WPS5319 Policy Research Working Paper 5319 Is There a Distress Risk Anomaly? Pricing of Systematic Default Risk in the Cross Section of Equity Returns Deniz Anginer Çelim Yıldızhan The World Bank Development Research Group Finance and Private Sector Development Team May 2010 Policy Research Working Paper 5319 Abstract The standard measures of distress risk ignore the fact premia, that is stocks with higher systematic default that firm defaults are correlated and that some defaults risk exposures, have higher expected equity returns. are more likely to occur in bad times. The paper uses Consistent with structural models of default, they show risk premium computed from corporate credit spreads that the premium to a high-minus-low systematic default to measure a firm’s exposure to systematic variation in risk hedge portfolio is largely explained by the market default risk. Unlike previously used measures that proxy factor. The authors confirm the robustness of these results for a firm’s physical probability of default, credit spreads by using an alternative systematic default risk factor for proxy for a risk-adjusted default probability and thereby firms that do not have bonds outstanding. The results explicitly account for the non-diversifiable component of show no evidence of firms with high systematic default distress risk. In contrast to prior findings in the literature, risk exposure delivering anomalously low returns. the authors find that stocks that have higher credit risk This paper—a product of the Finance and Private Sector Development Team, Development Research Group—is part of a larger effort in the department to understand the asset pricing implications of systematic credit risk.. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at danginer@ worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Is there a Distress Risk Anomaly? Pricing of Systematic Default Risk in the Cross Section of Equity Returns Deniz Anginer and Çelim Yıldızhan 1 JEL Classifications: G11, G12, G13, G14. Keywords: Default risk, systematic default risk, credit risk, distress risk, bankruptcy, credit spread, asset-pricing anomalies, pricing of default risk, corporate bonds 1 Deniz Anginer can be reached at Pamplin School of Business, Virginia Tech, Blacksburg, VA, 24061, Email:danginer@vt.edu. Çelim Yıldızhan can be reached at Terry College of Business, University of Georgia, Athens, GA, 30602, E-mail: celim@uga.edu. We would like to thank Alexander Barinov, Tobias Berg, Sugato Bhattacharyya, Dennis Capozza, Ilia Dichev, Stu Gillan, Jack He, Jens Hilscher, Sara Holland, Alex Hsu, Paul Irvine, Haitao Li, Jim Linck, Russell Lundholm, Harold Mulherin, Jeff Netter, Shawn Park, Paolo Pasquariello, Bradley Paye, Annette Poulsen, Amiyatosh Purnanandam, Uday Rajan, Nejat Seyhun, Tao Shu, Tyler Shumway, Jeff Smith, Ralph Steuer, Ginger Wu, Julie Wu, Lu Zhang, and seminar participants at the University of Michigan, University of Georgia, Virginia Tech, World Bank, University of Delaware, BlackRock, Wilfrid Laurier, University of Connecticut, CFTC, Cornerstone Research, Ozyegin Universitesi, Sabanci Universitesi, 37th EFA Annual Meeting for helpful discussion and guidance. 1. Introduction A fundamental tenet of asset pricing is that investors should be compensated with higher returns for bearing systematic risk that cannot be diversified. As default risk remains a major source of potential large losses to equity investors, a number of recent papers have examined whether default risk is a systematic risk and whether it is priced in the cross section of equity returns. From a theoretical perspective, default risk can be a priced factor if a firm’s capital asset pricing model (CAPM) beta does not fully capture default- related risk. Empirical work has focused on determining the probability of firms failing to meet their financial obligations using accounting and market-based variables and testing to see if estimated default probabilities are related to future realized returns. The existing empirical evidence contradicts theoretical expectations and suggests that firms with high default risk earn significantly lower average returns. 2 The low returns on stocks with high default risk cannot be explained by Fama-French (1993) risk factors. Stocks with high distress risk tend to have higher market betas and load more heavily on size and value factors. This leads to significantly negative alphas for the high-minus-low default risk hedge portfolio and makes the anomaly even larger in magnitude. These empirical results provide a challenge to the standard risk-reward trade- off in financial markets and to the contention that small firms and value firms earn high average returns because they are financially distressed (Chan and Chen 1991; Fama and French 1996; Kapadia 2011). We argue that the anomalous results documented in the literature are due to incorrectly measuring systematic default risk. Figure 1, which plots the historical default 2 See for example Dichev (1998) and Campbell, Hilscher, and Szilagyi (2008) for a discussion of this anomaly. 2 rates on Moody’s rated corporate issuers, suggests that default rates are highly dependent on the stage of the business cycle. This casual analysis of the historical data suggests that there is an important systematic component of default risk and that the incidence of �nancial distress is correlated with macroeconomic shocks such as major recessions. Previous papers measure financial distress by determining firms’ expected probabilities of default inferred from historical default data. This calculation ignores the fact that firm defaults are correlated and that some defaults are more likely to occur in bad times, and therefore fails to appropriately account for the systematic nature of default risk. Investors, however, will take into account the covariance of default losses from a company with the rest of the assets in their portfolio when pricing distress risk. We use credit risk premium computed from corporate credit spreads to proxy for a firm’s exposure to the non-diversifiable portion of default risk. The fixed-income literature provides evidence of a significant risk premium component in corporate credit spreads, justifying our use of this measure as a proxy for firm exposure to systematic default risk. 3 It has been well-documented (Almeida and Philippon 2007; Berndt, Duffie, Ferguson and Schranz 2005; Hull, Predescu, and White 2004) that there is a substantial difference between the risk-adjusted (or risk-neutral, as commonly designated in contingent claim pricing) and physical probabilities of default. Ranking stocks based on their physical default probabilities inferred from historical default data—as done in Dichev (1998), Campbell, Hilscher, and Szilagyi (2008), and others in this literature— implicitly assumes that stocks with high physical probabilities of default also have high 3 The spread between corporate bond yields and maturity-matched treasury rates is too high to be fully captured by expected default and has been shown to contain a large risk premium for systematic default risk. See, for detailed analysis, Elton et al. (2001), Huang and Huang (2003), Longstaff et al. (2005), Driessen (2005), and Berndt et al. (2005). 3 exposures to systematic variation in default risk. George and Hwang (2010) show that a firm’s physical probability of default does not necessarily reflect its exposure to systematic default risk. In fact, George and Hwang (2010) show that firms with higher sensitivities to systematic default risk make capital structure choices that reduce their physical probabilities of distress. It is therefore not correct to rank firms based on their physical default probabilities when pricing financial distress, because such a ranking does not properly reflect firms’ exposures to systematic default risk, the only type of default risk that should be rewarded with a premium. Moreover, previous papers have shown that three stock characteristics—high idiosyncratic volatility, high leverage, and low profitability—are associated with high historical default rates. However, these are the same characteristics that are known to be associated with low expected future returns. Within the q-theory framework (Cochrane 1991; Liu, Whited and Zhang 2009), low profitability (more likely to default) firms have low expected future returns. Similarly, firms with high leverage (more likely to default) and high idiosyncratic volatility (more likely to default) have low expected future stock returns (Korteweg 2010; Dimitrov and Jain 2008; Penman, Richardson and Tuna 2007; Ang, Hodrick, Xing and Zhang 2009). It is not clear if the distress anomaly is at least partially attributable to one or more of these previously documented return relationships. 4 4 There is a strong relationship between distress risk and the three stock characteristics. When we form quintile portfolios sorted on historical probabilities of default -computed using coefficients from Column 1 of Table 2-, idiosyncratic volatility increases monotonically from 2.5% for the lowest distress group to 4.5% for the highest distress group. Leverage increases from 0.22 for the lowest distress group to 0.61 for the highest distress group. Similarly, profitability for the lowest distress group is 1.2% and decreases monotonically to -1.1% for the highest distress group. The 3-factor alpha for the zero cost portfolio formed by going long high distress stocks and shorting low distress stocks is -1.078% per month, yet this premium decreases to -0.36% after controlling for leverage. When we control for idiosyncratic volatility, the return spread between high and low distress stocks reduces to -0.29%. Finally, controlling for profitability reduces the spread to -0.29% per month, making it statistically insignificant. 4 We take a different approach and use a market-based measure, credit risk premium computed from corporate credit spreads, to proxy for systematic default risk exposure. We compute credit spreads as the difference between the bond yield of the firm and the corresponding maturity-matched treasury rate. We then compute credit risk premium by taking into account expected losses, taxes, and liquidity effects (Elton, Gruber, Agrawal and Mann 2001; Chen, Lesmond, and Wei 2007; Driessen and de Jong 2007) and using only the fraction of the spread that is due to systematic default risk exposure. This measure offers two distinct advantages over others that have been used in the literature. First, unlike stock characteristics used to measure default risk, which may reflect information about future returns unrelated to distress risk, credit spreads reflect the market consensus view of the credit risk of the underlying firm. Second, credit spreads contain risk premium for systematic default risk, and are a proxy for the market-implied risk-adjusted probability of default. Using credit risk premia sorted portfolios, we find that firms with higher exposures to systematic default risk have higher expected equity returns. This premium is subsumed by the market factor, as predicted by structural models of default and rational asset pricing theory, and is further reduced economically and statistically by the Fama-French risk factors. Our measure of systematic default risk exposure, calculated from credit spreads, limits the sample of firms to those that have issued corporate bonds. To ensure the robustness of our results, we show that when firms are ranked based on their physical default probabilities, as previously done in the literature, the distress anomaly is also observed in the Bond sample. To further alleviate sample selection issues, we extend the analysis to the full CRSP-COMPUSTAT sample. We compute a measure of systematic 5 default risk exposure for all firms regardless of whether they have bonds outstanding. Following Hilscher and Wilson (2010), we assume a single factor structure for default risk and measure a firm’s systematic default risk exposure as the sensitivity of its default probability to the common factor. We refer to the common factor as the systematic default risk factor, and the sensitivity of a firm’s default probability to the common factor as its systematic default risk beta. First, we verify that systematic default risk beta is significantly priced in the cross section of corporate bond risk premia, justifying our use of corporate bond risk premium as a measure of systematic default risk exposure. This relationship is robust to controlling for bond ratings, physical default probabilities, accounting variables, market variables, and structural model parameters. Second, and differently from Hilscher and Wilson (2010), we form decile portfolios by sorting all equities in the CRSP-COMPUSTAT sample based on their systematic default risk betas. Consistent with the bond sample results, we find that the portfolio with the highest systematic default risk exposure has higher equity returns than the lowest systematic default risk exposure portfolio. Moreover, we find that once we control for the market factor, the difference in returns between the highest and lowest systematic default risk portfolios becomes insignificant. In our analyses of the sample of firms with bonds outstanding and of the full CRSP- COMPUSTAT sample, we find no evidence of firms with high systematic default risk exposure delivering anomalously low equity returns. These results are consistent with the basic structural models of default in which aggregate risk factors drive default probabilities as well as the returns on bonds and equities (Merton 1974; Campello, Chen and Zhang 2008). 6 Ours is not the first paper to study the relationship between default risk and equity returns. Dichev (1998) uses Altman’s z-score and Ohlson’s o-score to measure financial distress. He finds a negative relationship between default risk and equity returns for the 1981–1995 time period. In a related study, Griffin and Lemmon (2002), using the o- score to measure default risk, find that growth stocks with high probabilities of default have low returns. Using a comprehensive set of accounting and market-based measures, Campbell, Hilscher, and Szilagyi (2008, hereafter CHS) show that stocks with high risk of default deliver anomalously low returns. Garlappi, Shu, and Yan (2008), who obtain default risk measures from Moody’s KMV, find results similar to those of Dichev (1998) and CHS (2008). They attribute their findings to the violation of the absolute priority rule. Vassalou and Xing (2004) find some evidence that distressed stocks, mainly in the small value group, earn higher returns. 5 George and Hwang (2010) suggest that firms with higher sensitivities to systematic default risk make capital structure choices that reduce their overall physical probabilities of default. They show that when in distress, low leverage firms suffer greater losses and have greater exposures to systematic risk compared to high leverage firms. Avramov, Jostova, and Philipov (2007) show that the negative return for high default risk stocks is concentrated around rating downgrades. Chava and Purnanandam (2010) argue that the poor performance of high distress stocks is limited to the post-1980 period, when investors were positively surprised by defaults. When they use implied cost of capital estimates from analysts' forecasts to proxy for ex-ante expected returns, they find a positive relationship between default risk and expected returns. Kapadia (2011) creates a 5 Da and Gao (2010) argue that Vassalou and Xing’s results are driven by one-month returns on stocks in the highest default likelihood group that trade at very low prices. They show that returns are contaminated by microstructure noise and that the positive one-month return is compensation for increased liquidity risk. 7 portfolio that tracks changes in aggregate firm failure rate in the U.S. He uses the return to the tracking portfolio as an asset pricing factor along with the market risk premium to explain size and value premiums. Our paper contributes to the literature by constructing a default risk measure that ranks equities explicitly based on their exposures to systematic default risk rather than ranking firms based on their physical probabilities of default. The rest of the paper is organized as follows. Section 2 describes the data. Section 3 describes the physical default probability measure used in this study. Section 4 describes the use of credit spreads as a proxy for systematic default risk exposure. Section 5 contains asset pricing tests, in which equities are ranked based on their physical default probabilities and systematic default risk exposures. Section 6 describes the construction and use of an alternative systematic default risk factor and extends the equity return analyses to the full CRSP-COMPUSTAT sample. Finally, Section 7 concludes. 2. Data Corporate bond data used to compute the credit risk-premium in this study comes from three separate databases: the Lehman Brothers Fixed Income Database (Lehman) for the period 1974 to 1997, the National Association of Insurance Commissioners Database (NAIC) for the period 1994 to 2006, and the Trade Reporting and Compliance Engine (TRACE) system dataset for the period 2003 to 2010. We also use the Fixed Income Securities Database (FISD) for bond descriptions. Due to the small number of observations prior to 1980, we include only the period 1980 to 2010 in the analyses that follow. We match the bond information with firm-level accounting and price information obtained from COMPUSTAT and CRSP for the same time period. We exclude financial 8 firms (SIC codes 6000–6999) from the sample. To avoid the influence of microstructure noise, we also exclude firms priced less than one dollar. Our sample includes all U.S. corporate bonds listed in the above datasets that satisfy a set of selection criteria commonly used in the corporate bond literature. 6 We exclude all bonds that are matrix-priced (rather than market-priced) from the sample. We remove all bonds with equity or derivative features (i.e., callable, puttable, and convertible bonds), bonds with warrants, and bonds with floating interest rates. Finally, we eliminate all bonds that have less than one year to maturity. For all selected bonds, we extract beginning of month credit spreads, calculated as the difference between the corporate bond yield and the corresponding maturity-matched treasury rate. There are a number of extreme observations for the variables constructed from the different bond datasets. To ensure that statistical results are not heavily influenced by outliers, we set all observations higher than the 99th percentile value of a given variable to the 99th percentile value. All values lower than the first percentile of each variable are winsorized in the same manner. Using credit spreads we compute credit risk premia (CRP) as described in the next section. For each firm, we then compute a value-weighted average of that firm’s CRP, using market values of the bonds as weights. There are 121,714 firm-months and 1,071 unique firms with CRP and corresponding firm-level accounting and market data. There is no potential survivorship bias in our sample as we do not exclude bonds of firms that have gone bankrupt or bonds that have matured. 6 See for instance Duffee (1999), Collin-Dufresne, Goldstein, and Martin (2001), and Avramov et al. (2007). 9 We use hazard regressions using historical defaults to compute physical default probabilities. Corporate defaults between 1981 and 2010 are identified from the Moody’s Default Risk Services’ Corporate Default database, SDC Platinum’s Corporate Restructurings Database, Lynn M. LoPucki's Bankruptcy Research Database, and Shumway’s (2001) list of defaults. We choose 1981 as the earliest year for identifying defaults because the Bankruptcy Reform Act of 1978 is likely to have caused the associations between accounting variables and the probability of default to change. Furthermore, we have little corporate bond yield information prior to 1980. In all, we obtain a total of 1,290 firm defaults covering the period 1981–2010. We have complete accounting-based measures for 728 of these failures. Of these 728 failures, 118 also have corresponding corporate bond information. For the full CRSP-COMPUSTAT sample as well as for the subsample of firms that have bonds outstanding we use accounting and market-based variables used by CHS (2008) when predicting defaults. The variables we use are the following: NIMTAAVG is a geometrically declining average of past values of the ratio of net income to the market value of total assets; TLMTA is the ratio of total liabilities to the market value of total assets; EXRETAVG is a geometrically declining average of monthly log excess stock returns relative to the S&P 500 index; SIGMA is the standard deviation of daily stock returns over the previous three months; RSIZE is the log ratio of market capitalization to the market value of the S&P 500 index; CASHMTA is the ratio of cash to the market value of total assets; MB is the market-to-book ratio, PRICE is the log price per share truncated at $15 for shares priced above $15; DD is the Merton (1974) “distance-to-default� measure, which is the difference between the asset value of 10 the firm and the face value of its debt, scaled by the standard deviation of the firm’s asset value. These variables are described in detail in the Appendix. The bond sample covers a small portion of the total number of companies, but a substantial portion in terms of total market capitalization. For instance, in the year 1997, the number of firms with active bonds in our sample constitutes about 4% of all the firms in the market. However, in terms of market capitalization, the dataset captures about 40% of aggregate equity market value in 1997. We compute summary statistics for default measures and financial characteristics of the companies in our bond sample and for all companies in CRSP. These results are summarized in Table 1. As not all companies issue bonds, it is important to discuss the limitations of our bond dataset. Not surprisingly, companies in the bond sample are larger and show a slight value tilt. They also have higher profitability, more leverage, and higher equity returns; they hold less cash and are less likely to default. There is, however, significant dispersion in size, market-to-book ratio, default probability, and credit spread values of firms in the bond sample. To ensure that our results are not driven by sample selection, in Section 5, we show that when firms are ranked based on physical default probabilities the distress anomaly is observed in the Bond sample. In Section 6, we extend the analyses to the CRSP/COMPUSTAT sample. 3. Physical Default Probabilities There is a vast literature on modeling the probability of default. In this paper, we utilize dynamic models of default prediction (Shumway 2001; Chava and Jarrow 2004; CHS 2008), that avoid biases of static models by adjusting for potential duration dependence 11 issues. 7 We compute physical default probabilities by estimating a hazard regression using the set of defaults described in the previous section. We use information available at the end of the calendar month to predict defaults 12 months ahead. Specifically, we assume that the probability of default in 12 months, conditional on survival in the dataset for 11 months, is given by: 1 PDti - 1(Yti- 1+ 12 = 1|Yti- 2+ 12 = 0)= (1) 1 + exp (- a 12 - b12X ti - 1 ) where Yti- 1+ 12 is an indicator that equals one if the firm defaults in 12 months conditional on survival for 11 months. X ti - 1 is a vector of explanatory variables available at the time of prediction. We use accounting and market-based variables used in CHS (2008) when predicting defaults. In addition we use Merton’s distance to default measure that has been utilized in a number of previous studies. 8 All the variables included in the hazard regressions are described in detail in the Appendix. We use quarterly accounting variables lagged by two months and market variables lagged by one month to ensure that this information is available at the time of default prediction. We run two sets of hazard regressions, one using the sample of firms in the Bond sample, and the other using all firms in the CRSP-COMPUSTAT sample. As mentioned earlier, to ensure that our results are not driven by sample selection, we construct physical default probabilities for the Bond sample using coefficients obtained from hazard 7 Altman (1968) and Ohlson (1980) are examples of such static models. 8 Merton’s (1974) structural default model treats the equity value of a company as a call option on the company’s assets. The probability of default is based on the “distance-to-default� measure, which is the difference between the asset value of the firm and the face value of its debt, scaled by the standard deviation of the firm’s asset value. There are a number of different approaches to calculating the distance- to-default measure. We follow CHS (2008) and Hillegeist et al. (2004) in constructing this measure, the details of which are provided in the appendix. 12 regressions that use only the firms in the Bond sample. This ensures that the distress anomaly documented by the prior literature exists for the subset of firms that have bonds outstanding. Table 2 reports the results from the hazard regressions. In the first column, we use the same covariates (NIMTAAVG, TLMTA, EXRETAVG, SIGMA, RSIZE, CASHMTA, MB and PRICE) used in CHS (2008) to predict corporate defaults. The sample includes all CRSP-COMPUSTAT firms for the 1980 to 2010 time period. As a comparison, we report the estimates from the CHS (2008) study in column 2. The coefficient estimates from these two regressions are very similar, suggesting that our default dataset, although smaller than the CHS (2008) default dataset, captures a significant portion of the variation in firm defaults. In column 3, we limit the sample to firms with only bonds outstanding. Relative value (MB), liquidity position (CASHMTA), and share price (PRICE) are no longer statistically significant predictors of failure. In the bond sample, relatively larger firms are less likely to default, consistent with the full CRSP- COMPUSTAT sample. We also use Merton’s distance to default (DD) measure as a predictor of defaults in the bond sample (reported in column 6). We obtain qualitatively similar results to those in the full CRSP-COMPUSTAT sample using our own set of defaults (reported in column 4) as well as when compared to CHS (2008) results (reported in column 5). 4. Corporate Spread as a Measure of Systematic Default Risk Exposure In this section, we describe our use of corporate bond risk premia to measure systematic distress risk exposure. 13 There is now a significant body of research that shows that compensation for default risk constitutes a considerable portion of credit spreads. Huang and Huang (2003), using the Longstaff-Schwartz (1995) model, find that distress risk accounts for 39%, 34%, 41%, 73%, and 93% of the corporate bond spread, respectively, for bonds rated AA, A, BAA, BA, and B. Longstaff, Mithal, and Neis (2005) use the information in credit default swaps (CDS) to obtain direct measures of the size of the default and non-default components in corporate spreads. They find that the default component represents 51% of the spread for AAA/AA-rated bonds, 56% for A-rated bonds, 71% for BBB-rated bonds, and 83% for BB-rated bonds. Blanco, Brennan, and Marsh (2005) and Zhu (2006) show significant similarity in the information content of CDS spreads and bond credit spreads with respect to default. They confirm, through co-integration tests, that the theoretical parity relationship between these two credit spreads holds as a long run equilibrium condition. 9 As mentioned earlier, our focus in this paper is on measuring compensation for systematic default risk exposure. We create this measure by extracting the credit risk premium component from the credit spreads. Although credit risk makes up a significant portion of corporate spreads, liquidity risk and taxes have also been shown to be important (Elton et al. 2001; Chen, Lesmond, and Wei 2007; Driessen and de Jong 2007). In computing the credit risk premium, we take into account expected losses, taxes, and liquidity effects, and use only the fraction of the spread that is likely to be due to systematic default risk exposure. We follow Driessen and de Jong (2007), Elton et al. 9 In this study we have chosen to use bond spreads instead of CDS spreads because bond data is available for a substantially larger number of companies and is available for a much longer time period. 14 (2001), and Campello, Chen, and Zhang (2008) and compute the credit risk premium (CRP) for each firm i and month t as: 𝐶𝑅𝑃𝑖,𝑡 = �𝑃𝐷𝑖,𝑡 × �1 − 𝐿𝑖 ,𝑡 � + �1 − 𝑃𝐷𝑖 ,𝑡 �� × �1 + 𝐶𝑌𝑖,𝑡 � (2) −�1 + 𝑌𝐺𝑖 ,𝑡 � − 𝑇𝑋𝑖,𝑡 − 𝐿𝑄𝑖,𝑡 . In Equation (2), PD is the physical probability of default computed from hazard regressions described in Section 3. 10 L is the loss rate in the event of default. We follow Elton et al. (2001) and Driessen and de Jong (2007) and use historical loss rates reported in Altman and Kishore (1998) by rating category. The loss rates vary from 32% for AAA-rated firms to 62% for CCC-rated firms. CY is the corporate bond yield, and YG is the corresponding maturity-matched treasury yield. The equation assumes that all losses are incurred at maturity. Because bond investors have to pay state and local taxes on bond coupons whereas treasury bond investors do not, we also remove this tax differential from the corporate yields. Expected tax costs, TX, are computed as: ��1 − 𝑃𝐷𝑖 ,𝑡 � × 𝐶𝑜𝑢�𝑜𝑛𝑖 ,𝑡 + 𝑃𝐷𝑖 ,𝑡 × �1 − 𝐿𝑖,𝑡 �� × �. (3) The first part of Equation (3) captures the coupon rate, Coupon, conditional on no default. The second part captures the tax refund in the event of default. � is the effective tax rate and following Elton et al. (2001) is set to 4.875%. 10 We compute default probabilities using coefficients obtained from column 3 of Table 2. In computing default probabilities, we use quarterly accounting variables lagged by two months and market variables lagged by one month to ensure that this information is available at the beginning of the month over which default probabilities are measured. 15 The recent literature emphasizes the role of liquidity risk in the pricing of corporate bonds (Driessen and de Jong 2007; Lin, Wang and Wu 2011; Downing, Underwood and Xing 2005). We explicitly account for the liquidity effect in credit spreads by computing liquidity risk premium for each bond in our dataset. The analysis follows Driessen and de Jong (2007) and is based on a linear multifactor asset pricing model in which expected corporate bond returns are explained by their exposure to market risk and liquidity risk factors. 11 We consider two types of liquidity risk, one originating from the equity market and one from the treasury bond market. For the stock market, we use the liquidity innovations of Pastor and Stambaugh (2003); for the treasury market, we use changes in quoted bid-ask spreads on long-term treasury bonds. 12 We compute expected bond returns for 11 rating-maturity groups using equation (2), and use a cross-sectional regression to compute risk premium associated with liquidity innovations in the stock and treasury markets. 13 We then subtract the computed liquidity premium, LQ, from the corporate bond spreads with the corresponding rating and maturity. Table 3 summarizes the computations for different rating-maturity groups. Our results are in line with the findings in the literature (Driessen and de Jong 2007; Elton et al. 2001; Campello, Chen and Zhang 2008). Figure 2 plots the computed expected losses, taxes, and liquidity premium against corporate spreads. In the rest of this paper, we use the portion of credit spreads that compensates for systematic default risk exposure, net of expected losses, taxes, and liquidity premium. We call this variable CRP (Credit Risk Premium). 11 As in Driessen and de Jong (2007) we also included changes in implied market volatility orthogonalized by market returns as an additional factor, and we obtained similar results. 12 We thank Alex Hsu for providing the data on treasury bond bid-ask quotes. 13 We refer to bonds with maturity greater than seven years as having “long maturity� and with maturity less than seven years as having “short maturity.� 16 5. Pricing of Distress Risk 5.1. Physical PD’s and Equity Returns In this section, we analyze the relationship between physical default probabilities and future stock returns using the firms in the CRSP-COMPUSTAT sample and using the firms that have bonds outstanding in the Bond sample. For the CRSP-COMPUSTAT sample we compute default probabilities using coefficients obtained from column 1 of Table 2. 14 For the Bond sample we compute default probabilities using coefficients obtained from column 3 of Table 2. In computing these default probabilities, we use quarterly accounting variables lagged by two months and market variables lagged by one month to ensure that this information is available at the beginning of the month over which default probabilities are measured. We sort stocks in the full CRSP- COMPUSTAT sample into deciles each month from 1981 through 2010 according to their physical default probabilities, and compute value-weighted returns for each portfolio. If a delisting return is available, we use the delisting return; otherwise, we use the last available return in CRSP. We repeat the same analyses for stocks that have bonds outstanding. We construct physical default probabilities in the Bond sample using coefficients obtained from hazard regressions using the bond sample. This analysis ensures that the distress risk anomaly observed in the full CRSP-COMPUSTAT sample also exists for the bond sample when firms are ranked using physical default probabilities. To save space, we report returns for only the top and bottom deciles, and the difference between the top and bottom deciles. 14 We obtain similar results using CHS coefficients computed on a rolling basis (we thank Jens Hilscher for providing this data), Merton’s distance-to-default measure, Ohlson’s o-score and Altman’s z-score, which are not reported to save space. 17 We compute value-weighted returns for these decile portfolios on a monthly basis and regress the portfolio return in excess of the risk-free rate on the market (MKT), size (SMB), value (HML), and momentum (MOM) factors: i rti = a i + bMKT i MK Tt + bSMB i SMBt + bHML i HMLt + bMOM MOM t + eti . (4) In Panel A of Table 4, we report portfolio return results for the CRSP- COMPUSTAT sample. Our results are consistent with those obtained in previous studies. Stocks in the highest default risk portfolio have significantly lower returns. The difference in returns between the highest and lowest default risk portfolios is -1.184% per month. The alphas from the market and the 3- and 4-factor models are economically and statistically significant. The monthly 4-factor alpha for the zero cost portfolio formed by going long on stocks in the highest default risk decile, and short on stocks in the lowest default risk decile is -0.83% per month. Portfolio return analyses that utilize historical default probabilities calculated using coefficients from the bond sample are reported in Panel B of Table 4. The results are weaker for the bond sample, but still economically and statistically significant. Using firms that have credit spread information, the monthly 4-factor alpha for the zero cost portfolio formed by going long on stocks in the highest default risk decile and short on stocks in the lowest default risk decile is -0.49%. Distressed stocks load positively on the size and value factors. The negative loading on the momentum factor is consistent with the intuition that distressed stocks tend to have low returns prior to portfolio formation. As a robustness check, we also compute risk adjusted returns per unit of distress risk for the bond sample as well as for the CRSP-COMPUSTAT sample. One reason that the 18 distress anomaly is smaller in the bond sample is that the companies in the highest distress decile in the CRSP-COMPUSTAT sample have higher default probabilities than the stocks in the highest distress decile in the bond sample. To take into account the differences in default probabilities, we follow CHS (2008) and regress the return of each long-short portfolio onto the differences in log default probabilities including no intercept in the regression. The coefficients from this regression would provide us with a distress premium per unit of log default probability. We use long-short distress portfolio returns adjusted for the Fama–French three-factor model. The coefficient estimate on the log default probability is 6.492 (t-stat = 5.02) for the CRSP-COMPUSTAT sample and 5.657 (t-stat = 3.24) for the bond sample, suggesting that per unit of log default probability, the distress effect is similar in the CRSP-COMPUSTAT and Bond samples. The analyses in this section show that using physical default probabilities computed in the Bond sample and the CRSP-COMPUSTAT sample produces results similar to those of CHS (2008) and others in the literature. The distress anomaly persists in our Bond sample when we use physical probabilities of default to rank firms. 5.2 Credit Risk Premium and Equity Returns In this section, we examine how CRPs (credit risk premia) are related to future realized equity returns. We sort stocks into deciles from 1981 to 2010, using CRPs in the previous month. We compute value-weighted returns for each portfolio and update the portfolios each month. As before, if a delisting return is available we use the delisting return; otherwise we use the last available return in CRSP. To save space, we only report returns for the top and bottom decile portfolios, and the return difference between the top and bottom deciles in Table 5. 19 Our results challenge those obtained in the previous studies. Using CRP’s as a measure of systematic default risk exposure, the difference in raw returns between the highest and lowest default risk portfolios is 0.521% per month and statistically significant. The 4-factor monthly alpha for a portfolio formed by going long on stocks in the highest default risk exposure portfolio and short on stocks in the lowest default risk exposure portfolio is -0.005% and statistically insignificant when we use CRP as our measure of systematic default risk exposure. There is a positive relationship between CRP and raw equity returns, and the return of the high-minus-low excess spread portfolio is statistically significant. CAPM and multi-factor regressions show that alphas are subsumed in all CRP portfolios, suggesting that variation in systematic default risk exposure is captured mainly by the market factor and partly by the size and value factors. The size and value factors have statistically significant positive loadings for the high minus low CRP portfolio suggesting that these factors are intimately related to systematic default risk exposure. These results are consistent with structural models of default in which aggregate risk factors drive default probabilities as well as the returns on bonds and equities (Merton 1974; Campello, Chen and Zhang 2008). Ranking stocks on their physical default probabilities inferred from historical data, as done in Dichev (1998), CHS (2008), and others, implicitly assumes that high default probability stocks also have high exposures to the systematic component of default risk. Using CRP, we explicitly rank firms based on their exposures to the systematic component of default risk and we find no evidence of systematic default risk being negatively priced. 20 6. Alternative Measure of Systematic Default Risk We now extend the analysis of Section 5.2 to the full CRSP-COMPUSTAT sample to ensure the robustness of our results. In particular, we follow Hilscher and Wilson (2010) and identify a measure of systematic default risk that can be calculated for all firms regardless of whether they have bonds outstanding. We form decile portfolios by sorting all equities in the CRSP-COMPUSTAT sample based on their systematic default risk betas and investigate the pricing of systematic default risk in the cross section of equity returns. We measure a firm’s systematic default risk exposure as the sensitivity of its default probability to the median default probability of all firms in the CRSP-COMPUSTAT sample. We refer to this measure as systematic default risk beta. We find that portfolios with high systematic default risk betas, on average, have higher returns than portfolios with low systematic default risk betas, verifying our results in Section 5.2. We also show that systematic default risk beta is significantly priced in the cross-section of credit risk premia validating the use of CRP as a measure of systematic default risk exposure. 6.1 Measuring Systematic Default Beta We assume that historical default probabilities have a single common factor and use the median cross-sectional default probability to proxy for this common factor. The assumption of a single factor is a good approximation as we find that the first principal component explains 74.7% of variation in default probabilities.15 The first principal 15 Extracting principal components in the standard way from the full panel of CRSP-COMPUSTAT firms is problematic because the cross-section is much larger than the time series. We therefore first shrink the size of the cross-section by assigning each firm-month to a given rating-month and calculating equal-weighted average 12-month cumulative default probabilities as done by Hilscher and Wilson (2010). We group all 21 component and the median default probability have a correlation of 0.96 and are significantly higher during and after recessions. This is consistent with economic theory that suggests that systematic risk (discount rate) is higher during recessions. To compute each firm’s sensitivity to the systematic default factor, we estimate the following regression for each firm over 48-month rolling windows: 𝑖 𝑖 𝑖 𝑃𝐷𝑡 = 𝛼� + 𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴𝑖 � × 𝑀𝑃𝐷𝑡 + 𝜀𝑡 . (5) 𝑖 𝑃𝐷𝑡 is the 12-month annualized physical default probability for firm i in month t. It is computed each month using coefficients from column 1 in Table 2. As before, in computing physical default probabilities, we use quarterly accounting variables lagged by two months and market variables lagged by one month to ensure that this information is available at the beginning of the month over which default probabilities are measured. 𝑀𝑃𝐷𝑡 is the cross-sectional median physical default probability across all firms.16 𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴𝑖 � is exposure to systematic default risk in month τ, obtained from rolling regressions using the past 48 months of data. 6.2 Physical PD’s, Systematic Default Risk Exposures and Firm Characteristics We examine how systematic default risk exposures are related to physical default probabilities and firm characteristics. Each month, from January 1981 through December 2010, we rank and put into decile portfolios companies in the CRSP-COMPUSTAT and Bond samples based on their systematic default risk exposures in the previous month. firms with ratings of CCC+ and below together. This leaves us with a panel of 17 ratings groups with 360 months of data. Forming industry groups rather than ratings groups yields similar results.. 16 The results are similar if we instead use the first principal component. 22 For the CRSP-COMPUSTAT sample we use SYSDEFBETA as our measure of systematic default risk exposure and for the Bond Sample we use CRP as our measure of systematic default risk exposure. We calculate average market-to-book ratio (MB), market equity (ME), physical default probability (PD), and Merton’s distance to default (DD) values for all the companies in a given systematic default risk exposure decile portfolio for the two samples. The results are reported in Table 6. Panel A of Table 6 reports results for the CRSP-COMPUSTAT sample while Panel B of Table 6 reports results for the Bond sample. Panel A shows that there is not a monotonic relationship between physical default probabilities and systematic default risk exposures. For example, while the average physical default probability of the lowest SYSDEFBETA portfolio is 0.130%, the average physical default probabilities of the next eight larger SYSDEFBETA decile portfolios are lower than 0.130%. Panel B yields similar results to Panel A. The average physical default probability of the lowest 𝐶𝑅𝑃 portfolio is 0.052%. This default probability is larger than the average physical default probabilities of the next seven CRP decile portfolios. The relationship between physical default probabilities and systematic default risk exposures is U-shaped both in the CRSP-COMPUSTAT and Bond samples. Firms with very high and very low physical default probabilities command greater credit risk premium. This result is consistent with prior work reporting that asset correlations implied from historical defaults are similarly U-shaped (Chernih, Vanduffel and Henrard 2006), and it highlights our main point that a firm’s expected probability of default does not necessarily reflect the firm’s exposure to systematic default risk. 23 6.3 Default Risk Beta and Credit Spreads In this section, we analyze the relationship between our measure of credit risk premium calculated in Section 4 and systematic default risk beta. We show that systematic default risk beta (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴) can explain the cross-sectional variation in credit risk premia in corporate bonds. This finding provides further evidence that SYSDEFBETA is a good measure of systematic default risk exposure, and that investors demand compensation for this exposure. This result also validates our use of CRPs to measure firms’ exposures to systematic default risk. Table 7 summarizes Fama-MacBeth cross-sectional regression results when monthly credit risk premium (in %) are regressed on lagged systematic default risk beta (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴 as calculated in equation 5) and firm characteristics that are related to credit risk. In the regression, we control for the CAPM beta (BETACAPM), return volatility (SIGMA), profitability (NIMTAAVG), leverage (TLMTA), amount of liquid assets (CASHMTA), market-to-book ratio (MB), and relative size of the firm (RSIZE). We also control for two bond characteristics: average issue amount (OAMT) and average time to maturity (TTM) of a firm’s outstanding bonds. As alternative credit risk measures, we include Merton’s distance to default (DD), physical default probability (PD), and the Standard & Poor’s (S&P) rating (RATING). The t-statistics for the slopes are based on the time series variability of the estimates, incorporating a Newey-West (1987) correction with four lags to account for possible autocorrelation in the estimates. In column 1, we control for stock characteristics that have been shown to be important determinants of credit risk by CHS (2008) as well as time to maturity and the offering amount of the firm’s outstanding bonds. In column 2 we control for rating and Merton’s 24 distance to default, in addition to time to maturity and bond offering amount. In column 3 we control for time to maturity, offering amount of the bond, Merton’s distance to default and the physical probability of default. In column 4 we control for all the CHS (2008) variables, firm rating, Merton’s distance to default, and the physical probability of default. In all specifications the loading on systematic default risk beta, 𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴, is positive and statistically significant. The impact of 𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴 on spreads is also economically significant. Results in column 4 of Table 7 suggest that moving from the 75th percentile systematic default risk beta firm (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴 = 0.156) to the 95th percentile firm (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴 = 0.954) leads to an increase of 45 basis points in bond risk premium after controlling for all parameters known to influence credit spreads. The results suggest that systematic default risk beta is an important driver of the credit risk premium in corporate bond spreads. CRP, our measure of exposure to systematic default risk computed from corporate bond spreads, and systematic default risk beta (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴) are comparable proxies for exposure to systematic default risk. In the next section we use systematic default risk beta (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴) to examine the pricing of systematic default risk in the cross section of equity returns in the CRSP- COMPUSTAT sample. 6.4 Pricing of Systematic Default Risk in the CRSP-COMPUSTAT Sample The systematic default risk beta described in the previous section allows us to test whether systematic default risk is priced in the larger CRSP-COMPUSTAT sample. In 25 Section 5.2, our analysis was confined to firms that have outstanding bonds because we used the bond credit risk premium as our proxy for systematic default risk compensation. We use the same portfolio approach described in Section 5. In particular, we sort stocks into deciles each month from January 1981 through December 2010 according to their systematic default risk betas obtained at the beginning of the previous month. We then calculate the value-weighted decile portfolio returns for all stocks in the CRSP- COMPUSTAT sample on a monthly basis and regress the portfolio return in excess of the risk-free rate on the market (MKTRF), size (SMB), value (HML), and momentum (MOM) factors. In Table 8, we report regression results for only the top and bottom decile portfolios along with the top decile minus bottom decile hedge portfolio to save space. Results in Table 8, which are obtained from the CRSP-COMPUSTAT sample, are similar to those reported in Table 5, which are obtained using the bond sample. Table 5 shows that the highest CRP decile portfolio earns on average 52 basis points more per month compared to the lowest CRP decile portfolio. Similarly, Table 8 shows that the highest systematic default risk beta decile portfolio in the full CRSP-COMPUSTAT sample earns 46 basis points more per month compared to the lowest systematic default risk beta decile portfolio. This result is significant at the 10% level. Once we control for the market factor, the statistical significance of the hedge portfolio return disappears, suggesting a strong link between systematic default risk and market risk. Controlling for Fama-French size and value factors further reduces the economic and statistical significance of the systematic default risk premium, supporting the Fama and French (1992) conjecture that size and value premiums may be related to systematic distress risk. 26 Overall, the results in this section verify the robustness of using credit spreads as a proxy for systematic default risk exposure and confirm our results in Section 5. 7. Conclusion We argue that the distress risk anomaly documented in the cross section of equity returns is due to mismeasuring systematic default risk. Previous papers measure financial distress by computing firms’ expected probabilities of default inferred from historical default data. This calculation ignores the fact that firm defaults are correlated and that some defaults are more likely to occur in bad times, thus failing to appropriately account for the systematic nature of default risk. We use credit risk premium obtained from corporate credit spreads to proxy for a firm’s exposure to systematic default risk. Unlike previously used measures that proxy for physical probabilities of default, credit risk premia proxy for risk-adjusted default probabilities, reflecting the risk premium for the non-diversifiable component of distress risk. We find that stocks that have higher credit risk premium have higher expected equity returns. Consistent with structural models of default, we also show that the premium to a high minus low systematic default risk hedge portfolio is largely explained by the market factor, suggesting that CAPM beta captures most of the variation in systematic default risk exposure. To show that our results are robust to sample biases, we conduct two analyses. First, we show that when firms in our Bond sample are ranked according to traditional measures of default risk used in the literature, the default risk anomaly exists in the bond sample. Second, we construct an alternative proxy to measure systematic default risk exposure (𝑆𝑌𝑆𝐷𝐸𝐹𝐵𝐸𝑇𝐴) and extend the analyses to the full CRSP sample. We obtain 27 results similar to what we find using the bond sample. These results are consistent with the basic structural models of default in which aggregate risk factors drive the default probability as well as the returns on bonds and equities. 28 APPENDIX Here we explain the details of the variables used to compute the physical probability of default (PD) and the Merton distance-to-default (DD) measure. We use quarterly accounting data from COMPUSTAT and monthly market data from CRSP. MB is the market-to-book ratio. Book equity, BE is defined as in Davis, Fama, and French (2000). To deal with outliers, we adjust total value of assets, TA (COMPUSTAT quarterly data item: ATQ) by the difference between the market equity (ME) and book equity (BE): MT Ai ,t = T Ai ,t + 0.1(MEi ,t - BEi ,t ) (A.1) . NIMTAAVG is a geometrically declining average of past values of the ratio of net income (data item: NIQ) to adjusted total assets: 1- f 2 NI MT AAVGt - 1,t - 12 = (NI MT At - 1,t - 3 + ... + NI MT At - 10,t - 12 ) (A.2) 1 - f 12 . EXRETAVG is a geometrically declining average of monthly log excess stock returns relative to the S&P 500 index: 1- f EXRET AVGt - 1,t - 12 = (EXRETt - 1 + ... + f 11EXRETt - 12 ) (A.3) 1 - f 12 . The weighting coefficient is set to φ = 2−1/3, such that the weight is halved each quarter. TLMTA is the ratio of total liabilities (data item: NIQ) to adjusted total assets. SIGMA is the standard deviation of daily stock returns over the previous three months. SIGMA is coded as missing if there are fewer than five observations. RSIZE is the log ratio of market capitalization to the market value of the S&P 500 index. CASHMTA is the ratio of the value of cash and short-term investments (data item: CHEQ) to the value of 29 adjusted total assets. PRICE is the log price per share truncated from above at $15. All variables are winsorized using a 1/99 percentile interval in order to eliminate outliers. We follow CHS (2008) and Hillegeist, Keating, Cram, and Lunstedt (2004) to calculate Merton’s distance-to-default measure. The market equity value of a company is modeled as a call option on the company’s assets: V E = V Ae- ¶T N (d1) - Xe- rT N (d2 ) + (1 - e- ¶T )V A 2 log(V A / X ) + (r - ¶ - (s A / 2))T d1 = (A.4) sA T d2 = d1 - s A T . V E is the market value of a firm. V A is the value of the firm’s assets. X is the face value of debt maturing at time T. r is the risk-free rate, and ¶ is the dividend rate expressed in terms of V A . s A is the volatility of the value of assets, which is related to equity volatility through the following equation: s E = (V Ae- ¶ T N (d1)s A ) / V E (A.5) . We simultaneously solve the above two equations to find the values of V A and s A . We use the market value of equity for V E and short-term plus one-half long-term book debt to proxy for the face value of debt X (data items: DLCQ+1/2*DLTTQ). s E is the standard deviation of daily equity returns over the past three months. T equals one year, and r is the one-year treasury bill rate. The dividend rate, d, is the sum of the prior year’s 30 common and preferred dividends, obtained from COMPUSTAT Annual, (data items: DVP+DVC) divided by the market value of assets. We use the Newton method to simultaneously solve the two equations above. For starting values for the unknown variables we use, V A = V E + X , and s A = s EV E (V E + X ) . Once we determine asset values, V A , we then compute asset returns as in Hillegeist et al. (2004): V + Dividends - V A,t - 1 ù é m = max ê A,t ,r ú (A.6) t ê V ú ê ë A ,t - 1 ú. û Because expected returns cannot be negative, if asset returns are below zero, they are set to the risk-free rate. 17 Merton’s distance to default is finally computed as: log (V A / X ) + ( m- ¶ - (s A 2 / 2 ))T DD = - (A.7) sA T . 17 We obtain similar results if we use a 6% equity premium instead of asset returns as in CHS (2008). 31 References Almeida, H., and T. Philippon. 2007. “The Risk-Adjusted Cost of Financial Distress.� Journal of Finance 62(6): 2557–2586. Altman, E. 1968. “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy.� Journal of Finance 23(4): 589–609. Altman, Edward I., and Vellore M. Kishore. 1998. “Defaults and Returns on High Yield Bonds: Analysis through 1997.� Working paper, NYU Salomon Center. Amihud, Yakov. 2002. “Illiquidity and Stock Returns: Cross-Section and Time Series Effects.� Journal of Financial Markets 5(1): 31–56. Ang, Andrew, Robert J. Hodrick, Yuhang Xing, and Xiaozan Zhang. 2006. “The Cross- Section of Volatility and Expected Returns.� Journal of Finance 61: 259–299. Ang A., R. Hodrick, Y. Xing, and X. Zhang. 2009. “High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence.� Journal of Financial Economics 91: 1–23. Avramov, Doron, Tarun Chordia, Gergana Jostova, and Alexander Philipov. 2009. “Credit Ratings and the Cross-Section of Stock Returns.� Journal of Financial Markets 12(3): 469–499. Avramov, Doron, Gergana Jostova, and Alexander Philipov. 2007. “Understanding Changes in Corporate Credit Spreads.� Financial Analysts Journal 63(2): 90–105 Bakshi, G., D. Madan, and F. Zhang. 2006. “Investigating the Role of Systematic and Firm-Specific Factors in Default Risk: Lessons from Empirically Evaluating Credit Risk Models.� Journal of Business 79: 1955–1988. Barberis, Nicholas, and Ming Huang. 2001. “Mental Accounting, Loss Aversion, and Individual Stock Returns.� Journal of Finance 56: 1247–1292. Berndt, A., R. Douglas, D. Duffie, M. Ferguson, and D. Schranz. 2005. “Measuring Default Risk Premia from Default Swap Rates and EDFs.� Working paper, Stanford University. Bharath, Sreedhar, and Tyler Shumway. 2008. “Forecasting Default with the KMV Merton Model.� Review of Financial Studies 21(3): 1339–1369. 32 Blanco, R., S. Brennan, and I. W. Marsh. 2005. “An Empirical Analysis of the Dynamic Relationship between Investment Grade Bonds and Credit Default Swaps.� Journal of Finance 60, 2255–2281. Brennan, Michael J., Tarun Chordia, and Avanidhar Subrahmanyam. 1998. “Alternative Factor Specifications, Security Characteristics, and the Cross-Section of Expected Stock Returns.� Journal of Financial Economics 49, 345–373. Campbell, John Y., Jens Hilscher, and Jan Szilagyi, 2008. “In Search of Distress Risk.� Journal of Finance 63, 2899–2939. Campbell, John Y., and Glen B. Taksler. 2003. “Equity Volatility and Corporate Bond Yields.� Journal of Finance 58, 2321–2350. Campello, M., L. Chen, and L. Zhang, 2008. “Expected Returns, Yield Spreads, and Asset Pricing Tests.� Review of Financial Studies 21, 1297–1338. Carhart, Mark. 1997. “On Persistence in Mutual Fund Performance.� Journal of Finance 52(1): 57–82. Chan, K. C., and Nai-fu Chen. 1991. “Structural and Return Characteristics of Small and Large Firms.� Journal of Finance 46: 1467–1484. Chava, Sudheer, and Robert A. Jarrow, 2004. “Bankruptcy prediction with Industry Effects.� Review of Finance 8, 537–569. Chava, Sudheer, and A. Purnanandam. 2010. “Is Default Risk Negatively Related to Stock Returns?� Review of Financial Studies 23, 2523–2559. Chen, L., D. A. Lesmond, and J. Wei. 2007. “Corporate Yield Spreads and Bond Liquidity.� Journal of Finance 62, 119–149. Chernih, Andrew, S. Vanduffel, and L. Henrard. 2006. “Asset Correlations: A Literature Review and Analysis of the Impact of Dependent Loss Given Defaults.� Working paper. Cochrane, John H. 1991. “Production-based Asset Pricing and the Link between Stock Returns and Economic Fluctuations.� Journal of Finance 46, 209–237. Collin-Dufresne, Pierre, Robert S. Goldstein, and J. Spencer Martin, 2001. “The Determinants of Credit Spread Changes.� Journal of Finance 56, 2177–2207. Conrad, Jennifer, Nishad Kapadia, and Yuhang Xing. 2012. “What explains the distress risk puzzle: death or glory?� Working paper, UNC Chapel Hill and Rice University. 33 Da, Zhi, and Pengjie Gao, 2010. “Clientele Change, Liquidity Shock, and the Return on Financially Distressed Stocks.� Journal of Financial and Quantitative Analysis 45: 27– 48. Das, Sanjiv R., Darrell Duffie, Nikunj Kapadia, and Leandro Saita. 2007. “Common Failings: How Corporate Defaults Are Correlated.� Journal of Finance 72(1): 93–117. Daniel, Kent, Mark Grinblatt, Sheridan Titman, and Russ Wermers. 1997. “Measuring Mutual Fund Performance with Characteristic-Based Benchmarks.� Journal of Finance 52(3): 1035–1058. Dichev, Ilia D. 1998. “Is the Risk of Bankruptcy a Systematic Risk?� Journal of Finance 53(3): 1131–1147. Dimitrov, Valentin, and P. Jain, 2008. “The Value-Relevance of Changes in Financial Leverage beyond Growth in Assets and GAAP Earnings.� Journal of Accounting, Auditing & Finance 23, 191–222. Downing, Chris, Shane Underwood, and Yuhang Xing. 2005. “Is Liquidity Risk Priced in the Corporate Bond Market?� Working paper, Rice University. Driessen, J. 2005. “Is Default Event Risk Priced in Corporate Bonds?� Review of Financial Studies 18(1): 165–195. Driessen, J., and Frank de Jong. 2007. “Liquidity Risk Premia in Corporate Bond Markets.� Management Science 53(9): 1439–1451. Duffee, Gregory. 1999. “Estimating the Price of Default Risk.� Review of Financial Studies 12, 197– 226. Duffie, Darrell, and Kenneth J. Singleton. 1995. “Modeling Term Structures of Defaultable Bonds.� Working paper, Stanford Graduate School of Business. Duffie, Darrell, and Kenneth J. Singleton. 1997. “An Econometric Model of the Term Structure of Interest-Rate Swap Yields.� Journal of Finance 52: 1287–1321. Duffie, D., L. Saita, and K. Wang. 2007. “Multi-Period Corporate Default Prediction with Stochastic Covariates.� Journal of Financial Economics 83(3): 635–665. Elton, Edwin J., Martin J. Gruber, Deepak Agrawal, and Christopher Mann. 2001. “Explaining the Rate Spread on Corporate Bonds.� Journal of Finance 56(1): 247–277. Eom, Young Ho, Jean Helwege, and Jing-Zhi Huang. 2004. “Structural Models of Corporate Bond Pricing: An Empirical Analysis.� Review of Financial Studies 17: 499– 505. 34 Falkenstein, Eric G. 1996. “Preferences for Stock Characteristics as Revealed by Mutual Fund Portfolio Holdings.� Journal of Finance 51: 111–135. Fama, Eugene F., and Kenneth R. French. 1992. “The Cross-Section of Expected Stock Returns.� Journal of Finance 47(2): 427–465. Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.� Journal of Financial Economics 33: 3–56. Fama, Eugene F., and Kenneth R. French. 1996. “Multifactor Explanations of Asset Pricing Anomalies.� Journal of Finance 51: 55–84. Fama, Eugene F., and James D. MacBeth. 1973. “Risk, Return, and Equilibrium: Empirical Tests.� Journal of Political Economy 81: 607–636. Ferguson, Michael F., and Richard L. Shockley. 2003. “Equilibrium Anomalies.� Journal of Finance 58: 2549–2580. Garlappi, Lorenzo, Tao Shu, and Hong Yan. 2008. “Default Risk, Shareholder Advantage, and Stock Returns.� Review of Financial Studies 21(6): 2743–2778. George, Thomas J., and Hwang, Chuan-Yang. 2010. “A Resolution of the Distress Risk and Leverage Puzzles in the Cross Section of Equity Returns.� Journal of Financial Economics 96: 56–79. Gompers, P., and A. Metrick. 2001. “Institutional Investors and Equity Prices.� Quarterly Journal of Economics 116, 229–259. Griffin, John M., and Michael L. Lemmon. 2002. “Book-to-Market Equity, Distress Risk, and Stock Returns.� Journal of Finance 57, 2317–2336. Hasbrouck, Joel. 2005. “Trading Costs and Returns for US Equities: The Evidence from Daily Data.� Unpublished paper, Leonard N. Stern School of Business, New York University. Hillegeist, Stephen A., Elizabeth Keating, Donald P. Cram, and Kyle G. Lunstedt. 2004. “Assessing the Probability of Bankruptcy.� Review of Accounting Studies 9, 5–34. Hilscher, Jens, and Wilson, M. 2010. “Credit Ratings and Credit Risk.� Working paper, Brandeis University. Hong, H., T. Lim, and J. C. Stein. 2000. “Bad News Travels Slowly: Size, Analyst Coverage, and the Profitability of Momentum Strategies.� Journal of Finance 55, 265– 295. 35 Huang, Jing-Zhi, and Ming Huang. 2003. “How Much of the Corporate-Treasury Yield Spread Is Due to Credit Risk?� Working paper, Pennsylvania State University. Hull, J., M. Predescu, and A. White. 2004. “The Relationship between Credit Default Swap Spreads, Bond Yields, and Credit Rating Announcements.� Journal of Banking and Finance 28(11): 2789–2811. Jegadeesh, Narasimhan, and Sheridan Titman. 1993. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.� Journal of Finance 48(1): 35– 91. Jones, Charles M., and Matthew Rhodes-Kropf. 2003. “The Price of Diversifiable Risk in Venture Capital and Private Equity.� Working paper, Columbia University. Kapadia, Nishad. 2011. “Tracking Down Distress Risk.� Journal of Financial Economics 102: 167–182. Korteweg, Arthur. 2010. “The Net Benefits to Leverage.� Journal of Finance 65: 2137– 2170. Li, E. X., D. Livdan, and L. Zhang. 2007. “Anomalies.� Review of Financial Studies 22(11): 4301–4334. Lin, Hai, Junbo Wang, and Chunchi Wu. 2011. “Liquidity Risk and the Cross-Section of Expected Corporate Bond Returns.� Journal of Financial Economics 99: 628–650. Lintner, John. 1965. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.� Review of Economics and Statistics 47, 13–37. Liu, Laura Xiaolei, Toni M. Whited, and Lu Zhang. 2009. “Investment�Based Expected Stock Returns.� Journal of Political Economy 117(6): 1105–1139. Longstaff, F., S. Mithal, and E. Neis. 2005. “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit–Default Swap Market.� Journal of Finance 60(5): 2213–2253. Longstaff, Francis A., and Eduardo S. Schwartz. 1995. “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt.� Journal of Finance 50(3): 789–821. Malkiel, Burton G., and Yexiao Xu. 2002. “Idiosyncratic Risk and Security Returns.� Working paper, University of Texas at Dallas. Merton, Robert C. 1974. “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.� Journal of Finance 29, 449–470. 36 Merton, Robert C. 1987. “A Simple Model of Capital Market Equilibrium with Incomplete Information.� Journal of Finance 42, 483–510. Nagel, Stefan. 2005. “Short Sales, Institutional Investors and the cross-section of Stock Returns.� Journal of Financial Economics 78, 277–309. Newey, Whitney, and Kenneth West. 1987. “A Simple Positive Semi-Definite, Heteroscedasticity and Autocorrelation Consistent Covariance Matrix.� Econometrica 55, 703–708. Ohlson, James A. 1980. “Financial Ratios and the Probabilistic Prediction of Bankruptcy.� Journal of Accounting Research 18, 109–131. Pastor, Lubos, and Robert F. Stambaugh. 2003. “Liquidity risk and expected stock returns.� Journal of Political Economy 111, 642--685 Pastor, Lubos, and Pietro Veronesi. 2003. “Stock Valuation and Learning about Profitability.� Journal of Finance 58(5): 1749–1790. Penman, S., S. Richardson, and I. Tuna. 2007. “The Book-to-Price Effect in Stock Returns: Accounting for Leverage.� Journal of Accounting Research 45, 427–467. Roll, R. 1984. “A Simple Measure of the Bid-Ask Spread in an Efficient Market.� Journal of Finance 39, 1127–1140. Saita, L. 2006. “The Puzzling Price of Corporate Default Risk.� Working Paper, Stanford University. Sharpe, William F. 1964. “Capital Asset Prices: A Theory of Market Equilibrium.� Journal of Finance 19, 425–442. Shumway, Tyler. 2001. “Forecasting Bankruptcy More Accurately: A Simple Hazard Model.� Journal of Business 74: 101–124. Vassalou, Maria, and Yuhang Xing. 2004. “Default Risk in Equity Returns.� Journal of Finance 59: 831–868. Zhang, Lu. 2007, March. “Discussion: ‘In Search of Distress Risk.’� Conference on Credit Risk and Credit Derivatives, Federal Reserve Board, Washington, D.C Zhu, Haibin. 2006. “An Empirical Comparison of Credit Spreads between the Bond Market and the Credit Default Swap Market.� Journal of Financial Services Research 29, 211–235. Zmijewski, Mark E. 1984. “Methodological Issues Related to the Estimation of Financial Distress Prediction Models.� Journal of Accounting Research 22, 59–82. 37 Table 1: Summary Statistics Table 1 reports summary statistics for firm characteristics and distress measures for companies in the CRSP sample (left panel) and the bond sample (right panel). MB is the market-to-book ratio, and ME is market capitalization in millions of dollars. CASHMTA is the ratio of cash to the market value of total assets. EXRETAVG is a geometrically declining average of monthly log excess stock returns relative to the S&P 500 index. NIMTAAVG is a geometrically declining average of past values of the ratio of net income to the market value of total assets. TLMTA is the ratio of total liabilities to the market value of total assets, and RSIZE is the log ratio of market capitalization to the market value of the S&P 500 index. IDIOVOL is the standard deviation of regression errors obtained from regressing daily excess returns on the Fama and French (1993) factors. TOTVOL is the standard deviation of daily stock returns over the previous twelve months. PRICE is the log price per share truncated at $15. PD is the physical probability of default reported as a percentage. DD is the Merton distance to default measure. The Appendix describes how these variables are calculated. P25, P50, and P75 represent 25th, 50th, and 75th percentiles, respectively. Statistical significance at the 10%, 5%, and 1% levels is denoted by *, **, and ***, respectively. CRSP Sample Bond Sample Variables Mean STD P25 P50 P75 Mean STD P25 P50 P75 Difference MB 1.983 1.466 0.900 1.533 2.644 1.794 1.131 0.999 1.486 2.268 0.189*** ME 1,273.8 5,713.0 20.7 91.8 271.6 5,327.7 17,251.1 417.5 1,297.2 3,811.6 -4,053.4*** CASHMTA 0.091 0.091 0.024 0.070 0.114 0.050 0.058 0.010 0.028 0.070 0.041*** EXRETAVG -0.010 0.043 -0.034 -0.006 0.018 -0.001 0.030 -0.017 0.000 0.016 -0.008*** NIMTAAVG 0.003 0.015 -0.001 0.005 0.012 0.008 0.008 0.003 0.008 0.012 -0.005*** TLMTA 0.413 0.282 0.159 0.374 0.643 0.536 0.229 0.360 0.535 0.708 -0.123*** RSIZE -10.708 1.604 -11.907 -10.790 -9.617 -8.031 1.160 -8.724 -7.701 -7.113 -2.677*** IDIOVOL 0.035 0.027 0.018 0.028 0.044 0.018 0.010 0.012 0.015 0.020 0.018*** TOTVOL 0.037 0.028 0.020 0.030 0.046 0.020 0.010 0.014 0.018 0.023 0.017*** PRICE 2.116 0.705 1.646 2.431 2.708 2.635 0.263 2.708 2.708 2.708 -0.519*** PD * 100 0.081 0.155 0.021 0.039 0.078 0.043 0.067 0.020 0.031 0.048 3.762*** DD 7.094 39.000 2.906 5.024 8.177 8.384 5.856 5.063 7.518 10.643 -1.290*** Table 2: Default Prediction Table 2 reports results from hazard regressions of the default indicator on the predictor variables. The data are constructed such that all of the predictor variables are observable 12 months before the default event. NIMTAAVG is a geometrically declining average of past values of the ratio of net income to the market value of total assets. TLMTA is the ratio of total liabilities to the market value of total assets. EXRETAVG is a geometrically declining average of monthly log excess stock returns relative to the S&P 500 index. SIGMA is the standard deviation of daily stock returns over the previous three months. RSIZE is the log ratio of market capitalization to the market value of the S&P 500 index. CASHMTA is the ratio of cash to the market value of total assets. MB is the market-to-book ratio; PRICE is the log price per share truncated at $15, and DD is Merton’s distance to default. These variables are described in detail in the Appendix. Results under “All Firms� are estimates computed using the full CRSP-COMPUSTAT sample of defaults with available accounting information. Results under “CHS Sample� show the estimates CHS (2008) report in their paper. Results under “Firms with Bonds� are estimates computed using the sample of defaults from companies that have issued bonds with available accounting information. Absolute values of z-statistics are reported in parentheses below coefficient estimates. McFadden pseudo R2 values are reported for each regression. Statistical significance at the 10%, 5%, and 1% levels is denoted by *, **, and ***, respectively. (1) (2) (3) (4) (5) (6) Sample Period: 1981–2010 1963–2003 1981–2010 1981–2010 1981–2010 1981–2010 Lag (Months) 12 12 12 12 12 12 NIMTAAVG -21.989*** -20.260*** -18.308*** (10.33) (18.09) (2.74) TLMTA 2.188*** 1.420*** 1.503*** (16.84) (16.23) (2.76) EXRETAVG -7.871*** -7.13*** -6.241** (10.28) (14.15) (2.13) SIGMA 1.461*** 1.410*** 1.774*** (11.19) (16.49) (5.17) RSIZE -0.063*** -0.045** -0.614*** (4.21) (2.09) (7.28) CASHMTA -1.516*** -2.130*** -1.064 (7.85) (8.53) (1.21) MB 0.085*** 0.075*** 0.127 (2.63) (6.33) (0.91) PRICE -0.167* -0.058 -0.017 (1.74) (1.40) (0.95) DD -0.356*** -0.345*** -0.460*** (17.18) (33.73) (8.07) CONSTANT -9.718*** -9.160*** -13.844*** -3.401*** Not -2.634*** (18.12) (30.89) (8.90) (48.52) Reported (11.10) Observations 993,560 1,565,634 54,551 993,560 1,565,634 54,551 Defaults 728 1968 118 728 1968 118 Pseudo R2 0.134 0.114 0.156 0.083 0.066 0.129 All Firms in All Firms in Firms with CHS Firms with Sample Type CRSP- CHS Sample CRSP- Bonds Sample Bonds COMPUSTAT COMPUSTAT Table 3: Expected Losses, Taxes, and Liquidity Premia in Credit Spreads In Table 3, we report average credit spreads, spreads in excess of expected losses and taxes and liquidity premium for various rating-maturity groups. Column (1) reports corporate bond yields minus maturity-matched government treasuries; column (2) reports spreads in excess of expected losses and taxes; and column (3) reports the liquidity premium for each corresponding rating/maturity portfolio. The estimation of these components is described in Section 4.1. Bonds with maturity greater than seven years are referred to as having “long maturity,� and bonds with maturity less than seven years are referred to as having “short maturity.� Spread in Excess of Expected Losses and Portfolio Spread Taxes Liquidity Premium AAA short-mat 0.97% 0.62% 0.13% AAA long-mat 0.95% 0.62% 0.23% AA short-mat 1.04% 0.56% 0.24% AA long-mat 1.26% 0.84% 0.35% A short-mat 1.32% 0.81% 0.33% A long-mat 1.28% 0.81% 0.41% BBB short-mat 1.99% 1.20% 0.50% BBB long-mat 2.06% 1.32% 0.73% BB 3.78% 2.09% 0.88% B 5.28% 2.10% 1.30% CCC 10.36% 4.75% 1.40% 40 Table 4: Distress Portfolio Returns Sorted on Physical Default Probabilities Table 4 reports time series averages, CAPM, 3-factor and 4-factor regression results for distress risk portfolios. We sort stocks into deciles each month from January 1981 to December 2010 according to their physical default probabilities, obtained at the beginning of the previous month, calculated using the hazard coefficients computed using the CRSP- COMPUSTAT sample (Panel A) and using the bond sample (Panel B). We compute the value-weighted returns for these decile portfolios on a monthly basis and regress the portfolio return in excess of the risk-free rate on the market (MKT), size (SMB), value (HML), and momentum (MOM) factors. The factors are obtained from Ken French’s website We report regression results for only the top and bottom decile portfolios as well as the high-minus-low distress risk hedge portfolio to save space. Absolute values of t-statistics are reported in parentheses below their respective coefficient estimates. Statistical significance at the 10%, 5%, and 1% levels is denoted by *, **, and ***, respectively. Panel A: Monthly Equity Returns For Default Risk Portfolios in the full CRSP-COMPUSTAT sample sample Physical PD’s constructed with coefficients from Column (1) of Table 2 Alpha * 100 MKT SMB HML MOM 10th 0.608** (2.01) 0.166 1.041*** (0.99) (28.01) 0.433*** 0.879*** 0.109** -0.462*** (2.86) (23.63) (2.17) (8.05) 0.096 0.949*** 0.083* -0.37*** 0.337*** (0.72) (29.23) (1.94) (7.42) (11.05) Alpha * 100 MKT SMB HML MOM 90th -0.576 (1.19) -1.216*** 1.507*** (3.87) (21.46) -1.509*** 1.511*** 0.923*** 0.43*** (5.29) (21.63) ( 9.82) (3.99) -0.736*** 1.351*** 0.981*** 0.219*** -0.772*** (3.24) (24.48) (13.45) (2.58) (14.89) Alpha * 100 MKT SMB HML MOM 90th - 10th -1.184** (2.34) -1.382*** 0.466*** (2.96) (4.28) -1.942*** 0.632*** 0.814*** 0.892*** (4.68) (6.04) ( 6.73) (6.02) -0.832*** 0.402*** 0.898*** 0.589*** -1.109*** (2.64) (5.69) (10.96) (6.25) (18.14) 41 Panel B: Monthly Equity Returns For Default Risk Portfolios in the Bond sample Physical PD’s constructed with coefficients from Column (3) of Table 2 Alpha * 100 MKT SMB HML MOM 10th 0.825*** (3.05) 0.382** 0.847*** (2.29) (22.64) 0.385** 0.891*** -0.274*** 0.003 (2.36) (22.27) (5.18) (0.05) 0.271* 0.913*** -0.283*** 0.031 0.114*** (1.65) (22.76) (5.41) (0.51) (3.07) Alpha * 100 MKT SMB HML MOM 90th 0.318 (0.82) -0.323 1.224*** (1.36) (22.92) -0.694*** 1.437*** 0.009 0.685*** (3.19) (26.89) (0.13) (8.39) -0.217 1.345*** 0.047 0.566*** -0.475*** (1.15) (29.42) (0.79) (8.14) (11.24) Alpha * 100 MKT SMB HML MOM 90th - 10th -0.507* (1.66) -0.705*** 0.378*** (2.60) (5.74) -1.079*** 0.546*** 0.284*** 0.682*** (3.83) (7.89) (3.10) (6.45) -0.487** 0.432*** 0.330*** 0.535*** -0.589*** (1.97) (7.17) (4.20) (5.84) (10.58) 42 Table 5: Monthly Equity Returns for Credit Risk Premium Portfolios In Table 5, we report time series averages, CAPM, 3-factor, and 4-factor regression results for distress risk portfolios. Each month from January 1981 through December 2010, we sort stocks into 10 portfolios based on their credit risk premia (CRP) at the beginning of the previous month. We compute the value-weighted return for these decile portfolios on a monthly basis and regress the portfolio return in excess of the risk-free rate on the market (MKT), size (SMB), value (HML), and momentum (MOM) factors. The factors are obtained from Ken French’s website. We report regression results for only the top and bottom decile portfolios to save space. Absolute values of t-statistics are reported in parentheses below coefficient estimates. Statistical significance at the 10%, 5%, and 1% levels is denoted by *, **, and ***, respectively. Equity Returns in Credit Risk Premia P tf li Alpha * 100 MKT SMB HML MOM 10th 0.463* (1.65) -0.074 0.826*** (0.52) (23.63) -0.021 0.890*** -0.319*** 0.020 (0.17) (27.51) (9.29) (0.47) 0.01 0.878*** -0.314*** 0.013 -0.03 (0.08) (26.00) (9.07) (0.29) (1.20) Alpha * 100 MKT SMB HML HML th 90 0.984*** (2.58) 0.325 1.014*** (1.33) (17.12) -0.193 1.28*** 0.157*** 0.715*** (0.93) (22.83) (2.63) (9.62) 0.005 1.205*** 0.191*** 0.668*** -0.193*** (0.02) (21.65) (3.34) (9.37) (4.64) Alpha * 100 MKT SMB HML HML 90th - 10th 0.521** (1.98) 0.399 0.188*** (1.50) (2.91) -0.172 0.391*** 0.476*** 0.695*** (0.75) (6.32) (7.25) (8.49) -0.005 0.327*** 0.505*** 0.656*** -0.163*** (0.02) (5.21) (7.84) (8.15) (3.48) 43 Table 6: Stock Characteristics and Systematic Default Risk Exposure In Table 6 we report summary statistics of stock characteristics for firms belonging to systematic default risk decile portfolios. Default risk is measured in two alternative ways: once using physical default probabilities and once using systematic default risk exposures. For the full CRSP-COMPUSTAT sample, each month from January 1981 through December 2010, we sort stocks into 10 portfolios based on their systematic default risk betas obtained at the beginning of the previous month. For the Bond sample, each month from January 1981 through December 2010, we sort stocks into 10 portfolios based on their value- weighted credit risk premia (CRP). We then compute cross-sectional average values for various stock characteristics in each group. Market-to-book ratio (MB) is calculated as the ratio of market equity in the previous calendar month to book equity in the previous month. ME is the market value of equity in millions of dollars. PD is the physical probability of default reported as a percentage. DD is Merton’s distance to default measure. For the full CRSP-COMPUSTAT sample PD’s are calculated using coefficients from column (1) of Table 2, whereas for the Bond sample PD’s are calculated using coefficients from column (3) of Table 2. Panel A: Systematic Default Beta Portfolios, CRSP Sample Portfolio MB ME PD*100 DD Low 2.17 1269 0.130 5.006 2 2.06 2,444 0.071 7.296 3 2.13 3,342 0.048 8.954 4 2.11 3,359 0.041 9.630 5 2.07 2,837 0.045 9.240 6 2.02 2,327 0.052 8.207 7 1.97 1,651 0.064 7.854 8 1.95 823 0.085 5.997 9 1.97 482 0.118 6.063 High 2.18 266 0.175 4.393 Panel B: Credit Risk Premium Portfolios, Bond Sample Portfolio MB ME PD*100 DD Low 2.03 9,442 0.052 7.938 2 2.10 12,902 0.042 8.763 3 2.24 13,086 0.040 8.905 4 2.18 13,170 0.038 9.551 5 2.14 15,638 0.041 8.713 6 2.12 12,881 0.044 8.748 7 2.03 10,544 0.046 8.531 8 1.86 9,095 0.051 8.030 9 1.82 8,764 0.060 7.714 High 1.74 6,065 0.098 6.109 44 Table 7: Pricing of Systematic Default Risk Beta in the Cross Section of Credit Spreads In Table 7, we run monthly Fama-MacBeth (1973) regressions of credit risk premium (in %) on default risk prediction variables used in CHS 2008, firm rating, market beta, and systematic default risk beta. Our sample period covers January 1981 to December 2010. We report Fama-MacBeth regression coefficients as well as their corresponding Newey-West (1987) corrected t-statistics in parentheses. Credit risk premium are calculated in month t+1 as the difference between the corporate bond yield and the corresponding maturity-matched treasury rate minus expected losses, liquidity compensation, and tax compensation. BETACAPM is the firm’s CAPM beta at time t and is calculated using rolling regressions over the t-48 to t-1 time frame. SYSDEFBETA is the firm’s systematic default risk beta (failure beta) at time t and is calculated as the sensitivity of its default probability to the median default probability. SYSDEFBETA is also calculated over the t-48 to t-1 time frame on a rolling basis. SIGMA, NIMTAAVG, TLMTA , CASHMTA, MB, RSIZE, RATING, and DD are all calculated at time t. These variables are described in detail in Table 2. OAMT is the market value of debt at the time of its issuance in millions of dollars, and TTM is the time to maturity of debt in years. PD is the physical probability of default reported as a percentage. Absolute values of t- statistics are reported in parentheses below coefficient estimates. Statistical significance at the 10%, 5%, and 1% levels is denoted by *, **, and ***, respectively. (1) (2) (3) (4) Credit Risk Credit Risk Credit Risk Credit Risk VARIABLES Premium Premium Premium Premium BETACAPM 0.072*** 0.187** 0.189*** 0.082*** (2.64) (4.54) (5.18) (2.90) SYSDEFBETA 0.555*** 1.424*** 1.408*** 0.567*** (3.74) (7.08) (6.93) (4.38) SIGMA 3.556*** 3.320*** (16.23) (13.18) NIMTAAVG -41.575*** -29.324*** (10.29) (8.75) TLMTA 0.442*** 0.411*** (5.75) (4.50) CASHMTA -1.296*** -0.661*** (5.16) (2.80) OAMT -0.098*** -0.103* -0.375*** 0.023 (4.39) (1.89) (10.28) (1.01) TTM 0.009*** 0.012*** 0.012*** 0.009*** (4.54) (7.13) (6.88) (4.30) MB -0.019 -0.009 (1.10) (0.70) RSIZE -0.569*** -0.428*** (18.00) (13.46) RATING 0.123*** 0.086*** (16.00) (18.19) DD -0.099*** -0.108*** 0.023* (9.20) (9.82) (1.80) PD*106 29.028*** 10.969*** (6.66) (3.73) Constant -3.715*** 0.889*** 1.828*** -3.843*** (16.49) (5.68) (14.42) (15.85) Observations 83,202 83,020 83,124 83,020 R-squared 0.501 0.459 0.370 0.601 45 Table 8: Equity Returns for Systematic Default Risk Beta Portfolios In Table 8, we report the time series averages, CAPM, 3-factor, and 4-factor regression results for distress risk portfolios. We sort stocks into deciles each month from January 1981 through December 2010 according to their systematic default risk betas—SYSDEFBETAs—obtained at the beginning of the previous month. We calculate the value-weighted decile portfolio returns for all stocks in the CRSP-COMPUSTAT sample on a monthly basis and regress the portfolio return in excess of the risk-free rate on the market-rf (MKTRF), size (SMB), value (HML), and momentum (MOM) factors. The factors are obtained from Ken French’s website. We report regression results for only the top and bottom decile portfolios along with the top decile minus bottom decile hedge portfolio to save space. Absolute values of t-statistics are reported in parentheses below coefficient estimates. Statistical significance at the 10%, 5%, and 1% levels is denoted by *, **, and ***, respectively. Equity Returns for SYSDEFBETA Portfolios in CRSP Alpha*100 MKT SMB HML MOM 10th 1.187*** (2.74) 0.214 1.199*** (0.81) (19.82) 0.204 1.069*** 0.897*** 0.096 (0.72) (21.3) (13.01) (1.29) 0.501** 0.962*** 0.910*** -0.031 -0.320*** (2.16) (20.35) (14.63) (0.45) (7.88) Alpha * 100 MKT SMB HML MOM 90th 1.644*** (3.13) 0.612* 1.313*** (1.66) (15.93) 0.502 1.172*** 1.250*** 0.322*** (1.52) (17.18) (13.33) (3.18) 0.909*** 1.024*** 1.270*** 0.144 -0.450*** (3.08) (16.03) (15.09) (1.55) (8.14) Alpha * 100 MKT SMB HML MOM 90th - 10th 0.457* (1.70) 0.398 0.114** (1.48) (1.97) 0.298 0.104* 0.353*** 0.226*** (1.13) (1.75) (4.32) (2.59) 0.408 0.062 0.360*** 0.175** -0.130*** (1.54) (1.00) (4.43) (1.95) (2.61) 46 Figure 1: Historical Corporate Default Rates This figure plots the historical default rates on Moody’s rated corporate issuers. The data is from Moody’s Investor Services. Grey areas indicate NBER recessions. 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 47 Figure 2: Components of Corporate Spreads This figure plots the expected losses, taxes, and liquidity premium components of corporate spreads. The estimation of these components is described in Section 4.1. Bonds with maturity greater than seven years are referred to as having “long maturity� and bonds with maturity less than seven years are referred to as having “short maturity.� 12.00% 12.00% 10.00% 10.00% Liquidity Premium Taxes 8.00% 8.00% Expected Loss Spread 6.00% 6.00% 4.00% 4.00% 2.00% 2.00% 0.00% 0.00% AAA short-mat AA short-mat A short-mat BBB short-mat AAA long-mat AA long-mat A long-mat BBB long-mat B CCC BB 48