Is Credit Risk Priced in the Cross-Section of Equity Returns?

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1 Is Credit Risk Priced in the Cross-Section of Equity Returns? Caren Yinxia Nielsen Department of Economics and Knut Wicksell Centre for Financial Studies, Lund University Abstract We examine the link between the cross-section of stock returns and credit risk (valued by CDS premium), and the relation between the size, value and momentum effects with credit risk. We find that the value effect concentrated in the firms with low credit risk and the momentum effect concentrated in the firms with high credit risk. Firms with higher credit risk lose more in stock returns. However, there is a positive credit risk effect for stocks who won most in the past year, and during crisis who co-move with the market most and have low credit quality. Furthermore, the size effect, but not the value effect, could be attributed to a positive credit risk effect. Keywords: Asset pricing; Equity returns; Size effect; Value effect; Credit-risk effect; Credit-default-swap JEL classification: G11;G21;G28 1. Introduction The capital asset pricing model (CAPM) developed by Sharpe (1964) and Lintner (1965) has paved the way how people think about stock returns and market risk. However, in empirical research, there exist portfolios not included in the CAPM, the "anomalies", that successfully explain average stock returns. One typical example is the success of the zero-investment portfolios SMB (small-minus-big for size) and HML (high-minus-low for book-to-market ratio) from Fama and French (1993), and WML (winners-minus-losers for momentum return in the last year) from Carhart (1997) based on the one-year momentum effect of Jegadeesh and Titman (1993). 1 Fama and French (1992, 1993, 1995 and 1996) state that the stocks with smaller size (market capitalization, stock price times number of shares outstanding) and higher book-to-market ratio (value stocks, where book-to-market is the ratio of a common stock s book value to its market value) earn higher expected returns. As Fama and French (1993) suggest, the reasons for these size and value effects lie in size s and book-to-market s association with financial distress. Small and value stocks are compensated due to their high sensitivities to state variables, although these two state variables are not identified. Whether firms with higher distress risk is rewarded with higher stock returns cross-sectionally remains a puzzle. Some studies find a positive link between distress risk and equity returns, a possible explanation of the size and value The author is grateful to Christian Wagner, Ali Ozdagli, Peter Nyberg, Bent Jesper Christensen and participants at Arne Ryde Workshop (Lund), the 2011 Nordic Finance Network Research Workshop (Helsinki), and the finance seminar at Knut Wicksell Centre for Financial Studies at Lund University, for their comments and suggestions. Special thanks go to Björn Hansson, Frederik Lundtofte and Hans Byström for their valuable advice. Of course, all errors are mine. The grant from Bankforskningsinstitutet is gratefully acknowledged for financing this research. Tel.: +46 (0) ; Fax: +46 (0) address: caren.nielsen@nek.lu.se; Postal address: P.O. Box 7082, S Lund, Sweden. 1 SMB, HML, and WML are small minus big, high minus low, and winners minus losers, referring to the difference in returns on portfolios of small and big stocks, of value (high book-to-market) and growth (low book-to-market) stocks, and of winners and losers in the last year, respectively. This version: August 2015

2 effects. Chan et al. (1985) measure default risk by the credit spread between low-grade bonds and long-term government bonds, explaining a large portion of the size effect. Vassalou and Xing (2004) employ the default probabilities, computed by Merton s (1974) option pricing model, as the proxies for individual firms default risks, concluding that both the size and value effects can be viewed as default effects and that SMB and HML appear to contain additional information that is not related to default risk. Chan-Lau (2006) uses a systematic default-risk measure extracted from collateralized debt obligations, referring to standardized North America investment-grade credit-derivative indices. He finds that the systematic default risk is an important determinant of equity returns beside the Fama-French three factors. Chava and Purnanandam (2010) use ex ante estimates of expected returns based on the implied cost of capital, and apply hazard-rate estimation and expected default frequency to measure default risk. They find a positive relationship between expected stock returns and default risk when including size and book-to-market as control variables. Friewald et al. (2014) estimate risk premiums from firms CDS forward curves and find that firms stock returns increase with these credit risk premiums. However, others reveal a negative distress premium or mispricing argument of the value effect. Dichev (1998) shows that bankruptcy risk, through Altman s (1968) Z-score and Ohlson s (1980) O-score, is not rewarded by higher returns. Campbell et al. (2008) estimate bankruptcy risk with a dynamic logit model: Financially distressed stocks have delivered anomalously low returns. Avramov et al. (2009) use credit ratings, finding higher returns for lowcredit-risk than high-credit-risk firms. Griffin and Lemmon (2002) apply Ohlson s O-score as a proxy for distress risk, demonstrating that the value effect reveals among firms with the highest distress risk; this value premium is due to the mispricing of high distress risk rather than the risk-based explanation. Garlappi and Yan (2011) use the expected default frequency from Moody s KMV and find lower returns for financially distressed stocks, stronger value effects for firms with high default likelihood, and the concentration of momentum profits among low credit quality firms. The disagreement of previous research appears to result from using different proxies for financial distress. We consider credit risk as the most intuitive proxy. Different from previous literature, this study employs the credit risk under the risk-neutral measure revealed from the five-year credit-default-swap (CDS) market. A CDS is a contract of protection against the reference entity s default. The protection buyer pays periodic premiums to the protection seller in exchange for compensation in the event of default by the reference entity. Different from O-score and Z-score, the CDS premium is a market-based measure of credit risk. Additionally, many studies have demonstrated that the CDS market is more important in revealing the information of credit risk compared to the bond market (Longstaff et al., 2003; Blanco et al., 2005; Norden and Weber, 2009; Forte and Peña, 2009). Elton et al. (2001) display that much of the information in the default spread in bonds is unrelated to default risk. Equity traders have turned their attention first to the CDS market before trading has been reported, especially during the recent financial crisis (Gaffen, 2008). The purpose of this study is to investigate the linkage between the cross-section of average stock returns and firms credit risks, measured by CDS premiums, and the relation between credit risk and other firm characteristics, i.e. market β, size, book-to-market ratio (B/M), and one-year momentum return, in explaining stock returns. Additionally, our sample (from January 2004 to September 2014) covers the recent financial crisis when distress risk hits the most. Meantime, the CDS market becomes more alert due to the crisis. This adds more dynamics to our study and the real positive link between credit risk and stock returns if there is. We find a positive value effect concentrated in the firms with low credit risk and a positive momentum effect concentrated in the firms with high credit risk. Firms with higher credit risks lose more in stock returns. However, we find a positive credit risk effect for stocks who won most in the past year, and during crisis who co-move with the 2

3 market most and have low credit quality. Due to the financial crisis, the more stocks co-move with the market, the more they lose. Furthermore, the size effect could be attributed to a positive credit risk effect, but credit risk is not the underlying common factor for the value effect. Our contribution is to use the credit risk under the risk-neutral measure revealed from the CDS market, to investigate its pricing in equity returns and its relation with other firm characteristics. In addition, this study carries on for portfolios and individual stocks, and uses a sample covering the financial crisis. We process the analysis as follows. Section 2 describes the data. Section 3 investigates the relation of stock returns and firm characteristics, i.e. market β 2, size, B/M, momentum, and credit risk, by portfolio groupings. Section 4 applies Fama-MacBeth regressions to individual stocks to examine the explanatory power of the firm characteristics in the cross-section of stock returns and their relations. Section 5 constructs portfolios mimicking risk factors, studies the relation of factor loadings and the firm characteristics, and conducts asset-pricing tests on the models including different risk factors. Section 6 concludes. 2. Data We obtain data for all non-financial firms in the U.S. market with common stocks listed and with available USDdenominated CDS contracts written referring to. The sample period is January to September 2014, which starts when the CDS market is mature and covers the recent financial crisis. The data set is the intersection of daily common stock data on major stock exchanges (NYSE, AMEX, and NASDAQ) and quarterly fundamentals from Capital IQ, and daily CDS data from Credit Market Analysis (CMA). It consists of 489 firms with matched data. Stock returns are holding-period returns adjusted for all distributions, such as dividends, splits, rights offerings, and spin-offs. All monthly excess returns are returns in excess of the one-month U.S. Treasury bill rate, which is collected from Kenneth R. French s home page 4, so are the market excess returns and Fama and French s calculated data on three zero-investment portfolios (S MB FF, HML FF, and WML FF ). Firms characteristics, i.e. market β, size, B/M, momentum, and CDS premium are month-end observations. Market β is the past 60-month (with at least 24-month stock prices available) β, collected from Capital IQ. Size is a stock s market capitalization at the end of each month. Momentum return is a stock s cumulative return from t 11 to t 1. B/M is the ratio of total common equity to market capitalization at the end of each month. Normally, firms are required to file form 10-Q quarterly reports within 40 or 45 days and form 10-K annual reports within 75 or 90 days with the Securities and Exchange Commission. To ensure that the book-to-market ratio is publicly available, we assign a two-month information lag for fiscal quarter one, two, and three, and a three-month lag for fiscal quarter four. 5 For example, if a firm s first fiscal quarter ends in March, then its B/M at end of March will be used as the firm s characteristic at end of May. Notice that the first decile of size in our sample is about the sixth and the fifth decile of size in the Fama-French sample June 2009 and June 2014 respectively. This is because there are not many CDS contracts written referring to very small firms. However, this is not the case for other characteristics in our sample. This property of our sample could influence the analysis on size effect. 2 Market β is the slope of the regression line of a stock s excess return relative to the market excess return. 3 Additional one-year monthly stock prices are collected before January 2004 in order to calculate momentum returns Standard & Poor s analysis also uses these lags ( 3

4 CDS premium is the mid-premium 6 of the most liquid five-year senior CDS written referring to each firm. The prices of the same security from different data sources, such as CMA, GFI, Fenics, Reuters EOD, Markit, and JP Morgan, differ to some degree. Compared to the other sources, CMA uses a buy-side aggregation model and employs data from a variety of contributors, including major global investment banks, hedge funds, and asset managers. Mayordomo et al. (2010) use the most liquid single-name five-year CDS of the components of itraxx and CDX to compare the above six major data sources and find that the CMA database quotes lead the price discovery process compared to the other data sources. 3. Portfolio excess returns and characteristics To investigate any potential linkage between credit risk and the characteristics used to explain the cross-section of stock returns in the literature, i.e. market β, size, B/M and momentum, we study their correlations first. Table 1: Cross-sectional correlation of time-series averages market β 1 market β size B/M momentum CDS premium size (0.00) B/M (0.00) (0.00) momentum (0.00) (0.09) (0.00) CDS premium (0.00) (0.00) (0.00) (0.00) In parentheses are the corresponding p-values (for the null hypothesis that the correlation is zero). Table 1 displays the cross-sectional correlation coefficients between the time-series averages of stock return, market β, size, B/M and CDS premium for all individual stocks. CDS premium is significantly negatively correlated with size, or momentum return, and positively correlated with market β or B/M across stocks. This is consistent with the story that smaller stocks tend to have higher book-tomarket, which results from their poor prospects, and smaller firms carry higher financial distress, which results in a higher CDS premium to pay for protection against their defaults. It also shows that small stocks tend to be past losers, and the co-movement of small stocks and the market is high. We now explore the link between stocks returns and firm characteristics and investigate the drivers of this linkage by conducting portfolio sorts. Table 2 shows the portfolios constructed from one-way sort on CDS premium, market β, size, B/M or momentum return. At the end of each month, we sort the stocks into five groups according to one of their characteristics from low to high. Then for each quintile portfolio, we calculate its expected value-weighted and equally weighted excess returns, as well as its post-ranking market β 7, average size, average B/M, average momentum, and average CDS 6 We use all premiums from actual trades or contributors quotes. The data including only premiums from actual trades produces qualitatively the same results. 7 The market β is an estimator of the time-series slope of the portfolio s excess returns over risk-free rates on the excess market returns. 4

5 Table 2: Portfolios formed on each characteristic Panel A: Portfolios formed on CDS premium CDS-Low CDS-High High-Low Newey-West t Excess return (value-weighted) (0.05) Excess return (equally weighted) (-0.94) Market β Size B/M Momentum CDS premium Panel B: Portfolios formed on market β β-low β-high High-Low Newey-West t Excess return (value-weighted) (0.38) Excess return (equally weighted) (-0.16) Market β Size B/M Momentum CDS premium Panel C: Portfolios formed on size Small Big Small-Big Newey-West t Excess return (value-weighted) (1.28) Excess return (equally weighted) (-0.16) Market β Size B/M Momentum CDS premium Panel D: Portfolios formed on B/M Growth Value B/M-Neg. Value-Growth Newey-West t Excess return (value-weighted) (1.73) Excess return (equally weighted) (0.10) Market β Size B/M Momentum CDS premium Panel E: Portfolios formed on momentum Losers Winners Winners-Losers Newey-West t Excess return (value-weighted) (-0.18) Excess return (equally weighted) (0.72) Market β Size B/M Momentum CDS premium Portfolios are formed monthly on each characteristic, with 55 to 57 stocks on average. Stocks with negative B/M (B/M-Neg.) are excluded in Panel A, B, C and E. This table shows the time-series average of the value-weighted and equally weighted excess returns (in percent), sizes (in millions of dollars), book-to-market ratios, momentum returns (in percent) and CDS premiums (in basis points), and the post-ranking market β for each of the portfolios. High-Low in Panel A and B, Small-Big, Value-Growth and Winners-Losers indicate the return differences between high- and low-cds premium stocks, high- and low-market β stocks, small and big stocks, value and growth stocks, and past winners and losers, respectively. In parentheses are t-statistics based on heteroskedasticity and autocorrelation consistent standard errors using Newey and West (1987) with optimal truncation lag according to Newey and West (1994). 5

6 premium in the next month. For example, the portfolios in Panel A are formed by assigning stocks to groups from low CDS premium firms (CDS-Low) to high CDS premium firms (CDS-High) according to CDS premium quintiles for individual firms at the end of the previous month. Panel A reveals that the relation between CDS premium and expected stock excess return is not monotonic, and the second and fourth quintile portfolios have relatively high excess returns, especially for value-weighted portfolios. Again, CDS premium is negatively correlated with size and momentum, and positively correlated with B/M and market β. The variation of market β or size among CDS-premium-quintile portfolios is large, compared to its variation among β- or size-quintile portfolios in Panel B or C respectively. This suggests that there is a strong correlation between CDS premium and market β or size. Panel B to E shows that there are weak β and size effects and a significant (at 10% level) value effect for valueweighted portfolios. There are big variations of CDS premium for β- and size-quintile portfolios, compared to its variation in Panel A. This indicates that credit risk could be one of the underlying drivers for β or size effect. 6

7 Table 3: Portfolios formed on market β, size, B/M or momentum, and CDS premium Panel A: Average excess return of value-weighted portfolio Panel B: Average excess return of equally weighted portfolio Panel C: Average CDS premium All CDS-Low CDS-Medium CDS-High High-Low Newey-West t All CDS-Low CDS-Medium CDS-High High-Low Newey-West t All CDS-Low CDS-Medium CDS-High All (0.90) (-0.77) Portfolios sorted on market β and CDS premium Portfolios sorted on market β and CDS premium Portfolios sorted on market β and CDS premium β-low (-0.31) (-1.40) β-medium (0.59) (-1.21) β-high (0.75) (-0.40) High-Low Newey-West t (0.53) (0.20) (-0.61) (1.18) (-0.17) (-0.21) (-0.89) (1.16) Portfolios sorted on size and CDS premium Portfolios sorted on size and CDS premium Portfolios sorted on size and CDS premium Small (1.49) (-0.29) Medium (-0.85) (-1.89) Big (0.56) (-0.03) Small-Big Newey-West t (1.48) (0.27) (1.70) (0.23) (-0.06) (0.13) (1.80) (-0.54) Portfolios sorted on B/M and CDS premium Portfolios sorted on B/M and CDS premium Portfolios sorted on B/M and CDS premium Growth (0.76) (-0.88) Medium (0.61) (-0.67) Value (-0.08) (-1.49) Value-Growth Newey-West t (1.68) (1.45) (0.27) (0.03) (-0.10) (3.50) (-0.44) (0.06) Portfolios sorted on momentum and CDS premium Portfolios sorted on momentum and CDS premium Portfolios sorted by momentum and CDS premium Losers (-0.23) (-1.59) Medium (0.64) (-0.75) Winners (-0.34) (-0.84) Winners-Losers Newey-West t (-0.20) (1.54) (0.69) (-0.46) (0.49) (0.05) (-0.33) (0.78) Portfolios are formed monthly by independent 3 3 sorts on CDS premium and market β, size, B/M or momentum. This table shows the time-series average of the value- and equally weighted excess returns (in percent) and CDS premiums (in basis points) for each portfolio, as well as for each of the portfolios sorted only on one characteristic (All). High-Low in the horizontal and vertical bars represent the return differences between high- and low-cds premium stocks, and high- and low-market β stocks, respectively. Small-Big, Value-Growth and Winners-Losers indicate the return differences between small and big stocks, value and growth stocks, and past winners and losers, respectively. In parentheses are t-statistics based on heteroskedasticity and autocorrelation consistent standard errors using Newey and West (1987) with optimal truncation lag according to Newey and West (1994). 7

8 Next, we use two-pass sorted portfolios to control for any effect of credit risk or of any other characteristic, so as to identify which characteristic contributes to the performance of our portfolios. We construct portfolios by the intersection of the independent 3 3 (bottom 30%, middle 40%, and top 30%) sorts on market β, size, B/M or momentum, and CDS premium. For example, for portfolios sorted on size and CDS premium, in the end of each month, all stocks are allocated into three size portfolios (small, medium, and big) according to the size breakpoints determined using the market capitalizations of all stocks. Then each size portfolio is subdivided into three CDS premium portfolios (CDS-low, CDS-medium, and CDS-high) based on CDS premium breakpoints determined using all firms. Thereafter, we calculate the properties of each portfolio in the next month. Table 3 displays the time-series averages of the value- and equally weighted excess returns and CDS premiums for each portfolio. For value-weighted portfolios (Panel A), there is a monotonic relation between average excess return and CDS premium, market β, size or B/M. The average excess return of value-growth is significant at 10% level. So, there are weak credit risk, β, and size effects, and a mild value effect. However, this is not the case for equally weighted portfolios (Panel B). Nevertheless, the relation between excess return and, market β or momentum, is stronger for portfolios with high or low CDS premiums respectively, and there is no correlated variation of CDS premiums (Panel C) among these portfolios. There is a significant (at 10% level) size effect for portfolios (value-weighted and equally weighted) with medium CDS premiums. At meantime, there is some variation of CDS premium among these portfolios. A weak value effect shows up for value-weighted portfolios with low CDS premiums and it becomes significant at 1% level for equally weighted portfolios. At meantime, there is very little variation of CDS premiums among theses portfolios. In short, the strengthening of β, momentum, sizes and value effects after controlling for CDS premium demonstrates that credit risk cannot replace other characteristics in explaining equity returns across stocks. β, size, value, and momentum effects concentrate in firms with high, medium, low, and low credit risk, respectively. However, credit risk could contribute to the size effect within CDS-medium portfolios. In addition, there is a weak positive credit risk effect within small portfolios. 4. Individual stock returns and characteristics Since the research on firm characteristics and stock returns starts from that firm characteristics explain individual expected stock returns cross-sectionally. We investigate this using our sample with credit risk as an additional characteristic, so as to shed light on the relation between credit risk and other characteristics in explaining expected individual stock returns. As our sample period covers the recent financial crisis and the crisis is reflected significantly in the CDS market, we divide the sample into three sub-samples: pre-crisis (January 2004 to November 2007), during crisis (December 2007 to June 2009), and after crisis (July 2009 to September 2014). 8 Table 4 summarizes the data of the whole sample and of three sub-samples. Different from the pre-crisis and after crisis periods, crisis period is characterized with more volatile stock returns with lower average, negative average market return and momentum return, smaller minimum size, more variation of book-to-market ratios, and more volatile and higher CDS premium. Notice that the range of CDS premiums is much wider during and after crisis compared to pre-crisis period. This reflects that the CDS market is more alert since the occurrence of the crisis. 8 The National Bureau of Economic Research defines contraction period as December 2007 to June

9 Table 4: Summary statistics of the data Panel A: Whole sample period (129 months) Panel B: Pre-crisis period (47 months) VARIABLES Mean Std. Dev. Min. Max. VARIABLES Mean Std. Dev. Min. Max. stock return stock return market β market β B/M B/M MK MK size size ln(size) ln(size) CDS premium CDS premium ln(cds premium) ln(cds premium) momentum momentum Panel C: During crisis (19 months) Panel D: After crisis (63 months) VARIABLES Mean Std. Dev. Min. Max. VARIABLES Mean Std. Dev. Min. Max. stock return stock return market β market β B/M B/M MK MK size size ln(size) ln(size) CDS premium CDS premium ln(cds premium) ln(cds premium) momentum momentum This table summarizes data on stock returns (in percent), market β, size (millions of dollars), book-to-market, momentum returns (in percent), and CDS premium (basis points) for the whole sample and three sub-samples. 9

10 To investigate the explanatory power of the characteristics on average expected stock returns, we apply Fama- MacBeth s (1973) regression approach. 9 Each month, the cross-sectional expected stock returns are regressed on variables hypothesized to explain expected returns. Then the time-series average of the cross-sectional regression slopes for each explanatory variable tests whether the variable is on average priced. Table 5 and 6 display the results for the whole sample and pre-crisis sub-sample, and during crisis and after crisis sub-samples, respectively. A glimpse of Table 5 and 6 tells that size and credit risk are priced with negative risk premiums, book-to-market is priced with positive risk premium, and there is a positive momentum effect only during pre-crisis period. It is also not surprising that stocks loading more on market returns have lower expected returns, since our sample covers a severe financial crisis. We now explore the link between the risk premium of credit risk and of other characteristics through the significant interaction terms. For the whole sample (specification (4)), as long as ln(cds premium) is one standard deviation higher than its mean, i.e. CDS premium is above bp (see Table 4), there is a negative value effect. The same goes for precrisis sub-sample (specification (4), (7) and (8)), when ln(cds premium) is two standard deviations higher than its mean, i.e. CDS premium is above bp. For the whole sample (specification (6)), and after crisis sub-sample (specifications (6) and (7)), as long as ln(cds premium) is higher than its mean, there is a positive momentum effect. For the whole sample (specification (6)), the pre-crisis sub-sample (specification (6)), and after crisis sub-sample (specifications (6) and (7)), for stocks whose past momentum returns are at least two standard deviations higher than the mean, there is a positive credit risk effect. Differently, during crisis, the only interaction term that explains expected return is that of market β and credit risk. Specifications (6) and (8) say that when market β is extremely big, bigger than 4.97, there is a positive credit risk effect. In brief, the positive value effect concentrates in the firms with high credit quality, which confirms the findings in Section 3; past winners who won most and have low credit quality will earn higher returns; during crisis, the stocks who load on market most and have low credit quality will earn higher returns; there is no significant size effect without considering credit risk in explaining cross-sectional stock returns. 9 The tests according to Petersen (2009) verify that the residuals in our study are correlated across firms instead of across time, which supports the usage of Fama-MacBeth s (1973) approach here. 10

11 Table 5: Fama-MacBeth regressions of expected stock returns on firm characteristics: The whole sample and pre-crisis sub-sample Whole sample Pre-crisis sub-sample (1) (2) (3) (4) (5) (6) (7) (8) (1) (2) (3) (4) (5) (6) (7) (8) market β market β (0.31) (0.27) (0.27) (0.26) (0.28) (0.59) (0.61) (0.23) (0.24) (0.24) (0.24) (0.24) (0.34) (0.38) ln(size) ** -0.57** -0.18** -0.19*** -0.19*** -0.18** ln(size) *** * (0.10) (0.08) (0.22) (0.08) (0.07) (0.07) (0.07) (0.25) (0.16) (0.14) (0.11) (0.13) (0.13) (0.13) (0.13) (0.15) B/M ** B/M *** *** 3.56*** (0.22) (0.22) (0.20) (0.88) (0.21) (0.21) (1.14) (1.00) (0.51) (0.52) (0.46) (1.13) (0.47) (0.47) (1.44) (1.21) momentum * * momentum 0.02*** 0.02** 0.02** 0.02*** (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01) (0.01) (0.01) (0.01) (0.02) (0.02) (0.02) (0.02) ln(cds pre.) -0.60*** -1.43** -0.47** -0.62*** -0.60*** -0.57** ln(cds pre.) -0.29** -1.13* *** -0.42** (0.19) (0.59) (0.22) (0.15) (0.17) (0.24) (0.69) (0.12) (0.58) (0.16) (0.15) (0.17) (0.17) (0.69) ln(size)*ln(cds pre.) ln(size)*ln(cds pre.) (0.06) (0.07) (0.06) (0.06) (B/M)*ln(CDS pre.) -0.34* (B/M)*ln(CDS pre.) -0.75** -0.80** -0.69** (0.19) (0.24) (0.21) (0.31) (0.38) (0.32) momentum*ln(cds pre.) 0.01** 0.01*** 0.01** 0.01** momentum*ln(cds pre.) * (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (market β)*ln(cds pre.) (market β)*ln(cds pre.) (0.08) (0.08) (0.10) (0.10) Constant *** 8.33*** 4.24*** 4.92*** 4.83*** 4.50*** 6.73** Constant * 5.47*** ** 2.95** * (1.14) (1.05) (2.26) (1.29) (0.86) (0.96) (1.25) (2.66) (1.67) (1.31) (1.21) (1.61) (1.20) (1.15) (1.66) (1.84) Observations Observations Number of groups Number of groups F F p(f) e p_f avg. R-squared avg. R-squared This table shows, for the whole sample and pre-crisis sub-sample, the average of intercepts and slopes from the month-by-month Fama-MacBeth cross-sectional regressions of individual stock returns (in percent) on market β, size (millions of dollars), book-to-market, momentum return (in percent), CDS premium (basis points), and interaction terms of CDS premium and other characteristics in the previous month. Stocks with negative book-to-market are not included in the tests. In parentheses are heteroskedasticity and autocorrelation consistent standard errors using Newey and West (1987). The superscripts *, **, and *** indicate statistic significance at 10%, 5%, and 1% level, respectively. 11

12 Table 6: Fama-MacBeth regressions of expected stock returns on firm characteristics: During crisis and after crisis During crisis After crisis (1) (2) (3) (4) (5) (6) (7) (8) (1) (2) (3) (4) (5) (6) (7) (8) market β -1.97* ** -3.49* market β (1.13) (0.97) (0.99) (0.97) (1.04) (1.54) (1.71) (0.26) (0.24) (0.23) (0.24) (0.24) (0.68) (0.74) ln(size) ** ** -0.42** -0.42** -0.40** 0.47 ln(size) ** -0.71** -0.19* -0.20** -0.20** -0.20** -0.73* (0.37) (0.16) (0.79) (0.17) (0.17) (0.18) (0.19) (0.60) (0.10) (0.09) (0.35) (0.10) (0.09) (0.09) (0.09) (0.39) B/M B/M (0.43) (0.38) (0.29) (1.64) (0.33) (0.32) (1.43) (1.54) (0.23) (0.23) (0.23) (1.38) (0.22) (0.22) (1.73) (1.28) momentum * * momentum * -0.03** -0.03* -0.03* (0.02) (0.02) (0.02) (0.02) (0.05) (0.06) (0.05) (0.06) (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) (0.02) (0.01) ln(cds pre.) -1.81*** *** -1.38** -1.49** -1.80** 0.23 ln(cds pre.) -0.47*** -1.59* -0.42** -0.53*** -0.46** -0.57** -1.85* (0.61) (1.92) (0.56) (0.48) (0.53) (0.69) (1.70) (0.10) (0.90) (0.18) (0.13) (0.18) (0.28) (1.04) ln(size)*ln(cds pre.) ln(size)*ln(cds pre.) (0.18) (0.14) (0.10) (0.11) (B/M)*ln(CDS pre.) (B/M)*ln(CDS pre.) (0.29) (0.25) (0.27) (0.28) (0.34) (0.26) momentum*ln(cds pre.) momentum*ln(cds pre.) ** 0.01* 0.01 (0.01) (0.01) (0.01) (0.01) (0.00) (0.00) (0.00) (0.00) (market β)*ln(cds pre.) 0.30* 0.33* (market β)*ln(cds pre.) (0.17) (0.18) (0.11) (0.12) Constant *** *** 8.61*** 9.22*** 9.11*** 1.19 Constant *** 9.72*** 4.66*** 5.32*** 4.91*** 5.61*** 10.77*** (3.92) (1.35) (8.29) (1.28) (1.69) (2.06) (1.88) (6.94) (0.96) (1.00) (3.26) (1.56) (1.08) (1.43) (1.70) (3.96) Observations Observations Number of groups Number of groups F F p_f p_f avg. R-squared avg. R-squared Standard errors in parentheses Standard errors in parentheses This table shows, for during crisis (Panel A) and after crisis (Panel B) sub-samples, the average of intercepts and slopes from the month-by-month Fama-MacBeth cross-sectional regressions of individual stock returns (in percent) on market β, size (millions of dollars), book-to-market, momentum return (in percent), CDS premium (basis points), and interaction terms of CDS premium and other characteristics in the previous month. Stocks with negative book-to-market are not included in the tests. In parentheses are heteroskedasticity and autocorrelation consistent standard errors using Newey and West (1987). The superscripts *, **, and *** indicate statistic significance at 10%, 5%, and 1% level, respectively. 12

13 5. Asset pricing Since the reason why firm characteristics explain the differences in average returns across stocks is argued to be that they proxy for the sensitivities to the underlying common risk factors in stock returns. Could credit risk be one of these common risk factors? To test this hypothesis, we construct risk factors and conduct asset pricing tests of the models considering an additional credit risk factor. We construct zero-investment portfolios as proxies for the risk factors in returns related to firm characteristics, i.e. size, B/M, momentum, and CDS premium, as Fama and French (1993). We perform two-pass 2 3 independent sorts on size and one of other characteristics, i.e. B/M, momentum, and CDS premium, in the same manner as in Section 3. For example, the intersection of the independent 2 3 sorts 10 on size (bottom 50% and top 50%) and B/M (bottom 30%, middle 40%, and top 30%) produces six portfolios, SG, SM, SV, BG, BM, and BV, where S and B indicate small and big and G, M, and V indicate growth, medium, and value respectively. The size factor, SMB (small-minusbig), is the equally weighted average of the returns on the three small-stock portfolios (SG, SM, and SV) minus that of the returns on the three big-stock portfolios (BG, BM, and BV). The value factor, HML (high-minus-low), is the equally weighted average of the returns on two value-stock portfolios (SV and BV) minus that of the returns on two growth-stock portfolios (SG and BG). In the same way as constructing HML, the risk factors for momentum and CDS premium, WML (winners-minus-losers) and CHML (high-minus-low for credit risk), are constructed from the 2 3 size-momentum sorts and the 2 3 size-cds premium sorts, respectively. Table 7 shows that the correlation between our risk factor, SMB, HML, or WML, and the same factor from Fama- French sample, S MB FF, HML FF, or WML FF, is higher than 0.5, especial for the momentum factor. Statistically, they are not dramatically different, except the size factor during crisis period and the whole time span. This is due to that we do not have very small firms in our sample, mentioned in Section 2. To conduct asset-pricing tests, first, we run time series regressions of equity excess returns on factors: R i,t = α i + β i f t + ε i,t (1) to get estimates of α i and β i, where R stands for excess return and f is the vector of all risk factors in the model. Then, we run cross-sectional regression of average equity excess returns on estimated risk loadings β i : R i = β i λ + error i (2) to get risk premium λ Factor loadings To investigate whether some of the risk premiums of firm characteristics stems from that they proxy for financial distress risk, this section assesses relation between characteristics and the factor loadings in the model including all risk factors, MK, SMB, HML, WML, and CHML. We obtain time-series averages of each firm s characteristics and its loadings of excess returns on all risk factors. Then we allocate firms cross-sectionally into five groups on their averages of each characteristic from low to high and present the average risk sensitivities of each group in Table 8. This helps us identify the relation between firm characteristics and risk sensitivities cross-sectionally. 10 The intersection of the independent 3 3 sorts produces qualitatively the same results for asset pricing tests. 13

14 Table 7: Statistics of the risk factors and their correlations Panel A: Correlations between risk factors MK S MB HML WML CHML S MB FF HML FF WML FF MK 1 S MB HML W ML CHML S MB FF HML FF WML FF whole sample period Panel B: Summary statistics of risk factors before crisis Factors Mean Std. Dev. Min. Max. Factors Mean Std. Dev. Min. Max. MK MK S MB S MB HML HML W ML W ML CHML CHML S MB FF S MB FF HML FF HML FF WML FF WML FF during crisis after crisis Factors Mean Std. Dev. Min. Max. Factors Mean Std. Dev. Min. Max. MK MK S MB S MB HML HML W ML W ML CHML CHML S MB FF S MB FF HML FF HML FF WML FF WML FF The mimicking risk factors are MK (market excess returns over risk-free rates), S MB (smallminus-big for size), HML (high-minus-low for book-to-market), WML (winners-minus-losers for momentum return), and CHML (high-minus-low for credit risk). S MB FF, HML FF and WML FF denote the risk factors using Fama-French sample. This table displays statistics (in percent) of the factors and their correlations. 14

15 Table 8: Factor loadings Panel A: Stocks with different CDS premiums CDS-Low CDS-High CDS premium β MK β S MB β HML β WML β CHML Panel B: Stocks with different market βs β-low β-high market β CDS premium β CHML Panel C: Stocks with different sizes Small Big size CDS premium β CHML Panel D: Stocks with different B/Ms Growth Value B/M CDS premium β CHML Panel E: Stocks with different momentums Losers Winners momentum CDS premium β CHML This table demonstrates the cross-sectional averages of each characteristic and of the factor loadings of the stocks in each quintile portfolio formed on the time-series average of the characteristic. β MK, β S MB, β HML, and β CHML stand for the factor loadings of stocks on the mimicking risk factors, MK, SMB, HML, WML, and CHML, all included in the model. size is in millions of dollars, CDS premium is in bp, and momentum is in percent. 15

16 Similar as the non-linear relation between stock excess returns and CDS premium in Table 2, there is no linear relation between credit risk and any factor loading. Panel B and C verify that there is a strong monotonic correlation between credit risk and size or credit risk and market β. High-β group and small-stock group load much more than low-β group and small-stock group, respectively. Then, size effect and market β effect could be attributed to credit risk effect. However, it is not the case for book-to-market and momentum Test models Now we move on to test different models and examine risk premiums as in Equation 2. Table 9 displays the results of the cross-sectional regressions of equity excess returns on factor loadings for the whole sample and three sub-samples. The tests are based on three benchmark models, the CAPM, the Fama-French three-factor model, and the Carhart (1997) four-factor model, the augmented versions of the three-factor and four-factor models with the credit-risk factor, CHML as an additional factor, and the model only including CHML. The risk premium of MK is significantly negative during criss and for the whole sample period, which verifies the previous results that the more stocks co-move with the market the more they lose due to the financial crisis. When HML is the only risk factor in the model, its risk premium is significantly negative during crisis period. The risk premium of SMB is only positive and significant after crisis. This supports the argument that size effect is attributed to credit risk effect which should not be negative during non-crisis period and when CDS market is more alert and developed after the occurrence of the crisis. HML only carries a significantly positive risk premium for the whole sample without CHML in the model, which is consistent with our statement that value effect concentrates in the stocks with high credit quality and it is not attributed to credit risk effect. The risk premium of WML is positive and significant for the sub-samples when we also consider CHML in the model. This is also consistent with the previous analysis that positive momentum effect concentrates in stocks with low credit quality and there is a positive credit risk effect for stocks win most in the past year. 16

17 Table 9: Asset pricing tests Panel A: whole sample period Panel B: pre-crisis period CAPM CHML 3-fac. model 4-fac. model 3-fac. and CHML 4-fac. and CHML CAPM CHML 3-fac. model 4-fac. model 3-fac. and CHML 4-fac. and CHML MK -0.86*** -1.23*** -0.68* -1.08*** -1.24*** MK *** (0.19) (0.25) (0.39) (0.28) (0.24) (0.21) (0.22) (0.27) (0.25) (0.18) SMB -0.36*** -0.24* -0.36*** SMB -0.44** -0.31* (0.13) (0.13) (0.12) (0.13) (0.18) (0.18) (0.18) (0.14) HML ** HML (0.15) (0.19) (0.19) (0.19) (0.13) (0.14) (0.13) (0.12) WML WML *** (0.34) (0.31) (0.25) (0.19) CHML -0.74*** -0.53** -0.48** CHML (0.19) (0.22) (0.24) (0.27) (0.22) (0.17) Constant 1.44*** 1.10*** 1.71*** 1.05*** 1.63*** 1.67*** Constant 0.83*** 0.70*** 1.07*** 0.57** 0.94*** 1.08*** (0.20) (0.19) (0.23) (0.40) (0.27) (0.22) (0.20) (0.17) (0.21) (0.24) (0.24) (0.15) Observations Observations chi chi Prob > chi2 3.45e e e e-06 Prob > chi e-05 adj. R-squared adj. R-squared Panel C: During-crisis period Panel D: After-crisis period CAPM CHML 3-fac. model 4-fac. model 3-fac. and CHML 4-fac. and CHML CAPM CHML 3-fac. model 4-fac. model 3-fac. and CHML 4-fac. and CHML MK -1.31*** -1.20*** *** MK ** (0.41) (0.41) (0.48) (0.61) (0.38) (0.16) (0.20) (0.30) (0.29) (0.31) SMB -0.87*** -0.61*** -0.64*** -0.59*** SMB * 0.17** 0.25*** (0.27) (0.20) (0.18) (0.20) (0.06) (0.08) (0.07) (0.07) HML -0.87*** -0.60*** -0.53*** -0.60*** HML * -0.22* -0.31** (0.16) (0.18) (0.13) (0.17) (0.12) (0.12) (0.12) (0.13) WML 1.11*** 0.91** WML *** (0.36) (0.44) (0.25) (0.18) CHML -1.39*** -1.24*** -1.18*** CHML *** -0.44*** (0.55) (0.38) (0.34) (0.11) (0.13) (0.15) Constant -1.03* -1.53** -0.99** -1.96*** -2.28*** -1.06** Constant 1.17*** 1.51* 0.98*** 1.21*** 0.99*** 1.14*** (0.55) (0.61) (0.43) (0.70) (0.74) (0.45) (0.15) (0.11) (0.17) (0.25) (0.26) (0.26) Observations Observations chi chi Prob > chi e Prob > chi e-06 adj. R-squared adj. R-squared This table shows cross-sectional regressions of Equation 2 for the CAPM, the Fama-French three-factor model, the Carhart (1997) four-factor model, augmented three-factor and four-factor models with an additional factor CHML, and the model only including CHML, for the whole sample and three sub-samples. Stocks with negative book-to-market are not included in the tests. In parentheses are bootstrapped standard errors. The superscripts *, **, and *** indicate statistic significance at 10%, 5%, and 1% level, respectively. 17

18 6. Conclusion This article examines distress risk puzzle in the context that there is a natural experiment of the financial crisis when distress risk hits the most and that there is a developing process for the CDS market becoming more alert due to the crisis. We apply the premium of a five-year senior CDS contract as a proxy for the distress risk of a firm which is referred to in the CDS contract. Through revisiting the research on how firm characteristics, market β, size, book-tomarket ratio and momentum return in the past year, explain stocks expected returns cross-sectionally, we are able to disentangle the relation of these characteristics with the firms credit risk in the context of pricing stock returns. We find a positive value effect concentrated in the firms with low credit risk and a positive momentum effect concentrated in the firms with high credit risk. That is, value premiums are higher for firms far away from default, and past winners will continue win if they have low credit quality. Firms with higher credit risks lose more in stock returns. However, we find that there is a positive credit risk effect for stocks who won most in the past year, and during crisis who co-move with the market most and have low credit quality. Due to our special sample covering a financial crisis, the more stocks co-move with the market, the more they lose. Furthermore, the size effect could be attributed to a positive credit risk effect, but credit risk is not the underlying common factor for the value effect. The asset-pricing tests confirm these results and reveal that its important to include credit risk in the models. Yet, more thorough tests should be performed on a much larger sample available in future. References Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. The journal of finance, 23, Avramov, D., Chordia, T., Jostova, G., and Philipov, A. (2009). Credit ratings and the cross-section of stock returns. Journal of Financial Markets, 12, Blanco, R., Brennan, S., and Marsh, I. (2005). An empirical analysis of the dynamic relation between investment-grade bonds and credit default swaps. The Journal of Finance, 60, Campbell, J. Y., Hilscher, J., and Szilagyi, J. (2008). In search of distress risk. The Journal of Finance, 63, Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of finance, 52, Chan, K. C., Chen, N., and Hsieh, D. A. (1985). An exploratory investigation of the firm size effect. Journal of Financial Economics, 14, Chan-Lau, J. (2006). Is systematic default risk priced in equity returns? A cross-sectional analysis using credit derivatives prices. Working Paper, International Monetary Fund. Chava, S., and Purnanandam, A. (2010). Is default risk negatively related to stock returns? Review of Financial Studies, 23, Dichev, I. D. (1998). Is the risk of bankruptcy a systematic risk? The Journal of Finance, 53, Elton, E. J., Gruber, M. J., Agrawal, D., and Mann, C. (2001). Explaining the rate spread on corporate bonds. The Journal of Finance, 56, Fama, E. F., and French, K. R. (1992). The cross-section of expected stock returns. The Journal of finance, 47, Fama, E. F., and French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, Fama, E. F., and French, K. R. (1995). Size and book-to-market factors in earnings and returns. The Journal of finance, 50, Fama, E. F., and French, K. R. (1996). Multifactor explanations of asset pricing anomalies. The Journal of Finance, 51, Fama, E. F., and MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. The Journal of Political Economy, 81, Forte, S., and Peña, J. I. (2009). Credit spreads: An empirical analysis on the informational content of stocks, bonds, and cds. Journal of Banking & Finance, 33, Friewald, N., Wagner, C., and Zechner, J. (2014). The cross-section of credit risk premia and equity returns. The Journal of Finance, 69, Gaffen, D. (2008). Stock investors catch a case of CDS. The Wall Street Journal, September 16. Garlappi, L., and Yan, H. (2011). Financial distress and the cross-section of equity returns. The Journal of Finance, 66, Griffin, J. M., and Lemmon, M. L. (2002). Book to market equity, distress risk, and stock returns. The Journal of Finance, 57, Jegadeesh, N., and Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48, Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47,