note that this finding should be treated 18 Â• Â• Â• While Rule 144A issues by non-reporting firms may choose not to have registration rights to remain private, the evidence does not support this argument. First, although more than a quarter of high-yield Rule 144A bonds are issued by non-reporting firms, 95% of them have registration rights. Second, for investment-grade Rule 144A issues, 39% of those by non-reporting firms have registration rights, while 44% of those by reporting firms have registration rights. Thus, there is no dramatic difference in the use of registration rights by reporting vs. non-reporting firms. We also run a regression on Rule 144A issues only, with a registration right dummy variable (1 if with registration rights and zero otherwise). The coefficient on the registration rights is negative and significant at the 10% level, indicating that high-yield Rule 144A issues with registration rights have lower yields than similar Rule 144A issues without registration rights. PAGE 35 28 with caution, because there are only 17 high-yield Rule 144 A issues without registration rights. The yield premium for investment-grade Rule 144A issues without registration rights is smaller than the yield premium on investment-grade issues with registration 20 rights, but the difference between the two coefficients is not statistically significant. These findings together suggest that registration rights help to reduce yield premiums for high-yield Rule 144A issues, and hence most issuers of high-yield Rule 144A issues choose to have registration rights. Registration rights do not seem to make a difference in yield premiums for investment-grade bonds, and issuing firms are thus relatively indifferent with respect to registration rights. These findings are consistent with several explanations. First, because of the greater riskiness of high-yield bonds, agency costs and moral hazard problems tend to be higher (Jensen and Meckling, 1976, and Campbell and Kracaw, 1990). Hence, investors would want more information disclosure for high-yield bonds. With registration rights, the issuing firm promises to register in the near future and meet stricter disclosure requirements of the 1933 Securities Act, signaling investors that the issuer is not hiding unfavorable information. Second, there is a smaller pool of potential investors for high-yield bonds than investment-grade bonds because of legal restrictions on investments in high-yield bonds for some institutional investors. The number of potential investors in Rule 144A issues 20 A chi-square test fails to reject the null hypothesis that the two coefficients are the same. We also run a regression on Rule 144A issues only, with a registration right dummy variable (1 if with registration rights and 0 otherwise). The coefficient on the registration rights is not statistically different from zero, indicating that registration rights do not have an impact on yields for investment-grade Rule 144A issues. PAGE 36 29 increases after the issue becomes registered. Consequently, registration rights would help to reduce the illiquidity premium on high-yield Rule 144A issues, but would have less of an impact on investment-grade Rule 144A issues. Underwriter Spread The impact of Rule 144A upon gross underwriter spread is shown in Table 2-8 In Column A, the Rule 144A dummy variable includes all issues sold through Rule 144A. This coefficient is not significant. In Column B, Rule 144A issues are separated into non-reporting firms (with no publicly traded securities) and firms filing periodic financial statements with the SEC. Neither coefficient is significantly different from zero. The first-time debt issue dummy variable is positive and significant. Log of issue frequency is negative and significant. Percentage of Years of Call Protection is negative and significant. Senior debt has a negative and significant coefficient. Maturity has a positive and significant coefficient. The utility firm dummy has a negative and significant coefficient. Note that the coefficients for all the investment-grade rating dummy variables are not significantly different from zero. As ratings fall below investment grade, coefficients become significant and increase, indicating that gross underwriter fees are much higher for high-yield bonds because of the greater difficulties in selling these bonds. This is consistent with Livingston and Miller (2000). An unreported regression for gross underwriter spread for high-yield bonds and investment-grade bonds separately finds that the coefficient for investment-grade Rule 144A issues is 4 basis points and significant, but a coefficient of this magnitude is not economically meaningful. The coefficient for the high-yield Rule 144A issues is not significant. PAGE 37 30 In summary, we find that gross underwriter spreads are not statistically different for Rule 144A and public debt issues in general. There are offsetting impacts of Rule 144A on the spread. On the one hand, fewer potential investors and information uncertainty make underwriting Rule 144A issues harder than public debt. On the other hand, underwriting Rule 144A issues may be less risky in some ways and involve less work for underwriters. Our finding of similar underwriter spreads suggests that the two impacts offset each other. Conclusion Rule 144A bonds do not require a registration filing with the Securities and Exchange Commission. They may be purchased by qualified financial institutions and traded to other qualified financial institutions, but may not be purchased by individuals. Some Rule 144A bonds require the issuer to replace the bonds with publicly traded bonds within a stipulated period of time and are designated as having registration rights. Although high-yield bonds issued under Rule 144A usually have registration rights, we find that the majority of investment-grade bonds do not. Our empirical results indicate that Rule 144A bond issues have higher yields to maturity than publicly issued bonds. The effect is greater for Rule 144A bonds issued by private firms without publicly traded securities. The yield premiums of Rule 144A issues are likely due to lower liquidity, information uncertainty, and weaker legal protection for investors. Gross underwriter spreads for Rule 144A bond issues and publicly registered bond issues are essentially equivalent. PAGE 38 Average Size (m Million $ 'S 'Total Proceeds (in Billion $ 31 Rule 144a I Private Debt Public Debt 1990 1991 1992 1993 1994 1995 1996 1997 1998 2-1 Annual Issues of Rule 144 A, Private, and Public Non-Convertible Debt Market Rule 144a B Private Debt Public Debt 1990 1991 1992 1993 1994 1995 1996 1997 1998 Figure 2-2 Average Issue Size PAGE 39 32 Figure 2-3 Distribution of Ratings Rule 144 A Public PAGE 40 33 Table 2-1 Descriptive Statistics for Full Sample, 1997 1999 Rule Public Issues 144A Issues Number of Issues 2652 1418 Number of Issuing Firms 663 944 Average Number of Issues Per Issuing Firm 4.0 1.5 Average Proceeds(in Millions) $129.04 (2635) $177.69* (1406) Percentage of Investment-Grade Issues 91.48% 31.59% Percentage of Senior Debt 98.30% 67.70% Avg. Gross Underwriter Spread (in Basis Points) 72 (1985) 200* (444) Original Yield 6.81% (2093) 9.18%* (1317) Avg. Basis Points of Treasury Spread 115 (2093) 351* (1317) Percentage of Industrial 64.89% 73.06% Percentage of Utility Firms 35.11% 26.94% Avg. Percentage of Years That are Call Protected 73.96% (2648) 57.75%* (1288) Average Years to Maturity 12.17 10.24* Percentage of Public Firms 97.70% 66.36% Percentage of First-Time Debt Issue 10.56% 51.20% Percentage of Issues by Non-Reporting Firms 0.68% 23.20% Significantly different from public issues at the 1% level(*) PAGE 41 34 Table 2-1 Continued Note: The sample is obtained from the New Issue Database of Securities Data Company (SDC) and consists of domestic Rule 144A and public non-convertible, fixed coupon rate bond issues by industrial and utility firms from January 1997 through the end of 1999. Issues that are not rated by both MoodyÂ’s and S&P are excluded. Also, perpetual issues are excluded. The numbers in parentheses are numbers of observations used to calculate the averages. PAGE 42 35 Table 2-2 Comparison of Gross Underwriter Spread and Treasury Spread by Ratings Gross Underwriter Spread Treasury Spread Rating Public Issues Rule 144A Issues Public Issues Rule I44A Issues AAA 65 51 78 103 (13) (7) (25) (23) AAA/AA 53 N.A.Â‘Â‘ 81 208 (7) (0) (7) (2) AA 62 68 80 lOI (144) (4) (142) (24) AA/A 57 88** 96 )46*** (92) (3) (73) (4) A 55 54 80 II8* (766) (28) (834) (92) A/BBB 67 59 II6 III (106) (19) (111) (55) BBB 61 67** 120 162* (647) (57) (684) (157) BBB/BB 81 91 169 I8I (26) (12) (26) (29) BB 154 176** 217 276* (112) (43) (115) (106) BB/B 237 254 337 357 (10) (18) (10) (50) B 258 266 379 453* (56) (223) (60) (704) B/CCC 288 279 507 563 (4) (24) (4) (51) CCC and 335 321 661 687 Below a V T 1 i A A A (2) (6) (2) (20) with gross underwriter spread information fall into the AAAJAA category. Significantly different from public issues at the 1% level(*), 5% level (**) and 10% level Note: This table compares the mean gross underwriter spread and Treasury spread of Rule 144A and public issues of all rating categories. When an issue has either a MoodyÂ’s or an S&P rating, that rating is used. If an issue is rated by both MoodyÂ’s and S&P, and the two rating agencies agree on the rating, then that rating is used. If MoodyÂ’s and S&P disagree on the rating, a split rating is assigned. For example, if MoodyÂ’s rates an issue Aaa and S&P rates AA, then split rating AAAJAA is assigned to the issue. The numbers in parentheses are numbers of observations used to calculate the means. PAGE 43 36 Table 2-3 Treasury Spread Regression Independent Variables Column A (One Dummy Rule 144 A Issues) Column B (Two Dummies for Rule 1 44A Issues) Column C (HeckmanÂ’s Treatment) Intercept -108.07* -122.78* -108.58* Rule 144A Dummy 18.97* 19.99* Rule 144A by Non-Reporting Firm 53.92* Rule 144A by Reporting Firm 19.03* First-Time Debt Issue Dummy 30.14* 24.38* 30.13* Public Firm Dummy -27.94* -9.42 -27.97* Log of Issue Frequency -7.56* -7.78* -7.57* Year 1998 Dummy -10.66* -10.51* -10.77* Y ear 1 999 Dummy 5.34 5.40 5.16 Default Risk Premium 1.00* 0.99* 0.99* Log of Proceeds -3.11* -3.19* -3.14* AA 9.73 9.12 9.82 AA/A 22.55 20.40 22.68 A 15.35 13.34 15.49 A/BBB 34.46* 33.65* 34.57* BBB 54.49* 52.62* 54.63* BBB/BB 93.50* 92.04* 93.14* BB 173.18* 171.58* 173.20* BB/B 286.43* 284.33* 286.16* B 370.58* 368.17* 370.53* B/CCC 483.48* 479.02* 480.61* CCC and Below Percentage of Years 592.77* 588.43* 592.39* of Call Protection 1.68 1.55 1.75 Senior Debt Dummy 48.95* 48.70* 49.34* Log of Maturity 17.27* 17.31* 17.31* Utility Firm Dummy -9.30* -8.87* -9.32* Inverse Mills Ratio -0.58 Number of Obs. 3258 3258 3258 Adjusted R^ 0.83 0.83 0.83 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*), 5% level (**) and 10% level (***). This table shows the regressions of Treasury spread on control variables for risks and test variables. The dependent variable is the Treasury spread. The base case is an AAA-rated bond issued in 1997. First-Time Debt Issue dummy equals one if the issuer has not issued any fixed income security (straight debt, convertible debt or preferred stocks) since 1970, PAGE 44 37 Table 2-3 Continued and zero otherwise. Public Firm dummy equals one if the issuer has publicly traded equity, zero otherwise. Log of Issue Frequency is the natural log of the number of the offerings each issuer had during the sample period. Year 1998 dummy equals one if the bond is issued in 1998 and zero otherwise. Year 1999 dummy equals one if the bond is issued in 1999 and zero otherwise. Default Risk Premium is the difference between the Merrill Lynch BBB Bond Index and the Merrill Lynch 10-Year Treasury Index. Percentage of Years of Call Protection is the percentage of years that the bond is call protected. Senior debt dummy equals one for senior debt issue, zero otherwise. Column A reports results when Rule 144A dummy is used. Rule 144A dummy equals one if the offering is issued under Rule 144 A, and zero otherwise. The regression tests whether the Rule 144A issues have higher yields over public issues. Column B uses two dummy variables for Rule 144A issues: one for Non-Reporting Firms, and one for Reporting Firms. If the issuing firm of a Rule 144A offering has not issued any public fixed income security (straight debt, convertible debt or preferred stock) since 1970, and the issuing firm and its parent firm do not have public traded equity, we classify the firm as non-reporting. Rule 144A by Non-Reporting Firms dummy equals one if the issuing firm is a non-reporting firm, and zero otherwise. Rule 144A by Reporting Firms dummy equals one if the issuing firm is a reporting firm, and zero otherwise. Column C reports the regression results of Column A after correcting for selection bias. We first estimate a probit model on the choice of Rule 144A issue or public issue and then calculate the inverse Mills ratio. It is then added to the regression as an additional variable to detect and correct for possible selection bias. PAGE 45 38 Table 2-4 Separate Treasury Spread Regressions for High-Yield Bonds and InvestmentGrade Bonds High-Yield Bonds Investment-Grade Bonds Column A Column B Column A Column B Regression Regression Regression Regression Rule 144A Rule 144 A by 35.39* 13.94* Non-reporting Firm 47.73* 58.37* Rule 144A by Reporting Firm 34.71* 12.49* First-Time Debt Issue Dummy 44.21* 40.94* 19.64* 15.97* No. of Obs. 1065 1065 2193 2193 R-square 0.59 0.59 0.54 0.54 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*). This table shows separate Treasury spread regressions for high-yield bonds and investment-grade bonds. Only coefficients on the Rule 144A dummies and first-time debt issue dummy are reported. The coefficients on other regressors are similar to those reported in Table 2-3. PAGE 46 39 Table 2-5 Comparison to Fenn (2000) Variables FennÂ’s Mimic Sample Mimic Sample with Modified Year Dummies Expanded Sample (1993-1999) Rating -0.67* -0.67* -0.67* -0.66* Log Issue Size -0.12* -0.22* -0.22* -0.09* Log maturity -0.26* -0.32* -0.32* -0.14** Senior 0.81* 0.83* 0.83* 0.70* Zero coupon 0.67* 0.45* 0.44* 0.56* Merrill Lynch Index 0.58* 0.58* 0.58* 0.70* Year -0.12* -0.09* Rule 144A 0.41* 0.58* 0.55* 0.35* 144 A* Year -0.08** -0.12* -0.09** 0.03 Year 1993 0.46* 0.18 Year 1994 0.62* 0.47* Year 1995 0.49* 0.16 Year 1996 0.30* -0.01 Year 1997 0.00 -0.38* Year 1998 -0.36* Adjusted R-square No. of obs. 0.67 1562 0.60 1566 0.61 1566 0.59 2088 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*) and 5% level (**). Note: The first column of this table reprints FennÂ’s results (column 2 of Table 5, p. 396 of FennÂ’s paper). The second column gives the regression coefficients for our mimic sample. The third column gives the regression coefficients after we change the year trend variable (issuing year-1993) to 0-1 dummy variables for each year. The fourth column reports the regression coefficients after we expand the sample by including the second half of 1998 and 1999 data. PAGE 47 40 Table 2-6 Use of Registration Rights by Rule 144A Issues High-yield Rule 144A Issues Investment-grade Rule 144A Issues All Rule 144A Issues No. of Issues with Registration Rights 936 163 1099 Percentage of Issues with Registration Rights 98.22% 43.70% 82.88% Total No. of Issues 953 373 1326 Note: This table gives information on the use of registration rights by Rule 144A issues. For every Rule 144A issue, we check Bloomberg and SECÂ’s EDGAR for post-issue registration and exchange offer. If a Rule 144A has been exchanged for an identical publicly registered debt issue, or the Rule 144A has been registered with the SEC after the initial issue, we classify it as Rule 144A issue with Registration Rights. Of 1,418 Rule 144A issues in our sample, we find 1,326 on either Bloomberg or EDGAR. PAGE 48 41 Table 2-7 Treasury Spread on Rule 144A Issues with and without Registration Rights High-Yield Bonds Investment-Grade Bonds Rule 144A with Reg. Rights 32.57* 14.30* Rule 144A w/o Reg. Rights 81.52* 7.11* First-Time Debt Issue Dummy 44.68* 14.94* Public Firm Dummy -26.90* -5.81 No. of obs 1054 2155 R-square 0.59 0.54 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*). Note: This table compares Treasury spreads on Rule 144A offerings with registration rights, Rule 144A without registration rights, and public debt. The sample includes both Rule 144A issues and public debt issues. Only coefficients on the Rule 144A dummies, first-time issuer, and public firm dummies are reported. Coefficients on other regressors are similar to those reported in table 2-3. The dummy Rule 144A with Reg. Rights equals 1 if the bond is a Rule 144A issue with registration right and zero otherwise. The dummy variable Rule 144A w/o Reg. Rights equals 1 if the bond is a Rule 144A issue without registration right and zero otherwise. The base case is public issues. Two separate regressions are run for high-yield bonds and investment-grade bonds respectively. PAGE 49 42 Table 2-8 Gross Underwriter Spread Regression Independent Variables Column A (One Dummy for Rule 144A Issues) Column B (Two Dummies for Rule 144A Issues) Intercept 44.30* 42.37* Rule 144A Dummy 4.36 Rule 144A by Non-Reporting Firm 8.15 Rule 144A by Reporting Firm 4.08 First-Time Debt Issue Dummy 4.28** 4.02** Public Firm Dummy -3.12 -1.12 Log of Issue Frequency -3.24* -3.25* Year 1998 Dummy -1.35 -1.33 Year 1999 Dummy -2.74 -2.72 Default Risk Premium -0.01 -0.56 Log of Proceeds -0.84 -0.83 AA 11.53 11.57 AA/A 7.25 7.23 A 10.27 10.30 A/BBB 13.62 13.68 BBB 11.73 11.73 BBB/BB 26.75* 26.74* BB 110.66* 110.80* BB/B 182.51* 182.51* B 194.81* 194.80* B/CCC 207.19* 206.61* CCC and Below 261.88* 261.93* Percentage of Years of Call Protection -6.09* -6.12* Senior Debt Dummy -14.21* -14.20* Log of Maturity 16.90* 16.89* Utility Firm Dummy -3.50* -3.47* Number of Obs. 2368 2368 Adjusted R^ 0.83 0.83 The White heteroscedastic-consistent t-statistic is significant at the 1% level(*) and 5% level (**). Note: This table shows the results of the regressions of gross underwriter spread on control variables for risks and test variables. The dependent variable is the gross underwriter spread in basis points. The base case in the regression is an AAA-rated bond issued in 1997. First-Time Debt Issue dummy equals one if the issuer has not issued any fixed income security (straight debt, convertible debt or preferred stocks) since 1970, and zero otherwise. Public Firm dummy equals one if the issuer has publicly traded equity, zero otherwise. Log of Issue Frequency is the natural log of the number of the offerings PAGE 50 43 Table 2-8 Continued each issuer had during the sample period. Year 1998 dummy equals one if the bond is issued in 1998 and zero otherwise. Year 1999 dummy equals one if the bond is issued in 1999 and zero otherwise. Default Risk Premium is the difference between the Merrill Lynch BBB Bond Index and the Merrill Lynch 10-Year Treasury Index. Percentage of Years of Call Protection is the percentage of years that the bond is call protected. Senior debt dummy equals one for senior debt issue, zero otherwise. Column A reports the results of the regression where the Rule 144A dummy is used. Rule 144A dummy equals one if the offering is issued under Rule 144 A, and zero otherwise. The regression tests if the Rule 144A issues have higher gross underwriter spread over public issues. Column B uses two dummy variables: Rule 144A by Non-Reporting Firms, and Rule 144A by Reporting Firms. If the issuing firm of a Rule 144A offering has not issued any public fixed income security (straight debt, convertible debt, or preferred stock) since 1970, and the issuing firm and its parent firm do not have public traded equity, we classify the firm as non-reporting. Rule 144A by Non-Reporting Firms dummy equals one if the issuing firm is a non-reporting firm, and zero otherwise. Rule 144A by Reporting Firms dummy equals one if the issuing firm is a reporting firm, and zero otherwise. PAGE 51 CHAPTER 3 BOND RATINGS AND PRIVATE INFORAMTION Introduction Bond ratings are an important component of the US financial world: almost all large corporate bonds have ratings. Bond ratings are used extensively as a proxy for bond riskiness and investors rely heavily on bond ratings to determine bond yields. Financial regulators also use bond ratings as a regulatory tool. For example, the Savings and Loan Associations are prohibited from investing in below investment-grade bonds. Because of their importance, there are extensive academic studies on bond ratings. One important question concerns about their information content. Rating agencies claim that bond ratings contain information beyond what is publicly available. When deciding on bond ratings, rating agencies usually meet with the management of the issuing firm that shares information with the rating agencies. Some of the information may be private information that the management does not disclose to the general public. Previous research on the information content of ratings takes two approaches. The first line of research studies the relationship between bond ratings and yields. West (1973), Liu and Thakor (1984), Ederington, Yawitz and Roberts (1987) and Reiter and Ziebart (1991) fall into this category. Generally, these studies find that ratings and bond yields are negatively correlated after controlling for some important publicly available information, implying that highly rated firms tend to have favorable private information. The second line of research examines the impact of rating changes on the bond yields and stock price. The results of these studies are mixed. While Weinstein (1977), 44 PAGE 52 45 and Pinches and Singleton (1978) do not find an impact of rating changes on bond yields, Katz (1974), Grier and Katz (1976), and Ingram, Brooks and Copeland (1983) find significant changes in bond yields in response to bond rating changes. More reeently, Holthausen and Leftwich (1986), and Hand, Holthausen and Leftwieh (1992) find stock price goes up (down) when the firmÂ’s bond rating is upgraded (downgraded) or likely to be upgraded (downgraded). On the other hand, Kliger and Sarig (2000) find that equity value decreases (increases) when the firmÂ’s bond receives a better (worse) than expeeted rating from MoodyÂ’s. Though the previous research has found some evidence that bond ratings have additional explanatory power of bond yields after controlling for a few pieces of public information, they fail to answer the question whether the bond ratings contain private information or additional publicly available information not included in their models. This study attempts to link the additional explanatory power of bond ratings to the degree of information asymmetry of the issuing firm in a latent variable model. Specifically, we use the latent variable methodology to identify two risk factors contained in the bond ratings. The first risk factor is common among bond ratings and four observable accounting variables: interest coverage ratio, leverage ratio, firm size and ROA. The second risk factor is not observable from the four financial variables, but is a common risk factor among bond ratings and proxies for information asymmetry. This second risk factor intends to capture private information in ratings. The larger the infomiation asymmetry problem, the more private information the management would share with the rating agencies. Hence, if bond ratings do contain private information, then the proxies for information asymmetry should be correlated with the second risk PAGE 53 46 factors. The three variables used to proxy information asymmetry are firm size, analystsÂ’ earning forecast errors, and the adverse selection components of the stock bid-ask spread. We find that the second risk factor is indeed related to the information asymmetry proxies. Furthermore, the second risk factor is priced by the bond market. This is consistent with the hypothesis that bond ratings contain private information and such private information can be conveyed to the bond market through bond ratings. Tbe rest of the chapter is organized as follows. The next section reviews the previous literature on the information content of bond ratings. The third section briefly discusses some technical issues of the latent variable model. Next, we describe the data and define the variables. The fifth section gives the empirical results and final section concludes the paper. Literature Review Rating agencies play a very important role in the US financial market through assigning credit ratings to corporate bonds. Bond rating is a significant determinant of bond yields and underwriter fees (see, for example, Jewell and Livingston, 1998). Ratings are also used extensively as regulatory tools. One important question then is how rating agencies determine bond ratings. Rating agencies claim that they incorporate private information beyond publicly available financial data into bond ratings. Much academic research uses various statistical models to predict bond ratings by several observable economic and financial variables and finds that only 50% to 70% of bond ratings can be explained by a few public available variables (see Kaplan and Urwitz, 1979, for a review). These studies seem to be consistent with the rating agenciesÂ’ claim that there is more in the bond ratings than several publicly available financial ratios. However, the statistical models used in the previous studies fail to incorporate all PAGE 54 47 publicly available information. Hence, the remaining 30% to 50% of the variations in bond ratings not explained in the statistical models may be due to other public information not controlled for in the models, rather than private information rating agencies may have. To investigate the private information content of bond ratings, previous research has taken two paths. The first line of research investigates the relationship between bond rating and bond yield. In a classic study, Fisher (1959) finds that about 75% of bond yields can be explained by four observable variables: earnings variability, period of solvency, equity/debt ratio and bonds outstanding. West (1973) extends the study and finds that the residuals in the FisherÂ’s bond yield regression are negatively correlated with the bond ratings: the higher the bond rating, lower the residual and, hence, the lower the bond yields. Based on the finding. West argues that the bond ratings have an independent impact on bond yields. However, the argument is problematic. It implicitly assumes that bond ratings are independent of the observable financial characteristics. However, since the bond ratings are partially determined by financial characteristics, only the surprise component of the bond ratings would have an impact on yield above and beyond the financial characteristics if they have an independent impact at all. For example, if a bond has similar observable financial characters as AAA bonds but carries an AA rating, then it would have a positive residual, or higher bond yields, in FisherÂ’s yield regression. It would have a negative residual only if it has AA rating but similar observable financial characters as A bond. Hence, if the bond ratings have an independent impact on yield. PAGE 55 48 WestÂ’s evidence only suggests that higher rated bonds are systematically rated higher than their financial characteristics predict. Ederington, Yawitz and Roberts (1987) regress bond yields on bond ratings as well as four financial variables (total assets, interest coverage ratio, leverage ratio and deviations of coverage ratio from historical trend). They find that both bond ratings and financial variables have explanatory power and therefore argue that bond ratings have information content above and beyond the four publicly observable financial variables. However, the methodology of this study is problematic. As previous research (see Kaplan and Urwitz, 1979) shows that 50-70% of bond ratings can be explained by a few observable financial variables, it is not appropriate to include both ratings and observable financial variables in the same regression because of potential multicollinearity problem. Liu and Thakor (1984) adopt a different methodology to avoid the potential multicollinearity problem. In their study of municipal bonds, they first regress the bond ratings on four observable economic variables and retrieve the residuals. They then regress the bond yields on the same four observable variables and the rating regression residuals. The rating regression residuals are found to have explanatory power in addition to the four observable economic variables. More recently, Reiter and Ziebart (1991) use a simultaneous equation technique and find that both bond ratings and financial information have impact on bond yields. Though these studies consistently find that bond ratings have an impact on bond yields above and beyond several observable financial or economic variables, they fail to directly address the question of whether bond ratings contain information that is not publicly available. Three plausible explanations may be consistent with the findings. PAGE 56 49 First, bond ratings contain publicly available information not captured in the few selected variables in the studies. For example, a pharmaceutical company may have a miracle drug for cancer pending FDA approval. This information may not be captured in the common financial variables like firm size or leverage ratio, but is publicly available to both the investors and rating agencies. Such information has an impact on bond ratings and yields concurrently. Hence, the observed additional impact of bond ratings on yields may be due to important omitted public information. Second, bond ratings may have an impact on bond yields due to their role as regulatory tools even if they do not have private information. In recent years, financial regulators are increasingly relying on bond ratings to regulate financial institutions. These regulations either prohibit certain financial institutions from investing in lower rated bonds, or require them to make larger capital reserve for investment in lower rate bonds (see Cantor and Packer, 1995 for a list of such regulations). Such regulations may force the issuing firms of lower rated bonds to increase bond yields to overcome the regulatory bias against them. Hence, even if bond ratings do not contain any private information, they would have an impact on bond yields because of their role as regulatory tools. The third explanation is that bond ratings have private information. However, the previous research has not provided any direct evidence that the additional explanatory power of ratings on bond yields derives from private information in ratings. The second line of research studies bond yields and stock price changes before and after rating changes, effectively controlling for all publicly available information for each firm. The basic argument of these studies is that rating changes should have an PAGE 57 50 impact on the bond yields and/or stock prices if they contain private information. On the other hand, if bond ratings only reflect publicly available information, then bond rating changes should not have an impact on bond yields and/or stock returns. Rather, there should be abnormal returns on bonds and/or stocks before the rating changes as new information becomes public that have an impact on bond yields and/or stock prices and also eventually lead to rating changes. The results of these studies are mixed. Earlier studies like Pinches and Singleton (1978) and Weinstein (1977) find that there are no abnormal returns on common stocks and corporate bonds after bond rating changes, but there seem to be abnormal returns before the bond rating changes. Such evidence indicates that rating agencies are lagging behind the capital market in incorporating new information on the bond ratings. On the other hand, Grier and Katz (1976), Katz (1974), and Ingram, Brook and Copeland (1983) find that bond yields do change in response to rating reclassifications. More recently, Holthausen and Leftwich (1986), and Hand, Holthausen and Leftwich (1992) use daily bond and stock price to study the reaction of bond and stock prices to both actual and potential rating changes. They generally find stock price goes up (down) when the firmÂ’s bond rating is upgraded (downgraded) or likely to be upgraded (downgraded). On the other hand, Kliger and Sarig (2000) find that equity value decreases (increases) when the firmÂ’s bond issues receives a better (worse) than expected rating from MoodyÂ’s. This line of research eliminates the difficulties of controlling for all public information, but it still fails to provide direct links between bond ratings and private information. As mentioned earlier, bond ratings may have an independent impact on bond yields because of their role as regulatory tools. Hence, evidence of impact of PAGE 58 51 ratings changes on bond yields and/or stock returns does not necessarily imply private information in bond ratings. Methodology This study tries to provide direct links between private information content and bond rating by using the latent-variable technique. By definition, private information is not observable and not available to the general public. Hence, it is impossible to relate private information to bond ratings directly in a traditional regression model. However, tbe latent-variable technique can estimate the impact of an unobservable independent variable on some dependent variable as long as there are proxies for the unobservable variable. The technique has been used extensively in social science studies, where many variables, such as a personÂ’s intelligence or social status, are not observable or measurable. The basic idea of the latent variable technique is to utilize several indicators or proxies for the unobservable variable. These indicator variables are related to the unobservable variable, or latent variable, in various aspects. For example, the default risk of a particular bond issue is an unobservable variable, but a firmÂ’s leverage ratio, interest coverage ratio, profitability and firm sizes are all related to the default risk. Each of these indicator variables itself is a poor proxy for the latent variable, but it is possible to get a better measurement of the latent variable if several indicator variables are utilized simultaneously. The basic idea of the latent variable technique is to use a set of linear equations, where there are some unobservable latent variables and multiple indicator variables for each latent variable. Provided all the parameters are identifiable, this technique can yield the estimates of the unknown coefficients in the model. PAGE 59 52 The latent variable technique is discussed in detail in Joreskog and Goldberger (1979), Bollen (1989), and other papers (see, for example, Zellner, 1970, Goldberger, 1972). A Simple Latent Variable Model Suppose that Y is an nxp matrix of observable indicator variables and Z is an nxq matrix of unobservable latent variables. ' P is the number of indicator variables, q is the number of latent variables and n is the number of observations. M is an nxp matrix of the means of Y (M consists of n rows of p, a p-dimension row vector of the means of the indicator variables). For simplicity, letÂ’s assume that all the latent variables have means of 0, variances of 1 and they are not correlated with each other.^ Assume that Y and Z are linearly related as in the following equation: Y = M + Zp + E (1) where p is an qxp parameter matrix and e is an nxp error terms. Z and e are assumed to be uncorrelated. Let E be the covariance matrix of Y. So we have: i: = (Y-M)'(Y-M) = p'Z'Zp + E'Zp + PÂ’Z'e + e'e As Z and e are assumed to be uncorrelated, E = p'ZÂ’Zp + e'e ' Capital letter in bold font stands for a matrix, lower case letter in bold font stands for a vector, and lower case italic letter stands for a scalar throughout the paper unless noted otherwise. 2 Because the latent variables are not observed, we can scale it to zero means and unit variances. PAGE 60 53 Since the latent variables are assumed to have means of 0 and variances of 1, ZÂ’Z is an identity matrix. So we have: L = P'P + c'Â£ (2) If we assume that the error terms are not correlated with each other, then eÂ’c is a diagonal matrix. Since Y is observable, we can estimate L from sample data. Let Sp^p be the sample covariance matrix of Y. So, we have S = P'P + Â£'e (3) where p= E(P| Y) and e= E(e|Y). The covariance matrix of Y, or I, is a function of p and eÂ’e and needs to be estimated. Let 0 stands for p and eÂ’e, the model parameters. So, L = E(0). S is the covariance matrix of the sample data and can be calculated as in the following formula: s = -X(y*-n)'(y*-0) where y* is a /^-dimensional row vector, representing one observation in Y (one row of Y). Equation system (3) has {p+l)p/2 equations, each equation representing one unique sample variance or covariance, and pxq + p unknown parameters. Among the unknown parameters, pxq parameters are coefficients on the q latent variables to be estimated and p parameters are error term variances. If {p+\)pH > pxq -ip, several methods can be used to estimate the model parameters. Notice that it has been assumed for simplicity that the error terms are uncorrelated with each other. However, it is possible to allow for correlation among some error terms, as long as the number of equations in (3) is greater than the number of unknowns. The PAGE 61 54 maximum number of correlations between error terms is p{p-\-2q)/2. The difference in the number of equations (or the number of unique sample variance and covariance) and the number of parameters to be estimated is called the model degree of freedom. Estimation Techniques The latent variable technique allows us to estimate the coefficients on the unobservable latent variables, even if these variables cannot be measured. Several techniques can be used to estimate the model. Maximum likelihood (ML) and weighted least squares techniques are the most common methods of estimation when the indicator variables are continuous and categorical variable method (CVM) is appropriate when some or all of the indicator variables are categorical variables. Maximum likelihood method (ML) Maximum likelihood (ML) estimation assumes that Y, or indicator variables, follow a multivariate normal distribution with mean vector p. The joint probability of observing y*, or one particular observation of the p indicator variables, is then: /(yJ = (27T) p/2 I yÂ« 1-1/2 exp = (27T) -p/2 I 1-1/2 exp Tri:-'(y,-p)'(y,-p) The log-likelihood function for a sample size of Â« is then: L = ~ Â— np\og2K Â— nlog\'L\Â— ntr'L 'S 2 2 2 The pxq + p unknown parameters can then be estimated by maximizing the loglikelihood function. How well the estimated model parameters fit the sample covariance matrix can be measured by ML fit function and tested by the likelihood ratio statistic. PAGE 62 55 Let E = P'P + Â£'e be estimated E. The null hypothesis in the likelihood ratio test is that E = E(Ho), or the estimated covariance matrix equals the true covariance matrix. An alternative hypothesis is that S = L (Hi), or the sample covariance matrix equals the true covariance. The alternative hypothesis is chosen because it does not have any constraint on the model parameters and it has the maximum value of log likelihood of observing the sample covariance. The difference in the log-likelihood of the model under the null hypothesis and alternative hypothesis is: /V, = { L(H J L(H, )} = { log I tl + trE-'S log I S I -p} (4) Equation (4) is also called the ML fit function. The fit function provides a way to measure the difference between the log likelihood of observing the sample covariance under Ho and the log likelihood of observation sample covariance under the Hi. Since the log likelihood is at the maximum value under H|, smaller value of the fit function indicates that the log likelihood under Ho is fairly close to the maximum likelihood and the estimated model fits the sample data well. However, the fit function does not take into consideration the sample size. A better measure of the goodness of fit is the likelihood ratio statistic, which is obtained by multiplying the fit function by (n 1). The likelihood ratio statistic is asymptotically distributed as chi-squared distribution. If the statistic is small and insignificant, the difference between the log likelihood under Ho is not statistically different from the maximum likelihood, and therefore we cannot reject Ho, which suggests that the model fit well. PAGE 63 56 Weighted least square method (WLS) The maximum likelihood estimation imposes a multivariate normal assumption on the indicator variables. In many cases, the indicator variables may not follow multivariate normal distributions. To get over the problem, Browne (1982, 1984) proposes the weighted least square estimation (WLS), which does not require the multivariate normal assumption. Even without the normality assumption, equation (2), S = PÂ’P + sÂ’c, still holds. One criterion for estimation is that the estimated S be as close to S, the sample covariance matrix, as possible. Since both S and S are in matrix form, we need to minimize some scalar measure of distance between E and S. One scalar measure is the sum of the squared differences between each distinctive element of the two matrices as follows; where s is a row vector of p{p + 1) / 2 elements, consisting of the non-duplicated elements of sample covariance matrix S, PAGE 64 57 consistent estimator of the asymptotic covariance matrix of s with s. He further shows that the weighted least square estimator produces asymptotically unbiased estimates of the chi-square goodness of fit test and standard errors. Categorical variable method (CVM) Both ML and WLS methods implicitly assume that the indicator variables are continuous. When some or all of observable indicator variables are categorical variables, some of the model assumptions are violated. In many cases, some or all of the continuous indicator variables, Y, in equation (1) is not observable. Instead, another set of indicator variables, Y*, an nxp matrix, are observable. Among the p observable indicator variables,/?/ of them are continuous and (/?-/?/) of them are categorical. For continuous indicator variables, y* = y . for all i = 1 to Pi, where y* and y. are (nxl) vectors. For categorical indicator variables. C, if ^ yj.k < Â“ C,-1 < . if Lx , -2 ^ yj.k < h.Cr 2 if 1 if -00 < y.^ < Tj, where y* is the k's observation in yÂ’s categorical indicator variables, and w^tis the k's element in the /Â’s unobservable underlying indicator variable, for all A: = 1 to Â« and j = pi to p. r /,r^^,...,ryc -1 are thresholds for the categorical variable j. In this case, several assumptions of the latent variable models are violated. First of all, since Y* Y for {p -pj) variables. Y*9i M + Zp + Â£ PAGE 65 58 In other words, the statistical model for Y in equation (1) does not hold for Y . Also, the covariance matrix of the categorical indicator variables of Y* differs from the true covariance matrix of the underlying indicator variables of Y. The parameter estimators based on S*, the estimated covariance matrix of Y*, is likely to be inconsistent estimator of p. To solve this problem, Muthen (1984) proposes a three-stage estimation technique, called CVM method (Categorical Variable Method). In the three-stage estimation procedure, the thresholds for each categorical variables and means of continuous indicator variables are first estimated with limited information ML method. Then, given the first stage estimators, sample variance and covariance (for continuous variables), polychoric correlation (correlation between two categorical variables) and polyserial correlation (correlation between a categorical variables and a continuous variables) are estimated with limited information ML method. Finally, in the third stage, the model parameters will be consistently estimated by the WLS method, using the consistent estimators generated by the previous two stages. Appendix A gives a brief overview of the three-stage estimation procedure. Goodness-of-Fit of the Model In addition to the fit function and likelihood ratio test. Goodness of Fit Index (GFI) is another indication of model fitness of the latent variable model. For ML method, GFI is calculated as follows: GFI = l-[/r(i: Â’S-I)' For WLS and CVM methods, GFI is defined as follows: GFI = 1 [(s c)W^' (s o) V s W's Â’] PAGE 66 59 GFI is similar to the R-square of OLS in the sense that it is a measure of the amount of variance and covariance in the observed S that are accounted for by the estimated model t. . When S = II (or equivalently s = o in WLS and CVM) GFI has the maximum value of 1 . GFI greater than 0.9 generally indicates a well specified latent variable model. Potential Problems with Latent Variable Model While the latent variable technique is superior to OLS regression when the independent variables are not observable or measured with error, it has some potential problems that researchers need to be aware of A theory-based a priori model specification in latent variable technique is very important. Unlike OLS, the latent variable technique gives researchers greater freedom in model specification. A sample covariance matrix may be consistent with several different model specifications in that the sample data may fit different models equally well. Different model specifications, however, may lead to different substantive interpretations (MacCallum, 1995). Hence, it is important to specify an a priori model based on theories and findings from previous research. In addition, without examining all possible model specifications, researchers need to be careful when interpreting results from a particular model fit. A particular model, even when it fits the sample data very well, can only mean that it is one plausible structure of the underlying variables that produce the observed data. When there are competing theories of potential model structure, it is necessary to build alternative model specifications and compare the different models. PAGE 67 60 A related issue of model specification concerns about the degrees of freedom of latent variable models. As discussed before, the model degrees of freedom is the difference between the number of unique sample variance and covariance and the number of parameters to be estimated. When the latent variable model has zero degree of freedom, parameters in the model can be calculated exactly and the model will have perfect fit. However, such a model is not very interesting because it is sample data specific. On the other hand, if a model has a large number of degrees of freedom, it is hard to find a good fit. Thus, if a model with large degrees of freedom is found to fit the sample data well, we will be more confident in its results. Researchers should be cautious when interpreting results of models with very low degrees of freedom because it is likely that such results are sample data specific and cannot represent the true structure underlying the sample data (MacCallum, 1995). A common problem in model estimation is that the sample covariance matrix is not positive definite, that is, some variables are linearly dependent on others. If this is the case, we cannot estimate the model because it is not possible to invert the sample covariance matrix during estimation procedure. The solution to this problem is to increase sample size to avoid perfect linear dependency and choose observable variables carefully to eliminate redundancy. Simple Bond Rating Latent Variable Model First, we build a simple bond rating latent variable model with only one unobservable variable: default risk, or DR. This unobservable default risk has four proxy variables: interest coverage ratio, leverage ratio, firm size and return on assets (ROA). In other words, the DR is the default risk that is reflected in the four publicly available accounting variables. The following is a simple latent-variable bond rating model: PAGE 68 61 Interest Coverage Ratio = a, + ^iDR + Â£/ (5a) Leverage Ratio = 0.2 + ^2DR + S2 (5b) Firm Size = + + Â£3 (5c) ROA = 04 + ^40R + Â£4 (5d) Bond Rating = Â«5 + fisDR + Â£5 (5e) These four observable variables are chosen to proxy for default risk because previous literature shows they can explain a significant amount of variation in bond ratings. Table 3-1 summarizes previous studies of determinants of bond ratings. Regardless of different statistical methodologies used, these studies generally find leverage ratio (measured by long-term debt/total asset, debt/total capital, equity/debt ratio, etc), interest coverage ratio, firm size (measured by total assets) and profitability (measured by ROA) are among the most common significant determinants of the bond ratings. These four variables have been shown to be significant determinants of ratings in at least two studies.^ Private Information Model Next, a latent variable for private information, PI, is added to the model. The difficulty is to find proxies for private information that issuing firms may share with rating agencies. Fortunately, there is large literature on the information asymmetry and many proxies have been developed to measure the degree of information asymmetry between firms and investors. If an issuing firm has a large problem of information asymmetry, it would have more private information to share with the rating agencies. PAGE 69 62 Thus, proxies for information asymmetry can also serve as good proxies for private information. There are two classes of proxy variables for information asymmetry: corporate finance based and market microstructure based proxies. Appendix B gives a brief literature review on the two classes of information asymmetry proxies. In corporate finance literature, analystsÂ’ earning forecast errors have often been used as a proxy for information asymmetry as well because it is hard for analysts to forecast earnings of firms with large private information. For example, Thomas (2002) uses analystsÂ’ earnings forecast errors as a measurement of information asymmetry of diversified firms. Firm size is another proxy used in corporate literature to proxy information asymmetry. Large firms are often followed by more stock analysts and under more scrutiny of the financial media and its asymmetry information problem is generally less due to the greater awareness of investors of larger firms (Merton, 1 987). Also, large firms generally access the capital markets more frequently and reveal more information to investors to lower their cost of capital. In market microstructure literature, information asymmetry is often measured by the adverse selection component of the bid-ask spread of a firmÂ’s stock. The bid-ask spread can generally be decomposed into three components: order processing, inventory costs, and adverse selection. The first two components compensate the market maker for ^ Another common variable is bond subordination. Since I am only interested in the information content of bond ratings in this study, the impact of bond features on credit ratings is beyond the scope of this study. Therefore, bond subordination is not used to proxy for default risk and subordinated debts are excluded from sample data. PAGE 70 63 the cost of handling the orders and holding an inventory. The third component, adverse selection, is a compensation to the market maker for trading with informed traders who take advantage of their private information on the value of the stock to make a profit. For firms with large asymmetric information problem, the market maker will widen the bidask spread to compensate for their potential losses from trading with informed traders. Holding the other two components constant, a wider bid-ask spread means a large adverse selection component for firms with large information asymmetry. Therefore, the adverse selection component has been recently used as a measurement of asymmetric information in corporate finance literature. For example, Flannery, Kwan and Nimalendran (2000) uses the adverse selection component of banksÂ’ bid-ask spread to measure the relative Â‘opaquenessÂ’ of the assets of banking firms. Appendix B briefly explains several methodologies to estimate the adverse selection component. Although there are other proxies for information asymmetry, such as market to book ratio and number of institutional investors, we choose the three proxies discussed above to build a parsimonious model. Fewer proxies for private information will bias against finding any private information content in bond ratings. The private information model is therefore as follows: Interest Coverage Ratio = a/ + PiDR + Â£/ (6a) Leverage Ratio = 02 + fiiDR + Â£2 (6b) Firm Size = Â«5 + (ijDR + ys PI + Â£3 (6c) ROA = 04 + P 4 DR + Â£4 (6d) Bond Rating = 0.5 + /I 5 DR + ys PI + Â£5 (6e) Adverse Selection = 06 + /IdDR + J6 PI + Â£6 (6f) PAGE 71 64 Forecast Error = Â«/ + P7DR + y? PI + e? (6g) If bond ratings do contain private information, then 75, and 75 through 77 will be significant. Also, we will compare the results of this model with those of the simple model. If bond rating do contain private information, then the private information model should explain a larger proportion of the variation of bond rating than the simple model because it incorporates more information. Complete Model Finally, it will be interesting to see if the default risk and private information, if any, carried by the bond ratings are priced by the bond market. To test that, we add the bond yields in the previous model. However, bond yields vary over time and maturity. Hence, to control for the difference in the maturity and issuing time, we subtract the yields on US treasuries of similar maturity on the issuing date from the original yields to maturity to get the treasury spread. The final model is as follows: Interest Coverage Ratio = 0.1 + P,DR + Â£/ ( 7 a) Leverage Ratio = 0.2 + P2DR + Â£2 ( 7 b) Firm Size = 0.3 + /IsDR + 75 PI + Â£3 ( 7 c) ROA = 04 + P4DR + Â£4 ( 7 d) Bond Rating = + PsDR + 75 PI + Â£5 ( 7 e) Adverse Selection = 06 + PeDR + 7(5 PI + Â£6 ( 71 ) Forecast Error = 07 + P7DR + 77 PI + Â£7 ( 7 g) Treasury Spread = 08 + PsDR + ys PI + Â£8 ( 7 h) Notice that in the last two models, we include DR in both analystsÂ’ forecast errors and adverse selection equations, even though these two variables are intended to capture private information. Since these two variables are publicly available, it might be possible PAGE 72 65 for investors to derive private information from them directly instead of through the rating agencies. To control for this, we include DR in these two equations. Data Data Collection The initial data on corporate bonds come from the Fixed Investment Securities Database (FISD) by the Global Information Services Inc. FISD has all new bond issues with 9-digit CUSIP number since April 1995 to early 2000. We collect all domestic new issues of industrial bonds from April 1,1995 to the end of 1999 with both MoodyÂ’s and S&P ratings. Convertible bonds and bond issues with floating or zero coupons are excluded. Rule 144A issues have also been excluded because they are not registered with SEC. The initial dataset has 2,068 corporate bonds. Previous research finds that bond ratings are also partially determined by bond features, such as seniority. Since we are only interested in the information content of bond ratings in this study, the impact of bond features on credit ratings is beyond the scope of this study. Therefore, to create a more homogeneous sample, we exclude subordinated debt from the initial sample."* This reduces the sample to 1,775 bonds. Bonds with credit enhancement features, such as loan guarantee or insurance, are also excluded. This eliminates another 1 18 issues. Furthermore, many firms issue multiple bonds, usually with different maturity, on the same date. These bonds often have the same credit ratings. To avoid multiple observations for a single issuer on the same date, we eliminate multiple issues by the same firms on the same date with the same bond ratings from both MoodyÂ’s and S&P. This reduces the sample to 1,285 observations. "* Inclusion of subordinated debt does not change my results. PAGE 73 66 Next, we match the bond issues with the issuing firmsÂ’ financial data from COMPUSTAT, using the 6-digit CUSIP number. 266 observations fail to get a match and 88 observations have missing financial information. To get analysts' earning forecast errors, we match the sample with analysts earning forecasts from I/B/E/S. This further reduces the sample to 840 observations. Finally, another 59 issues are excluded because of lack of information on the stock bid-ask spread of the issuing firms. This leave 781 observations. A check of the 781 observations shows that several outliers have extreme values on accounting ratios and other variables that produce large kurtosis. Nine outliers are eliminated.^ The final sample has 772 observations. Variable Definitions Bond rating in the latent variable models is a numerical variable ranging from 1 (for issues rated CCC or below) to 7 (for issues rated AAA).^ Both MoodyÂ’s and S&PÂ’s ratings are used to estimate the models and, as shown later, the results are essentially the same. Four accounting variables, interest coverage ratio, leverage ratio, firm size and ROA, are used to proxy public information in bond rating. COMPUSTAT annual data are used to calculate the four variables.^ Interest coverage ratio is the ratio of earnings ^ Inclusion of the nine outliers does not change the model estimation, though the model goodness of fit index tends to be lower. ^ A numerical rating variable ranging from 1 (CCC and below) to 1 7 (AAA) that takes bond ratings at the notch level have been used as well. The results are essentially the same in the WLS estimation. Because the compute software, Mplus, that we use for the CVM estimation can handle only up to 10 categories for rating variables, the notch level rating variables are not used in CVM estimation. ^ I have also used quarterly data to calculate the four variables and the results do not change. PAGE 74 67 before interest, tax, depreciation and amortization (EBITDA) over Interest Expenses ((data item 18 + data item 14 + data item 16 + data item I5)/data item 15). Leverage ratio is the long-term debt divided by total assets (data item 9/data item 44). Firm size is the market value of the firmÂ’s equity. It is calculated by multiplying the issuing firmÂ’s stock price (average of the preceding year high and low, or (data item 197 + data item 198)/2) by the number of shares (data item 25)). ROA is the net income divided by total assets (data item 172/data item 44). All the financial variables are for the year prior to the bond offering date. Analyst earning forecast errors are defined as follows: _ abs( Average Analysts Annual EPS Forecast Actual Annual EPS) Stock Price g The analystsÂ’ forecasts are made nine months before the end of the fiscal year. The forecast errors are scaled by the issuing firmsÂ’ stock prices. Since both positive and negative earning surprises are indications of information asymmetry, we take the absolute value of the earning forecast errors as proxy for information asymmetry. For adverse selection component of bid-ask spread, we use the method proposed by George, Kaul and Nimalendran (1991). Appendix B gives the technical details of the GKN method of spread decomposition. Specifically, we use the last trading prices and quotes of the issuing firmÂ’s stock each day in the six months period before the bond issuing date to calculate the GKN adverse selection component. It is defined as the dollar adverse selection component as a percentage of the stock price. Â® Three months and six months forecasts are also used and there are no differences in results. PAGE 75 68 Descriptive Statistics Table 3-2 reports the summary statistics and correlation among variables. Note that some of the variables have very large kurtosis. Excess kurtosis makes maximum likelihood estimation method undesirable because it assumes that the model variables are multivariate normal. As a result, we use the weighted least square (WLS) method to estimate the model when bond ratings are treated as continuous variables because it does not assume multivariate normal distribution for the model indicator variable. ^ The correlation matrix indicates that the model variables are significantly correlated with each other. This is not surprising because these variables are proxies for the same underlying unobservable latent variables. Interest coverage ratio, leverage ratio, ROA and firm sizes are strongly correlated as they proxy for the unobservable default risk reflected in public information. In the meantime, firm size, analystsÂ’ earnings forecast errors and the adverse selection components are also correlated as they proxy for potential private information content in bond ratings. An interesting finding is that the proxies for private information and public information are also correlated. This makes the inclusion of DR in the last two equations in the private information model and complete model necessary. Empirical Results Model Estimation Results on simple model Tables 3-3 and 3-4 report the results of the simple bond rating latent variable model using S&P and MoodyÂ’s ratings respectively. The results from the two tables are ^ Maximum likelihood method is also used to estimate the model as a robust check. The results are basically the same. PAGE 76 69 very similar. This is consistent with findings by Ederington (1986) that MoodyÂ’s and S&P put similar weights or importance to the major financial accounting ratios when deciding on bond ratings. Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). Tbe WLS estimation method assumes that all indicator variables are continuous. However, bond ratings are ordered categorical variables and not continuous. As discussed in the previous section, violation of the continuous variable assumption may lead to inconsistent estimators of the model parameters. To overcome the problem, we use MuthenÂ’s CVM method and treat bond rating as an ordered categorical variable. One basic assumption of CVM is that there is an underlying, unobservable continuous rating variable behind the observed categorical rating variable, and certain value of the observable categorical rating variable corresponds to a certain range of values of the underlying continuous rating variable. The model seems to be well specified in both WLS and CVM estimations as the fit function and chi-squared values indicate. The main findings are consistent with previous research. Basically, higher interest coverage ratio, lower leverage ratio, higher ROA and larger firm size are associated with lower default risks that lead to higher bond ratings. The on the bond rating in WLS estimation is about 55%. A simple OLS regression of bond ratings on tbe four accounting variables (not reported) gives an Rsquare of 43%. Hence, tbe latent variable model seems to be superior to OLS in explaining the variations in bond rating. PAGE 77 70 A comparison of WLS and CVM estimation shows that the latter is more efficient as the t-statistics are much higher in CVM estimation though coefficient estimates are almost identical when the variables are continuous. The coeffieients on the bond rating are bigger and more significant in CVM estimation. The for the rating equations in CVM estimation measures the variations of the underlying, unobservable continuous rating variable that can be explained by the two latent variables. Not surprisingly, the in CVM estimation is much higher than the R^ in WLS estimation. Results on private information model Tables 3-5 and 3-6 report the results of the private information model using S&P and MoodyÂ’s ratings respectively. Again, the results of the two tables are very similar. The coefficients on DR remain largely unchanged from tables 3-3 and 3-4, suggesting that the latent variable, PI or private information, is orthogonal to DR or default risk reflected in public information. Interestingly, analystsÂ’ forecast errors and adverse selection components are also related to the default risk, or DR. This controls for the potential problem that the two variables only capture public information already reflected in the four accounting variables. The coefficients on PI are all significant. The three proxies for information asymmetry, firm size, analysts forecast errors and adverse selection components, are shown to be related to the unobservable private information. Specifically, large firms tend to have less private information, while firms with large forecast errors and adverse selection components have more private information. Does the private information variable have an impact on bond rating? Indeed it has. The coefficients on PI in WLS estimation (CVM estimation) are -0.177 (-0.247) and -0.199 (-0.295) for S&P and MoodyÂ’s ratings respectively and significant. This suggests that large information PAGE 78 71 asymmetry has a negative impact on bond ratings, both MoodyÂ’s and S&P. Similarly, in CVM estimation, the t-statistics are higher and the coefficients on PI are bigger and more significant in the bond rating equations. The significance of private information can be seen from the changes in on the bond rating equations. Notice that the on the bond ratings in WLS estimation (CVM estimation) has increase from about 55% (64%) in the simple model to 61% (72%) in the private information model, indicating that the additional private information latent variable has significant additional explanatory power on bond ratings. Since the two latent variables are assumed to have unit variance, it is easy to find out how much variation in the bond rating can be explained by each latent variable. Specifically, it can be shown from equation (6a) that Var {Bond Rating) = p] Var{ DR) + yl Var{PI) + Var{e^) or Var (Bond Rating) = P] +7s+ Var(e^). By definition, R^ = Pj /Var{ Bond Rating) + y^/ Var(Bond Rating). Given the estimated Pi, yi and R^, we can calculate p] /Var{ Bond Rating) and 7 ^/ Var{Bond Rating), or the contributions of the two latent variables to the R^. For the S&P regression in WLS (CVM) estimation, the DR reflected in the public information accounts for 56% (66%) of the variation of the rating and the private information reflected in the three information asymmetry proxies account for 5% (6%). For the MoodyÂ’s regression in WLS (CVM) estimation, the two latent variables account for 54% (67%) and 8% (9%) of the rating variations respectively. Hence, it seems that the private information plays a relatively smaller role in bond ratings. As a result, it is PAGE 79 72 not surprising that some of the previous studies fail to find evidence that bond ratings have impact on yields after controlling for public information. Results on complete model The last question remains unanswered is whether the private information contained in the bond ratings is priced by the bond market. The results on the complete model with bond yields reported in tables 3-7 and 3-8 can help to answer this question. Again, the results are very similar when we use either MoodyÂ’s or S&P ratings. First, notice that the default risk, or DR, has a very significant impact on bond yields. It is not surprising that higher default risk leads to higher bond yields. Secondly, the private information also has a significant impact on bond yields, though the coefficients and t-statistics are much smaller. Larger the private information, the higher the bond yields. This indicates that the bond market prices the private information conveyed in the bond rating. The on the bond yields in both WLS estimation and CVM estimation is around 40%. In a separate OLS regression (not reported) of bond yields on the same 7 variables, the is only about 30%. Hence, the latent variable technique performs better than simple OLS in explaining the variation in bond yields. To find out the relative importance of the two latent variables in explaining the bond yields, we calculate each variables contribution to tbe R^. For the model with S&P rating estimated by WLS (CVM) method, the DR accounts for 33% (30%) and PI accounts for another 8% (8%) of the variation in bond yields. For the model with MoodyÂ’s rating estimated by WLS (CVM) method, the two variables account for 32% (28%) and 8% (7%) of tbe bond yields PAGE 80 73 Specification Tests One of the assumptions in the latent variable models is that the error terms are not correlated with each other. If, however, there is omission of relevant variables in the model, then the assumption of non-correlated error terms will be violated, leading to an ill-specified latent variable model. This potential problem can be detected by the modification indexes of the model. The modification index measures the decrease in the model chi-square that would result from changes in constrained parameters (Sorbom, 1989). For example, if the model assumption of zero correlation among error terms is violated, then the modification index will be big, indicating that the model specification will improve (or chi-square will decrease) by removing the zero correlation constraint. The modification index is significant at the 5% level when it is equal to or greater than 3.84. There are two ways to fix this potential missing variable problem. Ideally, we would like to find and build all missing latent variables into the models. However, this is generally not possible nor efficient because the goal of this paper is not to build a Â‘perfect and all-inclusiveÂ’ rating model. Another simple way to solve the problem is to allow some error terms to be correlated in estimation. From the discussion on the technical issues on the latent variable models, we know that as many as p{p-\-2q)/2 covariances among error terms can be estimated, where p is the number of observable indicator variables and q is the number of unobservable latent variables. By estimating the covariances among some error terms, the latent variable model can control for the missing variable problem and focus on the latent variables of interest. PAGE 81 74 Since there is no ex-ante indication as to which error terms are likely to be correlated, we first estimate all the three models with the constraint that the correlation between all error terms be zero and then check for potential correlation from the modification indexes. With the constraint of zero correlation among error terms, the fitfunction and model chi-square all indicate that the models are not well-specified. Next, we relax the constraint on the pair of errors that have the largest modification index by estimating the covariance of the two error terms and re-estimate the model, we repeat the process until there is no obvious correlation in the remaining error terms. From table 3-3 through table 3-8, we report the pairs of error terms that have significant non-zero covariance. For example, for the simple bond rating latent variable models, tbe error terms between interest coverage ratio equation and leverage ratio (cov(ei, 02 )), between interest coverage ratio equation and ROA equation (cov(ei, 04)), between leverage ratio equation and firm size equation (cov(e 2 , 03)), and firm size equation and ratings equation (cov(e 3 , es)), are not constrained to be zero and the estimated covariance is statistically significant. Another potential problem of the latent variable bond rating model assumes that the PI variable, or private information, is not reflected in the other three publicly available accounting variables. This assumption may be problematic because the simple correlation matrix shows that the two proxies for information asymmetry used in the model are also correlated with the three accounting variables. The good news is that the modification index provides a good diagnosis for this potential problem. When we leave PI out of the equations of interest coverage ratio, leverage ratio ROA, we basically impose zero coefficients on tbe variable PI in these three equations. From the discussion PAGE 82 75 on modification index above, if the PI is also reflected in the other three accounting variables or, in other words, the zero coefficient assumption is violated, then the modification indexes will be large and significant. Table 3-9 presents the modification indexes for the complete model with S&P rating estimated by WLS method. Modification indexes for other models with MoodyÂ’s rating have similar results. Panel A of the table reports the indexes for the loading on the PI latent variable on the three accounting variable equations. All three indexes are less than 1, suggesting that these three accounting variables are not related to the PI latent variable. Panel B gives the modification indexes of the error term covariance. Except for the seven pairs of error terms on which no constraint has been imposed as shown in table 3-7, none of the error term modification indexes is greater than the 3.84 critical value. Split Rating and Private Information The two rating agencies, S&P and MoodyÂ’s, do not always give identical ratings to bond issues. About 13% to 18% of new bond issues receive different letter ratings from the two rating agencies (Ederington, 1986, Jewell and Livingston, 1998) and about 50% receive split ratings at the notch level (Jewell and Livingston, 1999).'Â” Ederington (1986) argues that split ratings occur due to random difference of opinion on the creditworthiness of bond issues. Jewell and Livingston (1998) shows that split ratings convey valuable information and are priced by the bond market. If an issuing firm has large information asymmetry problem, it is more likely to receive a split rating because it is harder for rating agencies to evaluate and agree on its creditworthiness. The implication is that the private information will play a larger role in PAGE 83 76 the determination of ratings if the bond issue receives a split rating. To test this, we form a sub-sample of 333 observations that have split ratings at the notch level and estimate the complete model. Table 3-10 and 3-1 1 report the results of the complete model on the split rating sub-sample with S&P and MoodyÂ’s ratings respectively. A comparison of tables 3-7 and 3-10 for S&P rating (3.8. and 3.1 1. for MoodyÂ’s rating) shows that the coefficients on PI, or private information, are much higher for the rating equations, suggesting that large information asymmetry makes it harder for rating agencies to agree upon the issuing firmÂ’s creditworthiness. In the same time, the coefficients on DR remain largely unchanged, consistent with EderingtonÂ’s (1986) finding that split ratings are not caused by different interpretation of financial ratios by different rating agencies. Table 3-12 compares the relative contributions of the two risk factors to the variation of bond ratings for the whole sample and split rating sub-sample, based on the estimated coefficients in tables 3-7, 3-8, 3-10, and 3-11. For the whole sample. P/only explains 5%-9% of the variations in ratings, while DR accounts for almost 58% to 70% of the variations. For the split rating sub-sample, PI accounts for a much larger proportion of the rating variations, ranging from 1 1% to 17%, than the whole sample. Tables 3-10, 3-1 1, and 3-12, though suggesting strongly that private information plays a larger role in bond ratings for issues with split rating, do not test directly the statistical significance in the difference in the bond issues with split rating. To do that, we create a split rating dummy variable, equal to 1 if S&P and MoodyÂ’s ratings split at If one rating agency gives an issue an AA rating, while another gives a rating of A, the ratings are split at letter lever. If one rating agency gives an AA-irating while another gives an AA rating, the rating are split at the notch lever. PAGE 84 77 the notch level and 0 otherwise. The dummy variable is then added to the complete bond rating model as an additional equation. Tables 3-13 and 3-14 report the estimated split rating model for the two ratings separately. The coefficients on PI in the split dummy variable equation are positive and significant, suggesting that larger information asymmetry makes it more likely to have split ratings. The coefficients on DR in the split dummy variable equation is not significant, suggesting that split ratings are not caused by different interpretation of public available accounting information which is consistent with the findings of Ederington ( 1 986). Conclusion This paper uses the latent variable technique to investigate the information content of bond ratings. Previous studies on bond ratings only provide indirect evidence on the potential private information in bond ratings. Since private information is not observable by definition, it is impossible to link such information with bond ratings directly in traditional statistical models. The latent variable technique, however, provides us a way to directly link potential private information with bond ratings, using three observable proxies for information asymmetry. We find that bond ratings do contain private information. Generally speaking, if a firm has higher degree of information asymmetry, its bond ratings tend to be lower. However, private information does not seem to account for a very significant amount of variation in bond ratings. Less than 10% of bond variation can be explained by private information, compared to about 60% of variation explained by publicly available information. Furthermore, investors seem to be able to infer the private information from the bond ratings and require a higher bond yields for firms with greater private information. About 8% of bond yields can be PAGE 85 78 explained by the private information, while more than 30% is explained by the public information reflected in the bond ratings. For bond issues that receive split ratings from the rating agencies, private information is more important in explaining the variation in bond rating. PAGE 86 79 Table 3-1 Comparison of Rating Determinants Studies Significant Percentage of STUDY Methodology Determinants of Ratings Rating Predicted Horrigan (1966) Regression Subordination Total Assets SALES/NET WORTH Net Worth/Total Debt Working Capital/Sales 50% -60% Pogue and Soldofsky (1969) Regression Debt/Total Capital Equity/Debt Ratio Bonds Outstanding Period of Solvency NA Pinches and Mingo (1973, 1975) Discriminant Function ROA Issue Size Subordination Interest Coverage Ratio Long-term Debt/Total Asset Years of Consecutive Dividend 60%-75% Altman and Katz (1974) Discriminant Function Cash Flow Coverage Ratio Std. Error of Coverage Ratio 77% Kaplan and Urwitz (1979) Ordered Probit Regression Subordination Total Assets Long-Term Debt/Total Assets 50-60% Ederington (1986) Ordered Probit Regression ROA Total Assets Subordination Coverage Ratio Variation in ROA Long-term Debt/Total Capital 72% to 76% PAGE 87 80 Table 3-2 Summary Statistics Variable Mean Standard Median Deviation Skewness Kurtosis Interest Coverage Ratio 9.242 7.239 7.677 2.901 12.151 Leverage 0.247 0.239 0.114 0.621 1.498 Firm Size (in Billions) $18,994 $6,319 33.556 3.402 12.665 Log (Firm Size, in millions) 8.905 8.751 1.316 0.295 -0.372 ROA 5.407% 5.238% 3.953% 0.330 2.775 Analysts Earning Forecast Error 0.965% 0.366% 1.519% 2.839 10.241 Adverse Selection Component 0.095% 0.090% 0.080% 2.204 9.452 Correlation Matrix Interest Coverage Ratio Interest Coverage Ratio LOGO Leverage Log of Firm Size ROA Analysts Forecast Errors Adverse Selection Leverage -0.580*** 1.000 Log of Firm Size 0.274*** -0.152*** 1.000 ROA 0.605*** -0.302*** 0.262*** 1.000 Analysts Forecast Error -0.089** 0.078 ** -0.212*** -0.124*** 1.000 Adverse Selection -0.142*** 0.161*** -0.501*** -0.186*** 0.077** 1.000 The correlation is significant at the 1% level (***) or 5% level (**) PAGE 88 81 Table 3-3 Simple Model for S&P Rating WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR DR R^ Interest Coverage -4.700 -4.709 Ratio (VI) (-8.11) 0.37 (-21.50) 0.38 Leverage Ratio 0.058 0.058 (V2) (11.40) 0.26 (20.36) 0.26 Firm Size -0.603 -0.602 (V3) (-8.29) 0.20 (-11.48) 0.20 ROA -2.330 -2.329 (V4) (-10.55) 0.35 (-19.29) 0.35 S&P Rating -0.569 -0.799 (V5) (-11.38) 0.55 (-20.72) 0.64 Model Fit Fit Function GFl Chi-Square (d.f) Pr > Chi-Square Non-Zero Error Covariance 0.000 1.000 0.010(1) 0.923 cov(ei,e 2 ), cov(ei,e4) cov(e2,e3), cov(e3,es) 0.000 1.000 0.004(1) 0.949 cov(ei,e 2 ), cov(ei,e4) cov(e2,e3), cov(e3,e5) Note: This table gives the estimated simple bond rating latent variable model with S&P rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=l; cov(ej,ej)=5i^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=0 (i,j=l,...5). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 89 82 Table 3-4 Simple Model for MoodyÂ’s Rating WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR RDR RInterest Coverage -4.410 -4.393 Ratio (VI) (-7.87) 0.33 (-21.08) 0.33 Leverage Ratio 0.061 0.060 (V2) (11.38) 0.28 (21.18) 0.28 Firm Size -0.636 -0.635 (V3) (-8.47) 0.22 (-11.63) 0.22 ROA -2.230 -2.251 (V4) (-9.61) 0.32 (-19.52) 0.33 MoodyÂ’s Rating -0.546 -0.814 (V5) (-11.79) 0.56 (-23.56) 0.66 Model Fit Fit Function GFI Chi-Square (d.f) Pr > Chi-Square Non-Zero Error Covariance 0.000 1.000 0.1498 (1) 0.699 cov(ei,e2), cov(ei,e4) cov(e2,e3), cov(e3,es) 0.000 1.000 0.201(1) 0.654 cov(ei,e2), cov(ei,e4) cov(e2,e3), cov(e3,es) Note: This table gives the estimated simple bond rating latent variable model with MoodyÂ’s rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=l ; cov(ej,ej)=5,^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=0 (i,j=l,. . .5). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 90 83 Table 3-5 Private Information Model with S&P Rating WLS Estimation Rating as Continuous VARIABLE CVM Estimation Rating as Categorical Variable DR PI DR PI R~ Interest Coverage -4.563 -4.711 Ratio (VI) (-8.16) 0.37 (-22.21) 0.37 Leverage Ratio 0.057 0.058 (V2) (11.60) 0.26 (20.74) 0.27 Firm Size -0.620 -1.004 -0.636 -1.065 (V3) (-8.63) (-7.64) 0.77 (-12.72) (-9.00) 0.83 ROA -2.300 -2.308 (V4) (-10.77) 0.34 (-19.82) 0.34 S&P Rating -0.570 -0.177 -0.814 -0.247 (V5) (-12.12) (-3.47) 0.61 (-21.63) (-4.93) 0.72 Adverse Selection 0.018 0.041 0.020 0.039 (V6) (4.15) (5.43) 0.34 (5.94) (6.71) 0.31 Forecast Error 0.309 0.170 0.315 0.161 (V7) (5.72) (2.89) 0.06 (6.50) (2.44) 0.05 Model Fit Fit Function GFI Chi-Square (d.f) Pr > Chi-Square Non-Zero Error Covariance 0.006 0.997 4.687(6) 0.585 cov(ei,e2), cov(ei,e4) cov(e2,e3), cov(e4,e6) 0.009 0.999 6.844(6) 0.335 cov(ei,e2), cov(ei,e4) cov(c2,e3), cov(e4,e6) Note: This table gives the estimated private information bond rating model with S&P rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=l ; cov(ei,ej)=8j^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, Ci)=cov(PI, Ci)=0 (i,j=l,. . .8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 91 84 Table 3-6 Private Information Model with MoodyÂ’s Rating WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR PI RDR PI R^ Interest Coverage Ratio (VI) -4.448 (-7.93) 0.34 -4.422 (-21.59) 0.33 Leverage Ratio (V2) 0.061 (11.77) 0.29 0.061 (21.61) 0.29 Firm Size (V3) -0.638 (-8.74) -0.920 (-8.85) 0.69 -0.662 (-12.96) -0.941 (-10.64) 0.71 ROA (V4) -2.210 (-9.71) 0.32 -2.230 (-19.78) 0.32 MoodyÂ’s Rating (V5) -0.530 (-11.95) -0.199 (-4.14) 0.62 -0.820 (-23.92) -0.295 (-5.77) 0.76 Adverse Selection (V6) 0.019 (4.23) 0.043 (6.29) 0.38 0.021 (6.01) 0.043 (8.17) 0.36 Forecast Error (V7) 0.301 (5.58) 0.192 (3.16) 0.06 0.319 (6.56) 0.163 (2.44) 0.06 Model Fit Fit Function GFI Chi-Square (d.f) Pr > Chi-Square Non-Zero Error Covariance 0.007 0.997 5.539 (6) 0.477 cov(ei,e 2 ), cov(ei,e4) cov(e2,e3), cov(e4,e6) 0.008 0.999 6.010(6) 0.422 cov(ei,e 2 ), cov(ei,e4) cov(e2,e3), cov(e4,e6) Note: This table gives the estimated private information bond rating model with MoodyÂ’s rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=l ; cov(ei,ej)=8i^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ej)=cov(PI, ej)=0 (i,j=l,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 92 85 Table 3-7 Complete Model with S&P Rating WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR PI DR PI R^ Interest Coverage -4.477 -4.633 Ratio (VI) (-8.24) 0.35 (-23.08) 0.36 Leverage Ratio 0.057 0.058 (V2) (11.85) 0.25 (20.81) 0.27 Firm Size -0.628 -0.972 -0.640 -1.045 (V3) (-8.68) (-7.51) 0.74 (-12.63) (-8.88) 0.81 ROA -2.256 -2.261 (V4) (-11.07) 0.32 (-20.77) 0.33 S&P Rating -0.585 -0.170 -0.835 -0.247 (V5) (-14.09) (-3.39) 0.64 (-23.87) (-4.82) 0.76 Adverse Selection 0.019 0.043 0.020 0.040 (V6) (4.20) (5.42) 0.35 (5.85) (6.66) 0.32 Forecast Error 0.307 0.169 0.322 0.158 (V7) (5.70) (2.88) 0.06 (6.64) (2.38) 0.06 Yield Spread 31.359 15.693 31.091 16.377 (V8) (10.26) (5.42) 0.41 (16.87) (6.24) 0.38 Model Fit Fit Function 0.010 0.011 GFI 0.996 0.999 Chi-Square (d.f) 7.608 (8) 8.754 (7) Pr > Chi-Square 0.473 0.271 Non-Zero Error cov(ei,C 2 ), cov(e,,e 4 ), cov(ei,C8) cov(ei,e2), cov(ei,C4), cov(ei,C8) Covariance cov(c 2 ,e 3 ), cov(e 3 ,eg), cov(c 4 ee) cov(c2,e3), cov(e 3 ,eg), cov(c4 ee) COV(C4,e8) cov(c4,e8), cov(ey,e8) Note: This table gives the estimated complete bond rating model with S&P rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=l; cov(ej,ej)=5i^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ej)=cov(PI, ei)=0 (i,j=l,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 93 86 Table 3-8 Complete Model with MoodyÂ’s Rating WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR PI DR PI R^ Interest Coverage -4.300 -4.338 Ratio (VI) (-7.91) 0.32 (-22.36) 0.32 Leverage Ratio 0.060 0.060 (V2) (11.83) 0.28 (21.64) 0.29 Firm Size -0.652 -0.868 -0.661 -0.932 (V3) (-8.82) (-8.39) 0.65 (-12.76) (-10.42) 0.71 ROA -2.161 -2.187 (V4) (-9.78) 0.30 (-20.41) 0.31 MoodyÂ’s Rating -0.551 -0.194 -0.837 -0.294 (V5) (-13.48) (-3.97) 0.65 (-25.41) (-5.67) 0.79 Adverse Selection 0.020 0.047 0.021 0.044 (V6) (4.30) (6.45) 0.42 (5.91) (8.11) 0.37 Forecast Error 0.303 0.178 0.324 0.162 (V7) (5.66) (2.96) 0.06 (6.64) (2.43) 0.06 Yield Spread 30.917 14.543 30.380 14.815 (V8) (10.78) (2.74) 0.39 (16.50) (6.18) 0.35 Model Fit Fit Function 0.014 0.011 GFI 0.995 0.999 Chi-Square 10.520(8) 8.276(7) Pr > Chi-Square 0.230 0.308 Non-Zero Error cov(ei,e2), cov(ei,e4), cov(ei,e8) cov(ei,e2), cov(ei,e4), cov(ei,e8) Covariance cov(e2,e3), cov(e3,es), cov(e4 65) cov(e2,e3), cov(e3,es), cov(e4 ee) cov(e4,e8) cov(e4,e8), cov(e7,eg) Note: This table gives the estimated complete bond rating model with MoodyÂ’s rating. The sample size is 772. Estimation constraints are as follows: Var(DR)=Var(PI)=l; cov(ei,ej)=8j^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ej)=cov(PI, ej)=0 (i,j=l,. . .8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 94 87 Table 3-9 Modification Indexes Complete Model with S&P Rating This table gives the modification indexes of the estimated complete bond rating model with S&P rating. The modifieation index measures the decrease in the model chi-square when a constrained parameter is allowed to vary (Sorbom, 1989). It basically measures the improvement in the model specification if the constraint on one parameter is removed. The modification index is significant at 5% level when it is equal to or greater than 3.84. NC: no constraint has been imposed on the parameter. Panel A: Modification Indexes for Latent Variable PI Equation PI Interest Coverage Ratio (VI) 0.00 Leverage Ratio (V2) 0.66 Firm Size (V3) ROA (V4) 0.20 S&P Rating (V5) Adverse Selection (V6) Forecast Error (V7) Yield Spread (V8) Panel B: Modification Indexed for the Error Covariance 61 62 63 64 65 66 ei 62 NC 63 0.55 NC 64 NC 0.58 0.15 65 O.OI 0.06 1.42 0.01 66 1.54 1.46 1.76 NC 1.08 67 0.65 0.45 0.26 0.18 0.32 0.85 68 NC 1.69 NC NC 0.81 2.60 PAGE 95 88 Table 3-10 Complete Model with S&P Rating on Split Rating Sub-sample WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR PI R" DR PI R^ Interest Coverage -4.407 -4.819 Ratio (VI) ( -5.98) 0.30 (-12.81) 0.34 Leverage Ratio 0.045 0.051 (V2) (5.35) 0.14 ( 11 . 21 ) 0.19 Firm Size -0.244 1.120 -0.4000 -1.074 (V3) (-2.13) (-10.53) 0.85 (-4.63) (-9.51) 0.86 ROA -2.199 -2.203 (V4) (6 . 88 ) 0.29 (-12.41) 0.29 S&P Rating -0.609 -0.311 -0.800 -0.331 (V5) (-8.30) (-4.90) 0.69 (-13.27) (-4.79) 0.75 Adverse Selection 0.001 0.043 0.011 0.046 (V 6 ) (0.17) (6.42) 0.29 (1.69) (6.54) 0.30 Forecast Error 0.272 0.400 0.310 0.368 (V7) (3.17) (4.72) 0.13 (4.54) (4.70) 0.12 Yield Spread 27.995 30.730 32.328 33.450 (V 8 ) (6.61) (7.93) 0.49 (11.30) (7.87) 0.56 Model Fit Fit Function 0.023 0.030 GFI 0.992 0.998 Chi-Square 7.500 ( 8 ) 9.903 (9) Pr > Chi-Square 0.484 0.358 cov(ei,C 2 ), cov(ei,C 4 ), cov(c 2 ,e 3 ) cov(ei,e 2 ), cov(ei,C 4 ), cov(c 2 ,e 3 ) Non-Zero Error cov(c 2 eg), cov(c 3 64 ), cov(e 3 ,eg) COV(C 2 eg), COv(C 3 ,eg), COV(C 4 C 6 ) Covariance COV(e4 66) Note: This table gives the estimated complete bond rating model with S&P rating on a split rating sub-sample. To be included in the sub-sample, the observation has different S&P rating and MoodyÂ’s rating at the notch level. There are 333 observations in the split rating sub-sample. Estimation constraints are as follows: Var(DR)=Var(PI)=l; cov(ej,ej)=5i^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ej)=cov(PI, ei)=0 (i,j=l,..., 8 ). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 96 89 Table 3-1 1 Complete Model with MoodyÂ’s Rating on Split Rating Sub-sample WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR PI DR PI R' Interest Coverage -4.301 -4.618 Ratio (VI) (-5.80) 0.27 (-11.45) 0.31 Leverage Ratio 0.060 0.058 (V2) (6.55) 0.23 (14.03) 0.23 Firm Size -0.354 -0.915 -0.447 -0.877 (V3) (-3.28) (-9.14) 0.63 (-5.07) (-8.87) 0.63 ROA -1.960 -2.016 (V4) (-6.27) 0.22 (-11.83) 0.24 MoodyÂ’s Rating -0.541 -0.310 -0.825 -0.386 (V5) (-8.61) (-5.57) 0.69 (-15.60) (-5.72) 0.83 Adverse Selection 0.010 0.053 0.013 0.054 (V6) (1.25) (6.15) 0.39 (1.91) (6.93) 0.39 Forecast Error 0.149 0.559 0.250 0.509 (V7) (1.71) (5.02) 0.17 (3.38) (5.48) 0.17 Yield Spread 32.730 27.05 33.190 26.371 (V8) (8.35) (7.04) 0.47 (12.03) (7.45) 0.47 Model Fit Fit Function 0.028 0.028 GFI 0.990 0.9980. Chi-Square 9.281 (8) 9.163 (9) Pr > Chi-Square 0.319 0.422 Non-Zero Error cov(ei,C 2 ), cov(ei,C 4 ), cov(ei,eg) cov(ei,C2), cov(ei,e4), cov(c2,e3) Covariance cov(c2,e3), cov(c3,e8), cov(c4 ee) COV(C 3 ,e 8 ), COV(C 4 66), COv(C6 Cy) cov(e6,e7) Note: This table gives the estimated complete bond rating model with MoodyÂ’s rating on a split rating sub-sample. To be included in the sub-sample, the observation has different S&P rating and MoodyÂ’s rating at the notch level. There are 333 observations in the split rating sub-sample. Var(DR)=Var(PI)=l; cov(ei,ej)=6j^ if i^, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ej)=0 (i,j=l,...8). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 97 90 Table 3-12 Relative Importance of DR and PI SÂ«&P Ratine Whole Sample WLS (CVM) Split Rating Sub-sample WLS (CVM) MoodyÂ’s Ratine Whole Sample WLS (CVM) Split Rating Sub-sample WLS (CVM) % of Rating Variation Explained by DR 59% (70%) 55% (64%) 58% (70%) 52% (68%) % of Rating Variation Explained by PI 5% (6%) 14% (11%) 7% (9%) 17% (15%) Total (R^) 64% (76%) 69% (75%) 65% (79%) 69% (83%) PAGE 98 91 Table 3-13 Split Rating Model with S&P Rating WLS Estimation RATING AS CONTINUOUS Variable CVM Estimation Rating as Categorical Variable DR PI R' DR PI R' Interest Coverage -4.553 -4.648 Ratio (VI) (-8.21) 0.36 (-23.21) 0.37 Leverage Ratio 0.058 0.059 (V2) (11.74) 0.26 (21.39) 0.27 Firm Size -0.635 -0.971 -0.647 -0.970 (V3) (-9.60) (-9.79) 0.74 (-13.38) (-11.93) 0.73 ROA -2.309 -2.316 (V4) (-11.23) 0.34 (-21.50) 0.35 S&P Rating -0.571 -0.175 -0.840 -0.251 (V5) (-12.96) (-3.55) 0.61 (-24.25) (-5.26) 0.77 Adverse Selection 0.018 0.043 0.019 0.045 (V6) (4.35) (7.13) 0.37 (6.05) (9.88) 0.37 Forecast Error 0.308 0.180 0.333 0.251 (V7) (5.94) (3.38) 0.06 (7.04) (4.46) 0.08 Yield Spread 27.038 36.788 27.28 30.48 (V8) (7.53) (4.55) 0.67 (13.39) (5.33) 0.51 Split Dummy (=1 -0.045 0.098 -0.111 0.263 if split rating) (V9) (-1.73) (4.34) 0.05 (-1.79) (4.62) 0.08 Model Fit Fit Function 0.008 0.022 GFI 1.000 0.999 Chi-Square 5.839 (11) 17.339 (12) Pr > Chi-Square 0.884 0.137 Non-Zero Error cov(ei,C2), cov(ei,C4), cov(c2,e3) cov(ei,e 2 ), cov(ei,C4), cov(e 2 ,C 3 ) Covariance cov(ei,e 8 ), cov(e 3 ,eg), cov(e 4 ,e 6 ) cov(ei,eg), cov(e 3 ,eg), cov(e 4 ,e 6 ) cov(c 4 , eg), cov(c6,eg), cov(c 2 ,e 9 ) cov(e6,eg), cov(c 2 ,e 9 ), cov(c 5 ,e 9 ) cov(es,e9) Note: This table gives the estimated split bond rating model with S&P rating. Estimation constraints are as follows: Var(DR)=Var(PI)=l; cov(ei,ej)=5i^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (i,j=l . .9). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 99 92 Table 3-14 Split Rating Model with MoodyÂ’s Rating WLS Estimation Rating as Continuous Variable CVM Estimation Rating as Categorical Variable DR PI DR PI R" Interest Coverage -4.393 -4.387 Ratio (VI) (-8.01) 0.34 (-23.04) 0.33 Leverage Ratio 0.061 0.061 (V2) (11.81) 0.29 (22.20) 0.29 Firm Size -0.648 -0.921 -0.679 -0.911 (V3) (-9.59) (-10.14) 0.70 (-13.98) (-12.15) 0.69 ROA -2.219 -2.254 (V4) (-10.20) 0.32 (-21.06) 0.32 MoodyÂ’s Rating -0.530 -0.190 -0.833 -0.285 (V5) (-12.61) (-4.05) 0.61 (-25.40) (-5.75) 0.78 Adverse Selection 0.019 0.043 0.022 0.045 (V6) (4.42) (7.39) 0.38 (6.61) (10.19) 0.39 Forecast Error 0.293 0.205 0.334 0.257 (V7) (5.66) (3.67) 0.06 (7.03) (4.61) 0.08 Yield Spread 25.376 34.83 26.82 30.635 (V8) (7.22) (7.35) 0.61 (13.01) (5.71) 0.51 Split Dummy (=1 -0.045 0.099 -0.105 0.262 if split rating) (V9) (-1.63) (4.11) 0.05 (-1.59) (4.24) 0.08 Model Fit Fit Function 0.009 0.018 GFI 0.999 0.999 Chi-Square 7.070(11) 13.760(12) Pr > Chi-Square 0.793 0.316 Non-Zero Error cov(ei,C2), cov(ei,C4), cov(c2,e3) cov(ei,C2), cov(ei,C4), cov(c2,e3) Covariance cov(ei eg), cov(e 3 ,eg), cov(c 4 ee) cov(ei,eg), cov(c 3 ,eg), cov(e 4 ,e 6 ) cov(c 4 ,eg), cov(e6,eg), cov(e 2 ,eg) cov(e6,eg), cov(c 2 ,e 9 ), cov(e 5 ,C 9 ) COV(C5,e9) Note: This table gives the estimated split bond rating model with MooyÂ’s rating. Estimation constraints are as follows: Var(DR)=Var(PI)=l; cov(ei,ej)=5i^ if i=j, 0 otherwise (except those in the last row of the table, which are estimated); and cov(DR, ei)=cov(PI, ei)=0 (i,j=l,...9). Two methods are used to estimate the model parameters. Weighted least square (WLS) estimation method treats bond ratings as continuous variable, ranging from 1 (CCC and below) to 7 (AAA). MuthenÂ’s categorical variable (CVM) estimation method treats bond ratings as categorical variable. The numbers in parentheses are t-statistics. PAGE 100 CHAPTER 4 CONCLUSION Rule 144A bonds do not require a registration filing with the Securities and Exchange Commission. They may be purchased by qualified financial institutions and traded to other qualified financial institutions, but may not be purchased by individuals. Some Rule 144A bonds require the issuer to replace the bonds with publicly traded bonds within a stipulated period of time and are designated as having registration rights. Although high-yield bonds issued under Rule 144A usually have registration rights, we find that the majority of investment-grade bonds do not. Our empirical results indicate that Rule 144A bond issues have higher yields to maturity than publicly issued bonds. The effect is greater for Rule 144A bonds issued by private firms without publicly traded securities. The yield premiums of Rule 144A issues are likely due to lower liquidity, information uncertainty, and weaker legal protection for investors. Gross underwriter spreads for Rule 144A bond issues and publicly registered bond issues are essentially equivalent. Tbe second essay uses the latent variable technique to investigate the information content of bond ratings. Previous studies on bond ratings only provide indirect evidence on the potential private information in bond ratings. Since private information is not observable by definition, it is impossible to link such information with bond ratings directly in traditional statistical models. The latent variable technique, however, provides us a way to directly link potential private information with bond ratings, using three observable proxies for information asymmetry. We find that bond ratings do contain 93 PAGE 101 94 private information. Generally speaking, if a firm has higher degree of information asymmetry, its bond ratings tend to be lower. However, private information does not seem to account for a very significant amount of variation in bond ratings. Less than 10% of bond variation can be explained by private information, compared to about 60% of variation explained by publicly available information. Furthermore, investors seem to be able to infer the private information from the bond ratings and require a higher bond yields for firms with greater private information. About 8% of bond yields can be explained by the private information, while more than 30% is explained by the public information reflected in the bond ratings. For bond issues that receive split ratings from the rating agencies, private information is more important in explaining the variation in bond rating. PAGE 102 APPENDIX A CATEGORICAL VARIABLE METHOD (CVM) Consider Y , an n^-p matrix of observable indicator variables, n is the number of observations and p is the number of indicator variables. Among the p variables,/)/ of them are continuous variables and (/)-/>/) of them are categorical variables. The underlying statistical structure is the same as represented in equation (1), Y = M + Zp + 8 For continuous variables, y* = y. for i = 1 top/, where y* and y. are (Â«xl) vectors. For categorical variables. if ,k<^ if ki.Cr2^yjM 2 if VI <\i.2 1 if < yj.k <^JJ where y*. ^ is the k's observation in yÂ’s categorical indicator variables and yj^k is the k's element in the fs unobservable continuous indicator variable, for all A: = 1 to Â« and j = P/+1 top. > thresholds for categorical indictor variable g. With all the usual assumptions laid out the in the text, we have the following relationship between the covariance matrix of Y, denoted as E, and model parameters of (3 and s as in equation (2), or E = P'P + Â£'8 95 PAGE 103 96 With consistent estimators of S, we should be able to estimate the model parameters by ML or WLS methods if the model is identifiable. When some or all of the indicator variables are categorical variables as in Y*, the sample covariance matrix of Y* is not a consistent estimator of the true I and model parameters estimated based on sample covariance matrix is likely to be inconsistent. MuthenÂ’s three-stage estimation procedure first provides a consistent estimator of Z with limited information ML method and then uses WLS method to generate consistent estimators of model parameters based on the estimated S. This appendix describes briefly a simple version of the three-stage estimation procedures (or Case A as in MuthenÂ’s paper). Assumptions and Definitions One important assumption of the three-stage method is that the underlying indicator variables, Y, are multivariate normally distributed, even though some or all observable indicator variables may be categorical. Let continuous indicator variable y,for i= 1 top/, and the unobservable underlying indicator variable yj ~A(0,1), for j =pi+\ top.' Also, assume (y^, y*) follow bivariate normal distribution: A(pg. p^, al, a], (TgJ if both y* and y* are continuous A(pg, 0, cr^, 1, p^^) if y* is continuous and y*^ is categorical A(0, 1, a\, p^^) if y* is categorical and y\ is continuous Y(0, 0, 1, 1, p*^) if both y* and y^ are categorical for g and /? = 1 to p, and g^h. Since yj is not observable, we can scale it to standard normal distribution. 1 PAGE 104 97 Pgh is called polyserial correlation, or correlation between one continuous variable and one categorical variable, and p*/, is polychoric correlation, or correlation between two categorical variables. p First, letÂ’s define two row vectors, yi and 72. yi has p, + '^{Cj -1) elements as J=Pi +1 follows: 7/ /^ 2 > > f^p,Â’ ^p,+UÂ’ ^p,+l.2Â’ Â•Â•Â• Â’ ^Pi+I.C,-lÂ’ ^Pi+2,1Â’ Â’ ^p,+2.C,-IÂ’ Â’ ^p.Cpj-l Each continuous variable y,contributes one element (its mean, p,), and each categorical variable y/ contributes Q 1 elements (its thresholds) to yi . 72 has (p(p+l) / 2 (p-p, )) elements. It consists of the followings: the variance ( cr^ , g = 1 to pi) and covariance ( , g and /i =1 to p/ and g ^ h) of the continuous variables, polychoric correlation {p*gh, g and h = pj +1 to p and g ^ h) between two categorical variables, and polyserial correlation (p/,Â„, / = 1 top/ and m =p/ +1 top) between one continuous variable and one categorical variable. Each pair of y^* and y/,* contributes one element (polychoric correlation) to 72 if both variables are categorical, and two elements (a polyserial correlation and a variance) if one variable is categorical and another is variable, and three elements (two variances and one covariance) if both variables are continuous. First Stage Estimation The first stage will use the limited information maximum likelihood method to consistently estimate y/, based on the univariate likelihood functions. Let lnL(y,*) and lnL(y,*) denote for the log-likelihood of observing the sample PAGE 105 98 variable y,* and y/ , where / = 1 to pi and j =pi +1 to p. For the case of continuous variables, the log-likelihood function is as follows: ,, ,, lnL(y;) = --ln(2;r)--ln,TÂ’ For the case of categorical variables, the log-likelihood function is as follows: lnL(y*) = XUlnP(y; =1) + J, lnP(y*, = 2)+L lnP(yÂ‘, =C,) k=\ ^ where d,= : if y].k = f otherwise if y].k = ^ otherwise 1 '^^y).k = Cj 0 otherwise and hi P(F*;t=i)= \ PAGE 106 99 ainL(y;) dn, = 0, for / = \,io P i For categorical variables, the thresholds can be estimated by solving for the following partial derivatives: glnL(y;.) ^^ ^.u glnL(y;.) ^i.2 : ioxj=pi+\,Xop ainL(y*) So, the first stage estimation gives consistent estimator of y/. Let s/ be a row vector of the estimated elements in y/. Second Stage Estimation Based on the consistent estimator of yi, the second stage will use the limited information maximum likelihood method to consistently estimate y 2 by maximizing pairsize bivariate likelihood function. Let P(yA*>Fg*) be the joint probability of observing k's observation in variables y/, and y^ as follows: PAGE 107 100 (p(yl.k^ylk'^ hÂ’^g^hygÂ’^hg) y*hk> y*gk continuous p(yl.kÂ’ylk) = j (p(yl.kÂ’yg.kÂ’' MhÂ’^Â’^l^Â’Phg) ifylk continuous, categorical j I (p(yh.k^yg.k^ dy^j^dy^j^ if yli^,y*gh both categorical *> 4 -' 'Â’Â•Â’A.* *'Â’*.* 'Â’'A*' ^>s.k' where and fi/,are estimated means for continuous variables, ... , are estimated thresholds for categorical variables, = -cÂ» and = oo, for g and /z = 1 to PThe log-likelihood function of a pair of variables, y^* and y/,*is then: n In L(y* , y*J = ^ In P(yÂ’ * , y* * ) , for g and // = 1 to /?, and g /j. k=l By taking the first derivatives of the bivariate normal log-likelihood function with respect to elements in j2 and setting them equal to 0 , the second stage will produce consistent estimator of yz Let S2be a vector with estimated elements in y2. Third Stage Estimation Let s be a vector of the estimated means, thresholds, variances, covariances and correlations estimated in the first two stages. That is, s = (s/ s^). Also, let y = (y/ y2) In the final stage, the WLS method, as discussed in the text, is used to estimate the model parameters, based on estimation results from the first two stages. Specifically, the model parameters are estimated by minimizing the weighted least squares fitting function: PAGE 108 101 Fwh= (s-y)W'(s-y)' where the weight matrix, W, is a consistent estimator of the asymptotic covariance matrix of s with s (see Muthen, 1984, for the derivation of W). Since the CVM method is essentially an WLS estimation, the statistic properties of CVM estimators are the same as those of WLS estimators. PAGE 109 APPENDIX B MEASUREMENT OF INFORMATION ASYMMETRY There are two sets of proxies for information asymmetry; proxies from corporate finance literature and proxies from market microstructure literature. This appendix gives a brief overview of these two sets of proxies. Proxies from Corporate Finance Literature There is a growing literature on the impact of information asymmetry on corporate finance. Since the information asymmetry problem is not directly observable or measurable, several proxies have often been used in the corporate finance literature to proxy for the degree of information asymmetry. These proxies generally fall into three categories: opinion-based, growth-based, and trader-based proxies. Opinion-Based Proxies The basic idea for the opinion-base proxies is that large information asymmetry problem makes it harder for investors and stock analysts to evaluate the value of the firm and, as a result, it is more likely that they will have different opinions on the firmÂ’s future earnings and stock price. The most often used opinion-based proxy is analystsÂ’ earning forecast errors. For example, Thomas (2002) uses this proxy to examine the asymmetric information problem of diversified firms. Krishnaswami and Subramaniam (1998) also utilize this proxy to study the changes in information asymmetry problem before and after subsidiary spin-off 102 PAGE 110 103 In addition to the forecast errors, dispersion of analystsÂ’ earning forecasts is another opinion-based proxy for information asymmetry. Large information asymmetry will make it harder for analysts to form a consensus of future earnings. Stock price volatility can also been used to proxy information asymmetry. If the price of a stock is very volatile, it indicates that investors have a hard time to evaluate the worth of firm, probably due to information asymmetry problem. Firm size is another proxy used in corporate finance literature to proxy information asymmetry. Large firms are often followed by more stock analysts and under more scrutiny of the financial media. Thus, asymmetry information problem is generally less due to the greater awareness of investors of larger firms (Merton, 1987). Also, large firms generally access the capital markets more frequently and reveal more information to investors to lower their cost of capital. Growth-Based Proxies Young firmsÂ’ with great growth opportunities may have a large problem of asymmetric information because they are usually in a new industry, or with new technology that fewer investors understand or are familiar with. Therefore, some empirical studies have used proxies for a firmÂ’s growth opportunity to measure information asymmetry. For example, McLaughin, Safieddine and Vasudevan (1998) use the market-tobook ratio to proxy for information asymmetry in their study of seasoned equity offerings. Other potential growth-based proxies include expenditures on R&D and the amount of intangible assets. PAGE 111 104 Trader-Based Proxies The argument for trader-based proxies is that the degree of information asymmetry is often related to the number of informed investors. If investors of a firmÂ’s stock are sophisticated and well-informed, the information asymmetry problem will be less than otherwise. There are two often used trader-based proxies: number of stock analysts and the number of institutional investors. Larger number of stock analysts may mitigate the information asymmetry problem. However, Brennan and Subrahmanyam (1995) find that the number of analysts and the degree of information asymmetry is positively related. Their argument is that stock analysts are more likely to follow firms that have large degree of information asymmetry. Additional information gathering and analysis by stock analysts are most beneficial and valuable when the firm has large information asymmetry problem. The number of institutional investors and the percentage of firms owned by institutional investors have also been used to proxy information asymmetry (see for example, Brennan and Subrahmanyam, 1995). Institutional investors are generally assumed to be more sophisticated and can achieve scale of economy in information gathering and analysis. Proxy from Market Microstructure Literature The notion of information asymmetry has also been developed in the market microstructure literature as well. Bagehot (1971) and Kyle (1985) argue that some informed traders may have more information than market maker and they can take advantage of their superior information by trading with market maker when the stock prices deviate from their true value. To protect themselves, market makers have to increase the bid-ask spreads to offset the potential losses from trading with informed PAGE 112 105 traders. Hence, if a firm suffers from large information asymmetry problem, the bid-ask spread of its stock tends to be higher. Stock bid-ask spread also compensates the market maker for the order processing and inventory costs that are not related to information asymmetry. The proxy for information asymmetry, therefore, can only be the so-called adverse selection component, or the part of bid-ask spread due to potential losses from trading with informed trade. Though the adverse selection component is not directly observable, a large body of literature has proposed several ways to decompose the bid-ask spread and estimate the adverse selection component. There are three general methods of bid-ask spread decomposition: covariance approach, trade-indicator approach and regression approach. The remainder of the appendix provides a brief discussion of some common methods. Table B-1 lists the notations used in the following discussion. Covariance Approach The covariance approached is pioneered by Roll (1984), followed by Glosten (1987), Stoll (1989) and George, Kaul and Nimalendran (1991). The basic idea of the covariance approach is that the transaction price, P,, bounces between bid and ask prices and produces certain pattern of auto-covariance in transaction prices as well as the midpoint of bid-ask spread. By examining such auto-covariance, these methods can decompose the bid-ask spread into different components. Glosten (1987) RollÂ’s model pioneers the covariance approach but it ignores the adverse selection component. Glosten is the first covariance model that derives adverse selection component. The model assumes the following: PAGE 113 106 W,=W,.,+{E + U,) + {\-k)^D, (Bl) (B2) The model basically assumes that the true value of the stock, If,, is updated by the amount of adverse selection component after each transaction while the transaction price, Pt, deviates from the true stock value by the order processing component. Under several assumptions on the order flow, the auto-covariance of price changes can be shown to be: GlostenÂ’s model decomposes the bid-ask spread into two parts: adverse selection and order processing. It does not allow for cost of holding an inventory. Stoll (1989) builds a similar covariance model, but assumes unequal probability of buy and sell. StollÂ’s model decomposes the bid-ask spread into three components (order processing cost, inventory cost, and adverse selection cost). Since inventory component is no the focus of the paper, we will not go into details of StollÂ’s model. George, Kaul and Nimalendran (GKN) (1991) One assumption of GlostenÂ’s model is that the expected return, or E, is constant. The GKN model relaxes on this assumption and introduces time varying expected return, or Ei. Accordingly, the GKN model can be presented in the following equations: (B3) Thus, the adverse selection component of the bid-ask spread is: (l-;r)5 = 5-ACov{APÂ„AP,_,) S (B4) W = W,,+{E, + U,)+{l-n)^D, (B5) PAGE 114 107 P,=W,+k^D, (B6) The changes in transaction price is then: APr(E, + UJ+(D,-nD,_,)^ (B7) The auto-covariance of price changes can be shown to be as follows: Cov{APj,APi_i )=-7T Â— + Cov(E, , Ej_! ) (B8) Notice that GKN model only differs from Glosten model in that the expected returns in GKN model are not constant but time varying. This difference makes it difficult to estimate equation (B8) because the auto-covariance of the expected returns is not observable. To overcome this problem, GKN model utilizes the information contained in the changes in the mid-point of the bid-ask spread. The model assumes that the true value of the stock is the mid-point of the bid-ask spread, or Wt = M,. Thus, the change in the mid-point of bid-ask spread is: The expected return, E,, is present at both the change in transaction price and the change in the bid-ask mid-point. Taking the difference of the two changes can flush out the expected returns. Let represents the difference in the two changes. AMr{E, + U,)+{\-K)^D, (B9) R,=AP,-AM, =n-AD, 2 ' (BIO) The auto-covariance of R, is then free of the expected return term as follows: Cov{R,,R,_i) = -n 4 (Bll) PAGE 115 108 Therefore, the adverse selection component is: i\-7r)S = S-2^-Cov{R,R,_,) (B12) Trade-Indicator Approach Covariance approach generally have some assumptions about the buy/sell, or order flow, patterns and do not need (or take advantage ol) the actual direction of each transaction (whether it is a buy or sell order). Trade-indicator approach differs from the covariance approach because it utilizes the information on the actual directions of trades. Glosten and Harris (1988) represent the first trader indicator model, followed by Madhavan, Richardson, and Roomans (1997), and Huang and Stoll (1997). Glosten and Harris (GH) (1988) The Glosten and Harris model can be described in the following two equations: W = W,_j+AS,D, + U, (B13) P, = W,+OP,D, (B14) where AS, is the adverse selection component and OPi is the order processing component. AS) is assumed to be a function of shares traded, or AS,= eVi (B15) while the order processing component is assumed to be a constant, or OPt=c (B16) The price changes from transaction to transaction is then: AP,=c(D,-D,_,)+eD,V, + U, (B17) With observed price changes (AP,), changes in the directions of trades {D, D,.j), and the signed number of shares traded (DtV,), we can regress the price changes on the changes in trade direction and the signed number of shares traded. The estimated coefficient on the PAGE 116 109 signed number of shares traded (e) is the adverse selection component of the bid-ask spread. Madhavan, Richardson, and Roomans (MRR) (1997) Previous models assume implicitly that every transaction will have an equal (or volume adjusted in GH model) adverse selection impact on the true value of stock. MRR model differs from the previous model in that the adverse selection component is related to the innovation in order flow. The basic idea is that there should be no adverse selection component if the order flow (whether it is buy or sell) is fully anticipated (or expected) by the dealer given the order flow of the previous transaction. Adverse selection component plays a role only when the order flow is not expected given the previous transaction. To model the innovation in order flow, MRR uses a slightly different trade indicator variable: D* . D* = -1 for sell order, D* = +1 for buy order, and D* = 0 if the trade occurs within the quoted spread (and cannot be determined if it is a sale or buy order). Hence, MRR explicitly take into consideration the possibility that an order may occur within quoted spread. The model can be represented in the following two equations: W, = WÂ„^e[D]-E{D:\Dl,)yU, (B18) P = W,+tzD] (B19) where ^[Z)*-Â£'(D*|D*|)j is the adverse selection component. Note that if the order flow is completely anticipated (or D]=E{D]\D].^) ) no adverse selection component is present at equation (B18). The changes in transaction price can then be express as: PAGE 117 110 AP=e d:-e(d:\di) + U,+kAD, (B20) The difficulty in empirically estimating equation (B20) is that the expected order flow, or E{^D'\DI^ ) is not observable. To overcome the problem, MRR has shown, under several assumptions, that , where p is the first-order auto-correlation of the trade indicators, D*. Therefore, equation (B20) can be rewritten as: AP=d[D^ -pDl ] + f/, +7tAD* ={^+6)D:-(k+p0)D:, + U, (B21) GMM can be used to estimate (B21). Huang and Stoll (1997) is another trade-indicator model that is similar to MRR model, but it allows a three-way decomposition of the bid-ask spread into adverse selection, inventory cost, and order processing components. Pure Regression Approach Lin, Sanger and Booth (1995) propose a pure regression method to estimate adverse selection component. The LSB model is specified in the follow equation: (B22) where Z,_i is one half the signed effective spread, and 6 is the fraction of the effective spread due to adverse selection. The model basically assumes that the mid-point of the bid-ask spread adjusts for the adverse selection components, which is a fraction of the effective spread. In empirically estimation, the changes in the mid-point of spread are regressed on the signed effective spread and the coefficient is the estimated adverse selection as a fraction of the effective spread. PAGE 118 Ill The LSB model can also estimate the order processing cost component with some assumption on order persistence. PAGE 119 112 Table B-1 Notations Notation Definition P, Observed Trading Pricing Wt True value of the stock Ut Unobservable changes in the true value of stock between t and t-\ Ml Midpoint of the bid-ask spread D, Buy/Sell indicator; =1 if a sale, = -1 if a buy E Expected return El Expected return between t and ?-l V, Number of shares traded S Quoted Spread 71 Fraction of the quoted (half) bid-ask spread due to order processing costs 1-7T Fraction of the quoted (half) bid-ask spread due to adverse selection PAGE 120 LIST OF REFERENCES Altinkilic, O. and R. Hansen, 2000, Â“Are There Economies of Scale in Underwriting Fees? Evidence of Rising External Financing Costs,Â” Review of Financial Studies 13, 191-218. Altman, E. and S. Katz, 1976, Â“Statistical Bond Rating Classification Using Financial and Accounting Data,Â” Michael Schiff and George Sorter, editors. 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Thomas, S., 2002, Â“Firm Diversification and Asymmetric Information: Evidence from AnalystsÂ’ Forecast and Earning Announcements,Â” Journal of Financial Economics 64, 532-568 Weinstein, M., 1977, Â“The Effect of a Rating Change Announcement on Bond Price,Â” Journal of Financial Economics 5, 29-44. West, R., 1973, Â“Bond Ratings, Bond Yields and Financial Regulation: Some Findings,Â” Journal of Law and Economics 16, 159-168 Zellner, A., 1970, Â“Estimation of Regression Relationships Containing Unobservable Independent Variables,Â” International Economic Review 1 1, 441-45. PAGE 125 BIOGRAPHICAL SKETCH Lei Zhou was bom in Suzhou, China in 1969. He received his B.A. in foreign trade at Suzhou University in 1991 . He then received an MBA from University of Alabama in 1994 and an MS in agricultural economics from Purdue University in 1997. In 1997, he started his Ph.D. at the University of Florida. He will graduate in August 2002 and continue his career in the finance department at the Miami University at Ohio as an assistant professor. 118 PAGE 126 I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. . Miles B. Livingston, Chair / Professor of Finance, Insurance, and Real Estate I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Andy Naranjo^ Associate Professor of Finance, Insurance, and Real Estate I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophv \(jWVVt'rv\^ CaaP^ Â— M. Nimalrendran Professor of Finance, Insurance, and Real Estate I certify that I have read this study and that in my opi acceptable standards of scholarly presentation and is fully ai as a dissertation for the degree of Doctor of Philosophy. it conforms to te, in scoae and quality. Karl Hackenbrack Associate Professor of Accounting This dissertation was submitted to the Graduate Faculty of the Department of Finance, Insurance and Real Estate in the College of Business Administration and the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August 2002 Dean, Graduate School |