Assessment of Credit Risk Models on Rule 144A Corporate Bonds
Mark Johnson Department of Finance Loyola University Maryland
[email protected] 410-617-2473
Karyl Leggio Department of Finance Loyola University Maryland
[email protected] 410-617-2097
Yoon S. Shin* Department of Finance Loyola University Maryland
[email protected] 410-617-2869
JEL Classification: G10, G11, and G24 Key Words: Credit Ratings, Credit Risk Models, and Merton Model *Corresponding Author
Assessment of Credit Risk Models on Rule 144A Corporate Bonds Abstract Accurate assessment of credit risk can improve the performance of bond portfolio managers. Utilizing credit ratings and market-based credit risk models from Standard & Poor’s (S&P) and Bloomberg, we investigate the performance of four different credit risk models in the Rule 144A corporate bond markets in the U.S. over the 1990-2015 periods. We divide our sample into straight bonds and convertible bonds, and find that (1) when it comes to straight bonds, discrete models such as S&P’s credit ratings and Bloomberg ratings determine yields more accurately than continuous market-based models of S&P and Bloomberg; (2) even though both S&P and Bloomberg market-based models affect the yields of straight bonds significantly, Bloomberg’s market-based model has more statistical power in determining the yields than S&P’s counterpart, (3) with regard to convertible bonds, a convertible option has a stronger effect than credit ratings in determining yields, and only Bloomberg default risk ratings, not S&P credit ratings, determine the yields; (4) for convertible bonds, continuous market-based models of S&P and Bloomberg affect yields more significantly than discrete models, and (5) when it comes to predicting actual defaults, Bloomberg models are superior to S&P’s models, and the Bloomberg discrete model has more power than its continuous counterpart. JEL Classification: G10, G11, and G24 Key Words: Credit Ratings, Credit Risk Models, and Merton Model
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I. Introduction
Asymmetric bond returns (capital losses are greater than capital gains for the same interest
rate changes) can be aggravated due to an inaccurate or untimely credit risk assessment. For example, Moody’s (2011a) reports that the recovery rate of defaulted speculative grade bonds is significantly lower than that of defaulted investment grade bonds. As a result, accurate credit risk assessment is priceless to debt investors. In general, there are two popular credit risk measures used by market participants – credit ratings and market-based credit risk models. Credit ratings provide certification and monitoring of credit risk for investors. Credit ratings are widely used not only for financing and investment decisions, but also for financial regulations. Investors in the U.S. are restricted to use ratings issued by the Nationally Recognized Statistical Rating Organizations (NRSROs), and many institutional investors are not allowed to buy speculative grade bonds. Additionally, according to the Basel II agreement of the Basel Committee on Banking Supervision (Bank for International Settlements, 2004), commercial banks can use the credit ratings of the External Credit Assessment Institutions (ECAIs) in assessing their capital requirements.1 Even though previous studies document that the credit rating is the most important factor to determine the cost of debt, numerous previous studies criticize the conflict of interest between the issuers and credit rating agencies as well as the accuracy and timeliness of credit ratings. For example, Manso (2013) argues that rating agencies are too tardy in downgrading credit ratings after a deterioration in credit quality. Ashcraft, Goldsmith-Pinkham, Hull, and Vickery (2011)
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While the NRSROs are certified by the Securities and Exchanges Commission (SEC) in the U.S., the ECAIs are determined by each government. In general, once a rating agency is certified as NRSROs, it is recognized as one of the ECAIs.
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conclude that the inaccurate credit ratings of mortgage-backed securities by rating agencies are partially responsible for the financial crisis in 2008. On the other hand, market-based credit risk models are generally based on option pricing models. The most widely used models such as S&P’s Market Signal Probability of Default (S&P, 2015), Moody’s Expected Default Frequency (Moody’s, 2011b), and Bloomberg’s Default Probability and Default Risk (Bloomberg, 2015) are modified from Merton’s (1974) option pricing model. The fundamental feature of the Merton model is that default can be viewed as a call or put option by the stockholders on the assets of the firm. This option is then exercised, or the issuer defaults if the enterprise value of the issuer’s assets declines below the value of its debt or a certain default point. According to the Merton (1974) model, the credit risk of corporate debt is a function of the leverage, market capitalization, and asset return volatility of the issuer. Many market participants believe that incorporating those market signals from stock price and asset volatility into the credit risk model can improve the quality of credit risk assessment and bond portfolio management. Bloomberg, S&P, and Moody’s add economically and statistically relevant factors to the Merton model to articulate default risk. For example, Bloomberg (2015) includes trailing 12–month adjusted operating cash flows and interest expenses for non-financial firms in addition to the variables used by the Merton model. Bloomberg (2015) also looks at different factors for finance, insurance, or foreign firms. The Merton model shows that default probability is the tail risk of the firm, and the model is very popular to bond portfolio managers in assessing the credit risk of debt. While credit ratings are based on inside information provided by the debt issuers to rating agencies, all the default determinants in the Merton model are publicly available. While credit ratings are discrete with a limited number of rating symbols and are updated infrequently, the Merton model
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is continuous and can estimate credit risk on a real-time basis. Bharath and Shumway (2008) find that the Merton model (1974) is useful for forecasting the probability of default of a firm in the U.S. In this research, we examine both discrete credit risk models such as S&P’s credit ratings and Bloomberg’s default risk ratings, as well as continuous credit risk models based on Merton models such as S&P’s Market Signal Probability of Default (MSPD) and Bloomberg’s 1-year Default Probability (DRSK) with regard to Rule 144A corporate bonds in the U.S. over the 1998-2015 periods (please see the Bloomberg’s default risk letter rating symbols, DRSK, and corresponding S&P’s rating symbols in the Appendix). It should be noted that Bloomberg default risk letter ratings (hereafter Bloomberg ratings) and DRSK are based on the Merton Model. Bloomberg also uses the Merton Model to determine the “5-year model CDS (Credit Default Swap) spread.” We hypothesize that S&P’s credit ratings are more accurate indicators than the Merton models in determining the cost of debt and in predicting default because the former contains inside information about the issuer. We also test whether discrete credit risk models (S&P’s and Bloomberg’s ratings) are better than their continuous counterpart (MSPD and DRSK). Showing as case studies, Bloomberg (2013) argues that its letter ratings and DRSK predicted the bankruptcy of American Airlines and MF Global much earlier than rating agencies. We also examine any differences in performance between S&P’s MSPD and Bloomberg’s DRSK, because the latter adds different modifiers to the original Merton (1974) model than the former. We find that (1) when it comes to straight bonds, discrete models such as S&P’s credit ratings and Bloomberg ratings determine yields more accurately than continuous market-based models such as the MSPD of S&P or DRSK of Bloomberg; (2) even though both S&P’s and
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Bloomberg’s market-based models affect the yields of straight bonds significantly, Bloomberg’s DRSK model has more statistical power in determining the yields than S&P’s MSPD, (3) with regard to convertible bonds, the convertible option has a stronger effect than credit ratings in determining yields, and only Bloomberg ratings, not S&P’s ratings, determine the yields of convertible bonds; (4) for convertible bonds, continuous market-based models such as the MSPD of S&P and DRSK of Bloomberg affect yields more significantly than discrete models such as S&P’s and Bloomberg ratings, and (5) when it comes to predicting actual defaults, Bloomberg models are better than S&P’s models, and Bloomberg default risk ratings have more power than its continuous DRSK. This study is structured as follows. Section II is a review of the related literature, Section III describes the research methodology, Section IV presents data used in this research, Section V provides empirical results, Section VI represents a robustness check, and Section VII concludes our study.
II. Literature Review Rating agencies have reputational capital through special knowledge and/or skills in evaluating credit risk information because not only can they mitigate information asymmetry in the credit markets, but they can also provide a delegated monitoring service for investors. For instance, numerous studies document the information certification role of bond ratings. Faulkender and Petersen (2006), Sufi (2009), and Bosch and Steffen (2011) show that rated firms have better access to public bond markets and borrow at lower interest rates than unrated ones. Recent studies indicate the role of rating agencies as a relatively effective credit monitor. Boot, Milbourn, and Schmeits (2006) set up a theoretical model that demonstrates how rating agencies
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monitor issuers through credit watch actions. For example, issuers placed under a negative credit watch attempt to improve their financial condition to mitigate or avoid a possible downgrade of their ratings. Bannier and Hirsch (2010) and Liu and Sun (2012) find that by comparing direct rating changes with credit watch-preceded rating changes, the latter provides more information than the former to credit markets. On the other hand, there is a strong argument that credit ratings are not reliable in assessing credit risk of the bond issuers. S&P, Moody’s, and Fitch maintained an A rating for Lehman Brothers until one day before the firm declared bankruptcy on September 15, 2008. Similar incidents occurred around the bankruptcies of WorldCom and Enron. After Enron’s collapse, the U.S. Congress passed the Credit Rating Agency Reform Act of 2006 to promote competition among NRSROs. Additionally, most investors, news media, and regulators believe that inaccurate and untimely credit ratings of sub-prime mortgage-backed securities are responsible for the financial crisis in 2008, which resulted in the enactment of the Dodd-Frank Act in 2010. Because of the rating failures, many studies suggest market-based credit risk measures such as Credit Default Swap (CDS) spreads and the Merton model should replace credit ratings. Several academic studies have sought to assess the relative performance in predicting credit risk using corporate credit ratings and market-based credit risk models. Most previous research shows that CDS spreads are more timely than credit ratings. Longstaff, Neis, and Mithal (2005) find that CDS spreads are significant indicators of default risk. Hull, Predescu, and White (2004) analyze the relationship between the CDS market and ratings announcements and find that reviews for rating downgrades make a significant impact on the CDS market, but rating downgrades and negative outlooks do not. Hull, Predescu, and White (2004) also find that CDS spread changes have predictive power for rating downgrades by Moody’s. Consistent with Hull,
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Predescu, and White (2004), Norden and Weber (2004) examine the stock and CDS market reactions to credit rating announcements by S&P, Moody’s, and Fitch and find that both markets anticipate rating downgrades approximately 60–90 days before the announcements. Galil and Soffer (2011) document that rating downgrades do not result in significant CDS market response, while negative rating reviews do. Finnerty, Miller, and Chen (2013) not only confirm previous results regarding the market impact of negative credit events on CDS spreads, but also obtain new results of significant announcement effects in response to positive credit events on CDS spreads. On the other hand, there are few studies on the relationship between credit ratings and market-based credit risk models based on the Merton model. S&P (2013) states that while credit ratings are discrete with a limited number of rating symbols and are updated very infrequently, its Market Signal Probability of Default (MSPD) based on Merton’s model (1974) is continuous and can estimate credit risk on a real-time basis. Merton’s credit risk model (1974) shows that the default probability of a corporate bond is a function of the issuer’s leverage as well as the market value and volatility of the issuer’s assets. All of the variables in the Merton’s model are public information. Bharath and Shumway (2008) find that the Merton’s model (1974) is useful for forecasting the probability of default of a firm in the U.S. Employing Merton’s credit risk model (1974), Vassalou and Xing (2004) find that the default probability of a U.S. firm is highly correlated with the size and book-to-market ratio used in Fama and French (1993). S&P (2015) announces that it provides the MSPD for 31,748 corporations and 5,881 financial institutions in 156 countries. Bloomberg (2016) also provides a 1-year default probability of a corporate bond for both public and private firms using the Merton model.
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Most practitioners combine the Merton models with credit ratings for their investment decisions. The Bloomberg measures are very popular with institutional investors. Comparing Moody’s credit ratings with its Expected Default Frequency (EDF) modified from the Merton model for the period of 1983-2002, Löffler (2004) simulates the portfolio performance of those two credit risk measures and finds that neither measure is better than the other. Our research is the first study to examine the actual performance of S&P’s credit ratings versus Merton models in the Rule 144A bond markets. There are two types of private placements – a traditional private placement and a SEC Rule 144A private placement. Even though SEC Rule 144A allows the trading of private placement bonds among qualified institutional investors such as banks and insurance companies, institutional investors who purchase traditional private placement bonds cannot trade them. Since the enactment of Rule 144A in 1990, the markets for 144A private placement bonds have increased remarkably and oftentimes dominated public bonds markets due to the fast speed of issuance, less onerous registration requirements, and allowance of trading among qualified institutional investors (Huang and Ramirez, 2010; Livingston and Zhou, 2002). Bank loans, private placement bonds, and public bonds are three different types of debt financing by U.S. corporations. While the general public can buy public bonds, only institutional investors are allowed to purchase private placement bonds. Because private placement bonds, unlike public bonds, are exempt from extensive registration requirements with the Securities and Exchange Commission (SEC), firms prefer private placement to public offerings if they want to issue debt quickly (Fenn, 2000; Huang and Ramirez, 2010). Denis and Mihov (2003) and Kwan and Carleton (2004) examine public bonds, private placement bonds, and bank loans for U.S. corporations and find that firms with lower credit risk prefer to issue public bonds, while firms
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with higher credit risk sell private placement bonds, and firms with intermediate-level credit risk use bank loans. While previous research has concentrated on why firms issue Rule 144A private placement bonds or what type of firms sell them, there has been no research on the role of credit risk models for those bonds. Even though the issuance of Rule 144A has substantially increased recently, researchers have not paid much attention to this area. This study focuses on the role of credit risk models in the Rule 144A private placement markets. Our study is the first research investigating the role of credit risk models in the markets for Rule 144A private placement bonds. We analyze Rule 144A bonds for the following four reasons. First, according to Fabozzi (2001), the majority of convertible bonds are issued in the 144A bond markets. Second, the effect of a convertible option dominates the certification effect of credit ratings, because most convertible bonds are issued without ratings. Third, convertible bonds are believed to be highly correlated to market-based credit risk models, which are primarily based on stock price and stock price volatility. Firms issue convertible bonds at lower yields than straight bonds in exchange for providing bondholders with an opportunity to acquire issuers’ common stock.2 Convertible bonds tend to be issued by small, young, and high-growth firms (Mikkelson, 1981; Stein, 1992; Lewis, Rogalski, and Seward, 1998). Finally, we can examine subsequent registrations of 144A bonds. Huang and Ramirez (2010) describe that 144A bonds can be registered with the SEC after issuance, and individual investors can trade registered bonds on the over-the-counter market. They argue that the issuers of registered bonds use the 144A market for the speed of
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According to Bloomberg, Tesla issued 5-year maturity convertible bonds (CUSIP 88160RAB7) at 0.25% coupon rate in 2014. S&P assigned unsolicited credit rating of B- to those bonds. Other rating agencies did not rate the bonds.
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issuance and subsequently register the bonds to improve liquidity. We hypothesize that bonds registered with the SEC are issued at lower interest rates due to greater liquidity.
III. Research Methodology We test two hypotheses in this study: Hypothesis 1: S&P’s ratings are superior to the other three credit risk models in determining the yields and predicting defaults. We set up Hypothesis 1 because credit ratings are based on private information of the bond issuers and rating agencies have special skills and knowledge in accessing this information. We choose S&P’s credit ratings because S&P has the largest market share (49%) with 1,146,932 outstanding credit ratings followed by Moody’s (34%) and Fitch (13%) at the end of 2015 (Verma, 2017). Hypothesis 2: When it comes to convertible bonds, market-based credit risk models are better than credit ratings in assessing the costs of debt and default probability. We test the second hypothesis because the exercise of the convertible option is significantly affected by the stock price, and the most important components of market-based models are the stock price and its corresponding volatility. We test those hypotheses using panel regressions and probit models. Our sample is a panel data set that consists of new bonds issued from 1990 to 2015 that are combined with crosssectional, bond-specific variables across different industries. Thus, it is important for us to use the fixed effects models to control for industry- and time-specific effects, as well as to adjust the standard errors for time and industry clustering as the same firm may issue several bonds in a cluster, or many firms may issue bonds at the same time due to a lower interest rate environment.
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In the panel regression model, the offering yields or yield spreads between Rule 144A bonds and comparable maturity Treasury securities are used as a dependent variable. When it comes to independent variables, we choose not only issue-specific variables such as maturity, issue amount, and embedded options (call or convertible options), but also include issuer-specific variables such as idiosyncratic risk of the issuer and total assets for the issuer. For example, we use total assets (Frank and Goyal, 2003) and idiosyncratic stock return volatility (Goyal and Santa-Clara, 2003) as our proxies for information asymmetry (with larger firm size and lower idiosyncratic risk suggesting less severe informational asymmetries). In addition, we include several macro-economic variables such as bond market spreads and the volatility index (VIX) because market conditions may affect the yields or defaults. Our panel regression model takes the following form: Offering Yields or Yield Spreads = α + β X + γ Y + φ Where the X and Y explanatory variables are described as follows: S&P’s Rating: ordered rankings of issuer credit ratings by S&P;3 Bloomberg Default Risk Ratings: letter ratings converted from DRSK;4 DRSK: 1-year default probability of the bond issuer by Bloomberg on the bond issue date; MSPD: average default probability of the bond issuer by S&P over the sample period; Maturity: log of maturities of the bond (in years);
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The letter ratings are converted into numeric ratings. The ratings of S&P are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1. When we add Moody’s and Fitch ratings, we have similar results. If a bond is rated by more than one agency, we use the average of multiple ratings (as in Reeb et al., 2001). We provide the results of only S&P’s ratings for consistency. 4 Please see the Appendix.
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Issue Amount: natural log of the issue amount of a bond (in millions); Call Option: dummy variable equal to 1 if the bond has a call option and 0 otherwise; Total Assets: natural log of the total assets of the bond issuer (in millions). Total assets at the fiscal year-end prior to the issue date; Idiosyncratic Risk: idiosyncratic risk volatility of the issuer estimated from the standard errors of market model;5 Debt Ratio: long term debt plus current portion of long term debt / total assets of a bond issuer at the fiscal year-end prior to the issue date; Profitability Ratio: EBIT / total assets of a bond issuer at the fiscal year-end prior to the issue date; Tangible Asset Ratio: tangible assets (fixed assets) / total assets of a bond issuer at the fiscal year-end prior to the issue date; Market-to-Book Ratio: market value of assets / book value of assets by a bond issuer at the fiscal year-end prior to the issue date; Interest coverage ratio: EBIT / interest expenses of the issuer; Financial Crisis: dummy variable equal to one if the bond is issued from 4/24/2007-3/31/2009 and 0 otherwise;6 VIX: volatility of S&P 500 stock index in the U.S. on the issue date;7 Bond Market Spreads: Moody’s seasoned Baa corporate bond yield – Moody’s seasoned 5
We estimate the standard errors based on the market model with 250 days of past stock returns for the firm ending one month prior to the debt issuance. 6 Following Han, Pagano, and Shin (2012), we use this period because The Wall Street Journal first reported problems with the global raters’ ratings of subprime debt in “Subprime Cloud Overshadows S&P, Moody’s” on April 24, 2007. 7 We assume that stock market volatility represents greater uncertainty and possibly heightened risk aversion which can, in turn, increase yield spreads.
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Aaa corporate bond yield; Convertible Option: dummy variable equal to 1 if the bond is a straight (nonconvertible) bonds and 0 for convertible bonds; Registered Bonds: dummy variable equal to 1 if a bond is registered with the SEC after issuance and 0 otherwise; Treasury yield: yield of maturity-matching Treasury securities on the issue date. We divide the whole sample into straight and convertible bonds and employ both yields and yield spreads as the dependent variable since many convertible bonds have negative yield spreads due to the convertible option, and matching the maturity of the corporate bonds with that of Treasury securities is oftentimes challenging because of the maturity structure of Treasury securities. We also specify a probit model to see which factors influence the bond issuer’s actual default. The dependent variable is a binary variable, and equals 1 for a defaulted bond and 0 otherwise. Like the panel regression model, we include both issue- and issuer-specific variables as independent variables. We add the following independent variables to the probit model. Firm Age: log of the age of the bond issuer, the number of years since the firm was first listed on the CRSP; Seniority Level: seniority level of the bonds such as senior secured=1, senior subordinate=2, senior unsecured=3, subordinate=4, and junior subordinate=5. We also test for sample selection bias.
IV. Data
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We investigate privately placed new corporate bonds issued via the SEC Rule 144A in the U.S. over the 1990-2015 periods. We start the sample period from 1990, because the SEC allowed the placement of 144A bonds in 1990. We identify approximately 15,000 Rule 144A bonds in S&P’s Capital IQ database. We exclude foreign currency-denominated bonds, floatingrate coupon bonds, and bonds without offering yields. We eventually obtain 2,074 straight bonds and 694 convertible bonds. We obtain issue-specific variables such as credit ratings, MSPD, maturity, offering yield, and issue amount from Capital IQ, Bloomberg letter ratings and 1-year default probability of the issuer (DRSK) from Bloomberg, issuer-specific financial variables such as total assets, market-to-book ratio, and long-term debt ratio from COMPUSTAT, and idiosyncratic stock return volatility from CRSP. When it comes to the daily default spread, Moody’s Seasoned Baa Corporate Bond Yield is obtained from WRDS, and Moody’s Seasoned Aaa Corporate Bond Yield is obtained from the Board of Governors of the Federal Reserve System, respectively. Table 1 reports the offering yields and credit rating distribution of 144A bonds in our study. Panel A shows the annual mean offering yields between straight bonds and convertible bonds. In Panel A, while the mean yield of 2,074 straight bonds is 7.45%, the mean yield of the 694 convertible bonds is 3.63%. We find that the mean yield of convertible bonds is much lower than that of straight bonds. We do not look at the yield spreads here because many convertible bonds have negative yield spreads due to convertible options. Panel B reports the credit rating distribution of S&P and Bloomberg. When it comes to the straight bonds, while S&P assigns only 30% (540/1790) of the bonds to investment grade ratings, Bloomberg provides 74% (1226/1648) of the bonds with investment grade. The Bloomberg ratings based on public information are much higher than S&P’s ratings from private
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information. With regard to the convertible bonds, we confirm the findings in the straight bonds that the proportion (29% = 76/260) of investment grade ratings by S&P is much lower than that (73% = 450/620) by Bloomberg. We also claim that, while only 260 (37%) out of 694 convertible bonds are rated by S&P, 620 (89%) of convertible bonds are rated by Bloomberg. The issuers are less likely to pay for S&P’s ratings when they sell convertible bonds. It should be noted that all Bloomberg ratings are unsolicited ratings based on public financial information. [Table 1 here] Table 2 provides the issue and issuer summary statistics of our sample. In Panel A, while the yield spreads (410.79 bps), issue amount ($452.06 m), S&P’s rating (11.22), total assets ($30,270.58 m), total market capitalization ($31,333.54 m), profitability ratio (12.24%), tangible asset ratio (36.15%), long-term debt ratio (35.50%), and age (24.66 years) of straight bonds are greater than those of convertible bonds, maturity (10.55 years), market-to-book ratio (4.40 times), interest coverage ratio (163.57 times), beta (1.65), idiosyncratic volatility (0.0299), and bank loan ratio (21.39%) of convertible bonds are higher than those of the straight bonds. Additionally, we do not find any difference in DRSK, MSPD, and Bloomberg ratings between the two different type of the bonds. We conjecture that the convertible bond issuers are younger and smaller firms with greater systemic and unsystematic risk and high growth potential. We do not see any big difference in terms of credit risk between the straight and convertible bonds. In Panel B, while 72.9% (1512/2074) of straight bonds are issued by industrial firms followed by utilities (15.81%) and financial firms (11.28%), 74.35% (516/694) of convertible bonds are sold by industrial firms followed by financials (16.28%) and utilities (9.37%). In addition, when it comes to seniority level, 78.74% (1633/2074) of straight bonds are issued with a senior subordinate covenant, and 69.86% (482/694) of convertible bonds are issued with a
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senior unsecured clause. Senior subordinate bondholders have a priority in claiming assets in bankruptcy to senior unsecured bondholders. Furthermore, even though 90.41% (1875/2074) of straight bonds are callable, only 36.89% (256/694) of convertible bonds are callable. The percentage of registered bonds after issuance is similar (78.35% for straight bonds and 80.26% for convertible bonds, respectively) for both types of the bonds. Moreover, 2.17% (45/2074) of straight bonds and 1.73% (12/694) of convertible bonds defaulted before maturity. While the portion of straight bonds with protective covenants is 19.33% (401/2074), 41.79% (290/694) of convertible bonds has protective covenants for bondholders. [Table 2 here] V. Empirical Results Table 3 reports the tests of mean differences between various pairs of the issue and issuer characteristics for different types of bonds. When it comes to credit risk models, we find no significant differences in DRSK, MSPD, and Bloomberg ratings between straight and convertible bonds. But the mean S&P rating (11.22) of straight bonds is higher than that (10.83) of convertible bonds at the 5% significance level (t = 2.00). On the other hand, S&P’s mean ratings are significantly lower than mean Bloomberg ratings for both straight and convertible bonds at the 1% significance level (t = -31.45 for straight bonds and t = -16.14 for convertible bonds, respectively). Additionally, Bloomberg’s DRSK has significantly lower default probability than S&P’s MSPD for both straight and convertible bonds at the 1% level.
Furthermore, the mean yield spread
(410.79 bps) of straight bonds is significantly higher than that (12.83 bps) of convertible bonds, and the mean difference is significant at the 1% level (t = 38.41). We also have similar findings for mean yield difference between straight and convertible bonds.
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Consistent with the findings in Table 2, the straight bonds have greater issue amounts (mean difference = $178.36 millions) and total assets (mean difference = $26,807 millions) than convertible bonds. We also report t-test results between defaulted and un-defaulted bonds. Defaulted bonds have significantly higher mean DRSK and MSPD and lower S&P and Bloomberg ratings compared to un-defaulted bonds at the 1% level. With regard to the comparison of defaulted bonds, mean DRSK (0.0263) is significantly lower than mean MSPD (0.0938) at the 5% level. Furthermore, the mean S&P rating (8.37) of defaulted bonds is significantly lower than the mean Bloomberg rating (11.24) of defaulted bonds at the 1% level. According to the t-tests, S&P provides more accurate credit risk assessment for defaulted bonds than Bloomberg. [Table 3 here] Table 4 reports the full sample results of three multivariate tests suggested by Equation (1). The dependent variable is the offering yield. We suggest three different credit risk models. In Model 1, we employ five independent variables such as market-to-book ratio, profitability ratio, tangible asset ratio, interest coverage ratio, and long-term debt ratio to incorporate the credit risk of the issuer.8 Model 2 uses S&P’s ratings and Model 3 uses Bloomberg ratings instead of the five financial variables. In Model 1, the coefficients of the profitability ratio and long-term debt ratio variables are significant at the 1% level. In Model 2, the coefficient of the S&P’s rating variable is negative and significant at the 1% level (t = -12.56) implying that a one letter-rating upgrade results in an average 35.73 bps reduction of yield. Bonds with greater issue amount are sold at lower interest rates, because the coefficients of the issue amount variable are negative and significant at the 5% (t = -2.28) level. In general, greater idiosyncratic volatility, Treasury yield, VIX, credit spread, and crisis period increase the yields because the coefficients of those variables
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Pottier and Sommer (1999), Poon (2003), and S&P (2017) claim that those financial ratios are the important determinants of credit ratings.
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are positive and significant at the 1% level. In Model 3, the coefficient of the Bloomberg rating variable is negative and significant at the 1% level (t = -9.79) implying that one Bloomberg letterrating upgrade results in an average 25.45 bps reduction of yield. More importantly, straight bond increases the yields by 427-434 bps compared to convertible bonds in every model.9 We find that both S&P and Bloomberg credit ratings significantly affect the offering yields. [Table 4 here] Table 5 reports the effect of credit ratings on yield spreads. Model 1 describes the results of testing S&P ratings and Model 2 tests Bloomberg ratings. Regardless of the model, the rating variables are negative and significant at the 1% level. While in Model 1 a one letter rating upgrade of S&P’s rating can result in significantly lower yields (46.02 bps lower), in Model 2, a one letter Bloomberg rating upgrade results in a 28.92 bps decrease in yield spread. The t-statistic of the S&P rating variable (t = -17.26) is higher than that of Bloomberg rating (t = -10.15) variable. Consistent with our findings in Table 4, bonds with greater issue amounts and by larger firms are issued at lower costs of debt, and the idiosyncratic volatility, crisis period, bond market spread, and VIX increase the yield spreads significantly. In addition, the coefficient of the registered bond dummy is negative and significant in the two models (t = -2.22 in Model 1 and t = -5.75 in Model 2, respectively), implying that greater liquidity of the bonds lowers the costs of debt. Most importantly, the convertible option has a greater effect in reducing yield spreads (about 274 – 277 bps) than bond ratings in each model because the coefficient of the straight bond dummy is positive and significant at the 1% level (t = 6.06 in Model 1 and t = 8.89 in Model 2, respectively). There is a caveat to the findings in Table 5. Because many convertible bonds have negative yield spreads
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We also test seniority level and protective covenants as independent variables, but the coefficients of the two variables are not significant in every model, and we drop them here.
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due to the convertible option, the coefficient of the maturity variable is negative and significant at the 1% level. [Table 5 here] Table 6 describes the effect of market-based credit risk models on yield spreads for S&P’s MSPD (Model 1) and Bloomberg’s DRSK (Model 2). Both Model 1 and 2 show that the coefficients of the MSPD and DRSK variables are positive and significant at the 1% level (t = 2.72 in Model 1 and t = 4.60 in Model 2, respectively). In other words, the probability of default based on the market value of assets and stock price volatility has significant statistical power in explaining the cost of debt, and Bloomberg’s model has a greater t-statistic than S&P’s model. Consistent with the findings in Table 5, the coefficients of the straight bond dummy is positive and significant at the 1% level (t = 9.02 in Model 1 and t = 8.72 in Model 2, respectively), and the convertible option can reduce the yield spreads by 251-270 bps. The test results of other variables in Table 6 are similar to those in Tables 4 and 5. [Table 6 here] In Table 7, we examine the impact of credit ratings on yields and yield spreads for straight bonds. We split the whole sample into straight and convertible bonds, because many convertible bonds have negative yield spreads due to the convertible options. Regardless of yields or yield spreads, credit ratings are the most important determinant in the cost of debt for straight bonds.10 In Models 1 and 2, the coefficient of the S&P’s rating variable is negative and significant at the 1% level (t = -20.18 in Model 1 and t = -17.94 in Model 2). A one letter rating upgrade may result in 40 – 48 bps reduction in yields. In Models 3 and 4, even though the coefficient of the Bloomberg rating variable is also negative and significant at the 1% level, the reduction of yields for a one
10
The coefficients of the credit rating variables have the highest t-statistics.
20
letter rating upgrade is 27 – 31 bps. The significance of the coefficients of the other variables is consistent with the results in the previous tables. [Table 7 here] Table 8 tests the impact of credit ratings on yields and yield spreads for convertible bonds. Whether we use yields (Model 1) or yield spreads (Model 2), S&P’s ratings do not have any relationship with the yields or yield spreads of the convertible bonds. Even though Bloomberg ratings do not explain yield spreads (Model 3), they are an important determinant of yields (Model 4). The coefficient of the Bloomberg rating variable is negative and significant at the 5% level (t = -3.32) in Model 4. In other words, a one Bloomberg rating upgrade decreases yields by about 14 bps for convertible bonds. In every model, even though large issue amount decreases the yields significantly, firm size has a positive and significant impact on yields. We claim that S&P’s credit ratings do not have any power to determine the yields of the convertible bonds. [Table 8 here] Table 9 presents the impact of market-based credit risk models on yields and yield spreads for straight bonds. In Models 1 and 2, the coefficient of the MSPD variable by S&P is significant and positive at the 5% level (t = 2.44 and t = 2.34, respectively). Models 3 and 4 also show that the coefficient of the DRSK variable by Bloomberg is significant and positive at the 1% level (t = 4.76 and t = 4.83, respectively). We claim that the market-based models can explain the cost of debt for straight bonds, and the Bloomberg model has a greater statistical power than S&P’s model. We also confirm that greater firm size and a registration covenant can reduce the yields of straight bonds. [Table 9 here]
21
Table 10 provides the impact of market-based credit risk models on yields and yield spreads for convertible bonds. Even though the MSPD of S&P determines the yield spreads of convertible bonds in Model 1 (t = 2.37) at the 5% level, it does not have any relationship with the offering yields in Model 2. On the other hand, regardless of the yields or yield spreads as dependent variable, the DRSK variable of Bloomberg is positive and significant in Models 3 and 4 at the 5% level. We argue that the market-based credit risk models have a greater explanation power for the yields of the convertible bonds than credit ratings. We also find that small issue amounts may lower the cost of debt in every model. [Table 10 here] In Table 11, we test default prediction capability of different credit risk models with probit models. We obtain information about defaulted bonds over the sample period from Capital IQ database and find that 45 out of 2074 straight bonds and 12 out of 694 convertible bonds defaulted on interest or principal payments over the sample period. In our probit models, the dependent variable is equal to one for defaulted bonds and 0 otherwise. Between the DRSK and MSPD variables in Model 1, only the coefficient of the DRSK variable is significant and positive at the 1% level (t = 2.68). In Model 2, while the coefficient of the Bloomberg rating variable is significant and negative at the 1% level (t = -2.84), that of S&P’s rating is not significant. Model 3 compares S&P’s models (credit ratings vs. MSPD) and Model 4 Bloomberg models (letter ratings vs. DRSK). In Model 3, S&P’s ratings are better than MSPD in predicting defaults because the coefficient of the S&P’s rating variable is negative and significant at the 10% level (t = -1.70). Model 4 reports that the higher the Bloomberg ratings, the less likely for the issuer to default on the bond. The coefficient of the Bloomberg rating variable is significant and negative at the 1%
22
level (t = -5.16). We conclude that Bloomberg models are superior to S&P’s models, and discrete models are better than continuous models in predicting actual defaults. [Table 11 here]
VI. Robustness Checks Lastly, we test whether our results are impacted by selection bias. Using Models 2 and 3 from Table 4, we test for endogeneity. Using beta as an instrument for idiosyncratic risk, we estimate a two stage regression and then conduct Durbin-Wu Hausman tests. Table 12 presents the results. The idiosyncratic instrumented variable (beta) in Model 2 is no longer statistically significant (t = 0.80), but is statistically significant and negative in Model 3 at the 1% level (t = 4.10). In Model 2, the coefficient of the S&P’s rating variable is negative and significant at the 1% level (t = -17.61) and in Model 3, the coefficient of the Bloomberg rating variable is negative and significant at the 1% level (t = -10.28). Both models result in Durbin-Wu Hausman test statistics that are statistically significant at the 1% level, resulting in us rejecting the null hypothesis that the variables employed are exogenous. [Table 12 here]
VII. Conclusion We investigate the performance of four different credit risk models (credit ratings and market-based credit risk models of S&P and Bloomberg) to the privately placed new corporate bonds issued via SEC Rule 144A in the U.S. over the 1990-2015 periods. We divide our sample into straight bonds and convertible bonds because the latter are oftentimes issued at lower yields than benchmark Treasury yields due to convertible options, and convertible bonds are believed to
23
be more correlated to market-based models. We find that (1) when it comes to straight bonds, discrete models such as S&P’s credit ratings and Bloomberg ratings affect yields more significantly than continuous market-based models such as the MSPD of S&P and DRSK of Bloomberg; (2) even though both S&P’s and Bloomberg market-based models affect the yields of straight bonds significantly, Bloomberg’s DRSK has more statistical power in determining the yields than S&P’s MSPD, (3) the convertible option has stronger effect than credit ratings in determining yields, and only Bloomberg ratings, not S&P’s ratings, affect the yields of convertible bonds; (4) when it comes to convertible bonds, continuous market-based models such as the MSPD of S&P and DRSK of Bloomberg affect yields more significantly than discrete models such as S&P’s credit ratings and Bloomberg ratings, and (5) when it comes to predicting actual defaults, Bloomberg models are better than S&P’s models and Bloomberg discrete model has more power than its continuous model. We conclude that discrete models such as credit ratings are better determinants of the yield or yield spreads of straight bonds, but continuous models such as MSPD and DRSK are more powerful in determining the yields of convertible bonds. There is a caveat in our findings because we examine only Rule 144A bonds, and the MSPD that we use in this study is based on average default probability of the issuer. Future research can be done studying public bonds.
24
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Mikkelson, W., 1981, “Convertible calls and security returns,” Journal of Financial Economics 9, 237-264. Moody’s, 2011a, Corporate default and recovery rates, 1920-2010, Moody’s Investors Service. Moody’s, 2011b, EDF Overview, Moody’s Analytics. Norden, L., and M. Weber, 2004, Informational efficiency of credit default swap and stock markets: The impact of credit rating announcements, Journal of Banking and Finance 28 (11), 2813-2843. Poon, W., 2003, “Are Unsolicited Credit Ratings Biased Downward?” Journal of Banking & Finance 27, 593-614. Pottier, S. and D. Sommer, 1999, “Property-Liability Insurer Financial Strength Ratings: Differences Across Rating Agencies,” The Journal of Risk and Insurance 66, 621-642. Reeb, D., S. Mansi, and J. Allee, 2001, “Firm Internationalization and the Cost of Debt Financing: Evidence from Non-Provisional Publicly Traded Debt,” Journal of Financial and Quantitative Analysis 36, 395-414. Stein, J., 1992, “Convertible bonds as backdoor equity financing,” Journal of Financial Economics 32, 3-21. Sufi, A., 2009, “The Real Effects of Debt Certification: Evidence from the Introduction of Bank Loan Ratings,” The Review of Financial Studies 22, 1659-1691. Standard & Poor’s Financial Services (S&P), 2013, “Credit risk indicators,” www.spcapitaliq.com. Standard & Poor’s Financial Services (S&P), 2015, “PD model market signals: An enhanced structural probability of default model,” www.spcapitaliq.com. Standard & Poor’s Financial Services (S&P), 2017, “S&P’s Global Ratings Corporate Criteria,” www.spcapitaliq.com. Vassalou, M., and Y. Xing, 2004, “Default risk and equity returns,” The Journal of Finance, 59 (2), 831-868. Verma, S., 2017, “The Great Escape: How the Big Three Credit Raters Ducked Reform,” Bloomberg Markets 26 (4), 17-19.
27
Table 1 Summary Statistics Panel A. Mean Offering Yields of Straight and Convertible Bonds Straight Bonds
Convertible Bonds
Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Mean Yield (%) 10.14 8.71 7.71 8.43 6.38 8.26 8.81 8.21 8.96 9.92 8.47 7.82 7.35 6.69 7.06 7.64 7.49 8.37 9.59 8.22 7.65 6.91 6.42 6.10 6.06
N 1 5 4 3 5 8 32 88 76 29 115 100 136 125 103 79 79 38 103 145 119 170 191 154 166
Mean Yield (%) 8 . 6 5 5.13 5.56 6.64 5.18 5.40 5.03 4.43 4.62 3.53 3.15 3.92 2.86 2.79 3.84 5.56 3.94 3.77 4.34 2.55 3.16 2.91
N 1 0 1 1 2 6 9 5 9 10 40 25 69 59 33 51 54 20 29 32 46 27 60 56 49
Total
7.45
2074
3.63
694
All bonds are fixed coupon rate Rule 144A corporate bonds obtained from S&P’s Capital IQ database. N is the number of bonds.
28
Table 1 Summary Statistics Panel B. Credit Rating Distribution of S&P and Bloomberg Straight Bonds IG - Investment Grade N Ratings (S&P)
N (Bloomberg)
IG1 (AAA) IG2 (AA+) IG3 (AA) IG4 (AA-) IG5 (A+) IG6 (A) IG7 (A-) IG8 (BBB+) IG9 (BBB) IG10 (BBB-) Sub-Total
5 1 7 13 24 59 54 99 149 129 540
3 8 43 63 85 141 192 252 242 197 1226
Total
1790
1648
HY - High Yield N Ratings (S&P) HY1 (BB+) 175 HY2 (BB) 233 HY3 (BB-) 265 HY4 (B+) 251 HY5 (B) 224 HY6 (B-) 77
1225
DS - Distressed N (Bloomberg) 169 129 64 33 7 8
410
Ratings DS1 (CCC+) DS2 (CCC) DS3 (CCC) DS4(CC) DS5 (C) DDD (D)
N (S&P)
N (Bloomberg)
14 4 0 5 0 2
8 3 1 0 0 0
25
12
Comparable long-term credit rating symbols of S&P are located in the parenthesis. S&P’s ratings are collected from Capital IQ and Bloomberg default risk ratings from Bloomberg L.P. N is the number of rated bonds.
29
Table 1 Summary Statistics Panel B. Credit Rating Distribution of S&P and Bloomberg Convertible Bonds IG - Investment Grade N N Ratings (S&P) (Bloomberg) IG1 (AAA) IG2 (AA+) IG3 (AA) IG4 (AA-) IG5 (A+) IG6 (A) IG7 (A-) IG8 (BBB+) IG9 (BBB) IG10 (BBB-)
0 0 0 0 3 7 1 14 29 22
2 11 15 26 35 47 76 69 88 81
Sub-Total
76
450
Total
260
620
HY - High Yield N Ratings (S&P)
N (Bloomberg)
HY1 (BB+) HY2 (BB) HY3 (BB-) HY4 (B+) HY5 (B) HY6 (B-)
21 26 51 38 20 16
67 44 30 16 8 4
172
169
Comparable long-term credit rating symbols of S&P are located in the parenthesis. S&P’s ratings are collected from Capital IQ and Bloomberg default risk ratings from Bloomberg L.P. N is the number of rated bonds.
30
DS - Distressed N Ratings (S&P) DS1 (CCC+) 8 DS2 (CCC) 1 DS3 (CCC) 1 DS4(CC) 2 DS5 (C) 0 DDD (D) 0
12
N (Bloomberg) 0 1 0 0 0 0
1
Table 2 Issue and Issuer Characteristics Panel A. Mean of Issue and Issuer Characteristics Straight Bonds Maturity (years) Yield Spread (bps) Issue Amount ($m) DRSK MSPD Bloomberg Rating S&P Rating Total Assets ($m) Market-to-Book Ratio Market Capitalization ($m) Profitability Ratio Tangible Asset Ratio Interest Coverage Ratio Long-Term Debt Ratio Beta Idiosyncratic Volatility Age (years) Bank Loan Ratio
Mean 9.23 410.79 452.06 0.0057 0.0219 14.31 11.22 30270.58 2.79 31335.54 0.1224 0.3615 21.46 0.3550 1.25 0.0237 24.66 0.1506
Convertible Bonds N 2074 2074 2074 1648 2067 1648 1790 2074 2002 2074 1963 2009 1859 1970 1624 1624 1964 1643
Mean 10.55 12.83 273.70 0.0060 0.0203 14.30 10.83 3463.42 4.40 3160.42 0.0331 0.2384 163.57 0.2897 1.65 0.0299 22.74 0.2139
N 694 694 694 620 686 620 260 692 650 691 649 653 477 597 635 635 669 462
When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1.
31
Table 2 Issue and Issuer Characteristics Panel B. Issue Summary Statistics Straight Bonds
Convertible Bonds
Industry
N
Percent
N
Percent
Industrials Utilities Financials Total
1512 328 234 2074
72.9 15.81 11.28 100
516 65 113 694
74.35 9.37 16.28 100
Seniority Level
N
Percent
N
Percent
Senior Secured Senior Subordinate Senior Unsecured Subordinate Junior Subordinate Total
186 1633 255 0 0 2074
8.97 78.74 12.30 0 0 100
2 187 482 14 5 694
0.29 27.10 69.86 2.03 0.72 100
Registered Bonds Registered Unregistered Total Callable Bonds
N 1625 449 2074 N
Percent 78.35 21.65 100 Percent
N 557 137 694 N
Percent 80.26 19.74 100 Percent
Callable Non-Callable Total
1875 199 2074
90.41 9.59 100
256 438 694
36.89 63.11 100
Defaulted Bonds
N
Percent
N
Percent
Defaulted Un-defaulted Total
45 2029 2074
2.17 97.83 100
12 682 694
1.73 98.27 100
Bonds with Protective Covenants Covenants No Covenants Total
N 401 1673 2074
Percent 19.33 80.67 100
N 290 404 694
Percent 41.79 58.21 100
N is the number of bonds. We obtain issue-specific variables such as credit ratings, MSPD, maturity, offering yield, and issue amount from Capital IQ, Bloomberg letter ratings and 1-year default probability of the issuer (DRSK) from Bloomberg, issuer-specific financial variables such as total assets, market-to-book ratio, and long-term debt ratio from COMPUSTAT, and idiosyncratic stock return volatility from CRSP.
32
Table 3 T-test Results Mean
N
Mean Difference
T-Statistics
DRSK (SB) DRSK (CB) MSPD (SB) MSPD (CB)
0.0057 0.0060 0.0219 0.0203
1648 620 2067 686
-0.0003
(-0.39)
0.0016
(0.6500)
S&P's Rating (SB) S&P's Rating (CB)
11.22 10.83
1790 260
0.39
(2.00)**
Bloomberg Rating (SB) Bloomberg Rating (CB) S&P's Rating (SB) Bloomberg Rating (SB)
14.31 14.29 11.22 14.31
1648 620 1790 1648
0.02
(0.11)
-3.09
(-31.45)***
S&P's Rating (CB) Bloomberg Rating (CB)
10.83 14.29
260 620
-3.46
(-16.14)***
DRSK (SB) MSPD (SB) DRSK (CB) MSPD (CB)
0.0057 0.0219 0.0060 0.0203
1648 2067 620 686
-0.0162
(-11.55)***
-0.0143
(-6.37)***
Offering Yield (SB) Offering Yield (CB)
7.45 3.63
2074 694
3.82
(40.41)***
Yield Spread (SB) Yield Spread (CB) Issue Amount (SB) Issue Amount (CB)
410.79 12.83 452.06 273.70
2074 694 2074 694
397.96
(38.41)***
178.36
(10.16)***
Total Assets (SB) Total Assets (CB)
30270.58 3463.42
2074 692
26807.16
(2.51)**
DRSK (Defaulted) DRSK (Undefaulted) MSPD (Defaulted) MSPD (Undefaulted)
0.0263 0.0055 0.0938 0.0200
29 2239 56 2697
0.0207
(7.77)***
0.0738
(10.11)***
S&P's Rating (Defaulted) S&P's Rating (Undefaulted)
8.37 11.21
27 2023
-2.84
(-4.99)***
Bloomberg Rating (Defaulted) Bloomberg Rating (Undefaulted) DRSK (Defaulted) MSPD (Defaulted)
11.24 14.34 0.0263 0.0938
29 2239 29 56
-3.10
(-5.95)***
-0.0675
(-2.46)**
S&P's Rating (Defaulted) Bloomberg Rating (Defaulted)
8.37 11.24
27 29
-2.87
(-3.89)***
33
SB stands for straight bonds and CB convertible bonds. DRSK and MSPD show the probability of default of the bond issuers in decimal. When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1. The unit of the offering yield is % and that of the yield spread is basis points. The unit of the issue amount and total assets is millions of dollars.
34
Table 4 Impact of Credit Ratings on Offering Yields Variable Market to Book Ratio Profitability Ratio Tangible Asset Ratio Interest Coverage Ratio Long-Term Debt Ratio Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk Treasury Yield S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Straight Bond Financial Crisis Issuer Credit Rating (S&P) Letter Rating (Bloomberg) N R-SQ
Model 1 0.148 (0.16) -421.331 (-5.37)*** 24.426 (1.18) 0.002 (0.10) 106.889 (3.51)*** -9.318 (-0.97) -5.042 (-0.72) -42.054 (-7.34)*** 4,027.107 (8.02)*** 0.365 (8.01)*** 3.971 (4.42)*** 0.546 (3.18)*** 14.097 (0.83) -9.616 (-0.81) 427.325 (24.43)*** 81.967 (2.99)***
1,702 0.659
Model 2
-9.086 (-0.83) -20.397 (-2.28)** -5.546 (-1.58) 1,985.337 (4.58)*** 0.496 (7.40)*** 6.434 (5.73)*** 0.696 (4.47)*** -34.292 (-2.29)** -10.146 (-0.93) 431.578 (19.76)*** 52.455 (2.48)** -35.733 (-12.56)*** 1,751 0.660
Model 3
-1.375 (-0.16) -31.797 (-3.18)*** -27.236 (-5.68)*** 1,391.561 (3.54)*** 0.230 (4.25)*** 3.077 (2.79)*** 0.363 (1.85)* -9.994 (-0.64) -25.111 (-2.07)** 434.082 (26.44)*** 79.232 (2.87)*** -25.453 (-9.79)*** 2,074 0.654
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1.
35
Table 5 Impact of Credit Ratings on Yield Spreads
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Straight Bond Financial Crisis Issuer Credit Rating (S&P) Letter Rating (Bloomberg) N R-SQ
Model 1 -40.296 (-3.68)*** -13.654 (-1.50) -1.301 (-0.34) 919.209 (2.37)** 3.510 (2.60)** 1.532 (6.12)*** 0.219 (0.02) -27.647 (-2.22)** 273.991 (6.06)*** 33.960 (1.30) -46.023 (-17.26)***
Model 2 -71.522 (-4.86)*** -18.441 (-1.74)* -32.527 (-6.20)*** 470.962 (0.93) -2.900 (-1.56) 1.387 (3.51)*** 28.173 (1.39) -71.060 (-5.75)*** 277.253 (8.89)*** 66.021 (1.59) -28.922 (-10.15)*** 1,750 0.451
1,593 0.596
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1.
36
Table 6 Impact of Market-Based Credit Risk Models on Yield Spreads
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Straight Bond Financial Crisis MSPD (S&P) DRSK (Bloomberg) N R-SQ
Model 1 -75.087 (-5.43)*** -17.040 (-1.60) -30.434 (-5.44)*** 3,110.766 (7.12)*** -2.313 (-1.34) 1.880 (4.67)*** 64.331 (3.68)*** -55.400 (-4.48)*** 251.984 (9.02)*** 58.878 (1.50) 1,344.877 (2.72)***
Model 2 -79.030 (-5.08)*** -17.032 (-1.54) -35.997 (-6.34)*** 1,983.467 (3.85)*** -2.215 (-1.19) 1.522 (3.46)*** 48.336 (2.16)** -61.783 (-5.41)*** 270.112 (8.72)*** 44.726 (1.00) 4,103.692 (4.60)*** 1,750 0.412
1,896 0.411
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. MSPD stands for S&P’s market signal probability of default of the bond issuer, and DRSK is 1year default probability of the bond issuer by Bloomberg. Both MSPD and DRSK present the default probability of the bond issuers and they are based on the Merton Model (1974).
37
Table 7 Impact of Credit Ratings on Yields and Yield Spreads for Straight Bonds
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk Treasury Yield S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Financial Crisis Issuer Credit Rating (S&P) Letter Rating (Bloomberg) N R-SQ
Model 1 -33.536 (-3.19)*** -11.312 (-1.08) 0.524 (0.11) 1,525.314 (3.39)*** 4.103 (3.19)*** 1.492 (6.34)*** 10.459 (0.82) -34.756 (-2.85)*** 49.466 (1.95)*
Model 2 6.824 (0.68) -14.436 (-1.48) -5.909 (-1.58) 2,429.654 (4.76)*** 0.581 (11.56)*** 6.282 (5.51)*** 0.749 (4.90)*** -19.456 (-1.36) -12.468 (-1.16) 71.281 (4.27)***
-48.654 (-20.18)***
-40.884 (-17.94)***
1,498 0.636
1,501 0.610
Model 3 -62.672 (-3.76)*** -10.585 (-0.94) -37.455 (-6.56)*** 1,053.246 (1.84)* -3.100 (-1.76)* 1.420 (3.61)*** 46.558 (2.23)** -81.781 (-5.72)*** 85.477 (1.85)*
Model 4 16.330 (1.42) -15.024 (-1.44) -37.993 (-7.25)*** 2,291.872 (4.28)*** 0.304 (6.14)*** 1.963 (1.85)* 0.308 (1.59) 0.341 (0.02) -30.307 (-2.41)** 109.266 (3.59)***
-31.523 (-10.65)***
-27.633 (-8.86)***
1,487 0.469
1,490 0.514
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. The dependent variable is the offering yields of the new bonds in Models 2 and 4 and the yield spreads in Models 1 and 3. When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1.
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Table 8 Impact of Credit Ratings on Yields and Yield Spreads for Convertible Bonds
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk Treasury Yield S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Financial Crisis Issuer Credit Rating (S&P) Letter Rating (Bloomberg) N R-SQ
Model 1 -52.949 (-1.22) -78.545 (-4.12)*** 43.982 (3.38)*** -1,523.351 (-1.93)* 2.515 (0.48) 1.337 (1.89)* -64.092 (-1.36) 4.973 (0.12) -51.676 (-1.08)
Model 2 -66.059 (-2.12)** -92.158 (-6.94)*** 48.077 (4.86)*** -283.134 (-0.50) 0.323 (2.10)** 10.072 (3.44)*** 0.380 (0.76) -16.941 (-0.57) -17.278 (-0.54) -72.363 (-1.88)*
-10.171 (-1.03)
-9.797 (-1.43)
95 0.436
250 0.425
Model 3 -71.301 (-2.75)*** -93.336 (-5.46)*** 13.316 (1.83)* -839.226 (-1.38) -0.876 (-0.28) 1.149 (2.24)** -44.341 (-1.65) -48.827 (-1.47) -38.149 (-1.08)
Model 4 -34.335 (-1.38) -108.160 (-8.10)*** 19.680 (3.12)*** -166.982 (-0.32) 0.135 (1.18) 6.068 (2.86)*** 0.354 (0.83) -1.224 (-0.06) -29.849 (-1.01) -14.613 (-0.42)
-9.752 (-1.62)
-13.934 (-3.32)***
263 0.306
584 0.386
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. The dependent variable is the offering yields of the new bonds in Models 2 and 4 and the yield spreads in Models 1 and 3. When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1.
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Table 9 Impact of Market-Based Credit Risk Models on Yields and Yield Spreads for Straight Bonds
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk Treasury Yield S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Financial Crisis MSPD (S&P) DRSK (Bloomberg) N R-SQ
Model 1 -69.454 (-4.51)*** -8.788 (-0.77) -36.451 (-6.10)*** 3,995.296 (7.27)*** -2.512 (-1.48) 1.932 (4.72)*** 78.285 (4.26)*** -60.378 (-4.32)*** 78.228 (1.77)* 1,325.351 (2.44)** 1,619 0.415
Model 2 13.633 (1.20) -17.035 (-1.64) -37.177 (-7.20)*** 4,894.795 (7.91)*** 0.295 (5.15)*** 3.115 (2.69)*** 0.529 (2.87)*** 17.129 (1.13) -15.436 (-1.21) 114.282 (4.16)*** 1,020.973 (2.34)** 1,624 0.452
Model 3 -72.280 (-4.13)*** -11.091 (-0.92) -40.365 (-6.40)*** 2,984.072 (5.26)*** -2.463 (-1.35) 1.559 (3.36)*** 67.062 (2.84)*** -68.444 (-5.39)*** 59.099 (1.13)
Model 4 11.933 (1.00) -16.877 (-1.54) -39.835 (-6.96)*** 3,840.38 (5.83)*** 0.271 (4.68)*** 2.707 (2.57)** 0.337 (1.52) 15.308 (0.79) -16.099 (-1.46) 87.777 (2.56)**
4,514.273 (4.76)*** 1,487 0.418
4,486.798 (4.83)*** 1,490 0.476
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. The dependent variable is the offering yields of the new bonds in Models 2 and 4 and the yield spreads in Models 1 and 3. MSPD stands for S&P’s market signal probability of default of the bond issuer, and DRSK is 1-year default probability of the bond issuer by Bloomberg. Both MSPD and DRSK present the default probability of the bond issuers and they are based on the Merton Model (1974).
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Table 10 Impact of Market-Based Credit Risk Models on Yields and Yield Spreads for Convertible Bonds
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk Treasury Yield S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Financial Crisis MSPD (S&P) DRSK (Bloomberg) N R-SQ
Model 1 -69.250 (-2.77)*** -90.944 (-5.62)*** 20.017 (3.01)*** -284.701 (-0.37) 0.011 (0.00) 1.347 (2.88)*** -26.864 (-1.06) -38.716 (-1.34) -48.601 (-1.50) 1,177.786 (2.37)** 277 0.322
Model 2 -55.735 (-2.16)** -119.229 (-9.75)*** 21.821 (3.76)*** 433.004 (0.80) 0.261 (2.36)** 8.230 (3.77)*** 0.214 (0.53) 18.888 (0.78) -49.795 (-2.02)** -15.027 (-0.45) 758.540 (1.57) 626 0.394
Model 3 -69.689 (-2.85)*** -84.267 (-5.15)*** 9.118 (1.22) -1,032.813 (-1.27) -0.749 (-0.26) 1.175 (2.46)** -35.697 (-1.29) -46.192 (-1.39) -47.381 (-1.31)
Model 4 -32.834 (-1.32) -106.248 (-8.03)*** 14.603 (2.49)** -122.599 (-0.20) 0.145 (1.25) 6.731 (3.15)*** 0.413 (0.97) 3.287 (0.15) -27.020 (-0.96) -29.077 (-0.88)
2,571.796 (2.38)** 263 0.322
3,522.263 (2.34)** 584 0.393
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. The dependent variable is the offering yields of the new bonds in Models 2 and 4 and the yield spreads in Models 1 and 3. MSPD stands for S&P’s market signal probability of default of the bond issuer, and DRSK is 1-year default probability of the bond issuer by Bloomberg. Both MSPD and DRSK present the default probability of the bond issuers and they are based on the Merton Model (1974).
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Table 11 Default Prediction Power for Different Credit Risk Models with Probit Models
Variable Log (Issue Amount) Log (Issuer Total Assets) Log (Issuer Age) Idiosyncratic Risk S&P 500 Volatility Index Bond Market Spreads Bond Seniority Issuer Credit Rating (S&P) Letter Ratings (Bloomberg) MSPD (S&P) DRSK (Bloomberg) N Pseudo R-SQ
Model 1 0.173 (1.88)* 0.679 (3.09)*** 0.252 (0.51) 9.967 (1.35) -0.103 (-1.96)** -0.003 (-0.67) -1.585 (-1.38)
1.917 (1.64) 24.526 (2.68)*** 2,065 0.710
Model 2 0.327 (2.01)** 1.122 (6.66)*** -1.484 (-1.61) 3.194 (0.19) -0.449 (-3.48)*** -0.007 (-0.54) 1.108 (1.57) 0.067 (0.35) -1.282 (-2.84)***
Model 3 0.150 (1.42) 0.517 (5.04)*** -0.368 (-1.67)* 7.158 (1.46) -0.073 (-1.11) 0.009 (1.83)* -0.452 (-0.55) -0.141 (-1.70)*
Model 4 0.233 (1.60) 0.694 (3.50)*** 0.337 (0.78) 8.784 (0.83) -0.186 (-3.15)*** -0.005 (-0.66) -1.096 (-1.10) -0.342 (-5.16)***
2.262 (1.16) 1,615 0.849
1,747 0.732
10.330 (1.09) 2,070 0.736
Test statistics (z values) are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. The dependent variable is equal to one for defaulted bonds and 0 otherwise. MSPD stands for S&P’s market signal probability of default of the bond issuer, and DRSK is 1-year default probability of the bond issuer by Bloomberg. Both MSPD and DRSK present the default probability of the bond issuers and they are based on the Merton Model (1974).
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Table 12 Endogeneity Tests
Variable Log (Maturity) Log (Issue Amount) Log (Issuer Total Assets) Idiosyncratic Risk (Instrument Variable = Beta) Treasury Yield S&P 500 Volatility Index Bond Market Spreads Callable Registered Bond Straight Bond Financial Crisis Issuer Credit Rating (S&P) Letter Rating (Bloomberg) N R-SQ Durbin Wu-Hausman
Model 2 -15.098 (-1.77)* -20.542 (-4.78)*** -3.736 (-1.35)
Model 3 -20.514 (-2.01)** -26.146 (-5.08)*** -35.023 (-10.82)***
499.834 (0.80)
-5,531.699 (-4.10)***
0.539 (15.43)*** 7.353 (9.61)*** 0.767 (5.36)*** -35.029 (-3.14)*** -11.222 (-1.25) 428.364 (37.44)*** 53.503 (3.47)*** -39.919 (-17.61)***
0.313 (8.73)*** 4.587 (5.47)*** 0.228 (1.41) -15.361 (-1.22) -36.427 (-3.51)*** 400.722 (29.76)*** 96.769 (5.42)***
1,752 0.654 6.932*** 6.904***
-48.285 (-10.28)*** 2,075 0.565 35.384*** 35.756***
Test statistics are reported in the parentheses. The ***, **, * denote statistical significance at the 1, 5, and 10% levels respectively. When it comes to the credit ratings of S&P and Bloomberg, the letter ratings are converted into numeric ratings. The ratings are defined as: AAA = 22, AA+ = 21, AA = 20, AA- = 19, A+ = 18, A= 17, A- = 16, BBB+ = 15, BBB = 14, BBB- = 13, BB+ = 12, BB = 11, BB- = 10, B+ = 9, B = 8, B- = 7, CCC+ = 6, CCC = 5, CCC- = 4, CC = 3, C = 2, and D = 1.
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Appendix: Bloomberg Ratings, 1-Year Default Probability (DRSK), and S&P's Ratings IG - Investment Grade
HY - High Yield
DS - Distressed
Credit Ratings
1-Yr Default Prob.
Credit Ratings
1-Yr Default Prob.
Credit Ratings
1-Yr Default Prob.
IG1 (AAA) IG2 (AA+) IG3 (AA) IG4 (AA-) IG5 (A+) IG6 (A) IG7 (A-) IG8 (BBB+) IG9 (BBB) IG10 (BBB-)
0.0000% - 0.0020% 0.0020% - 0.0040% 0.0040% - 0.0080% 0.0080% - 0.0152% 0.0152% - 0.0286% 0.0286% - 0.0529% 0.0529% - 0.0960% 0.0960% - 0.1715% 0.1715% - 0.3000% 0.3000% - 0.5200%
HY1 (BB+) HY2 (BB) HY3 (BB-) HY4 (B+) HY5 (B) HY6 (B-)
0.52% - 0.88% 0.88% - 1.50% 1.50% - 2.40% 2.40% - 4.00% 4.00% - 6.00% 6.00% - 10.00%
DS1 (CCC+) DS2 (CCC) DS3 (CCC-) DS4 (CC) DS5 (C) DDD (D)
10.0% - 15.0% 15.0% - 22.0% 22.0% - 30.0% 30.0% - 50.0% 50.0% - 100.0% Defaulted
Comparable long-term credit rating symbols of S&P are located in the parenthesis.
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