Is Default Risk Priced in Equity Returns?

Transcription

1 Is Default Risk Priced in Equity Returns? Caren Yinxia G. Nielsen The Knut Wicksell Centre for Financial Studies Knut Wicksell Working Paper 2013:2 Working papers Editor: F. Lundtofte The Knut Wicksell Centre for Financial Studies Lund University School of Economics and Management

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3 Is Default Risk Priced in Equity Returns? 1 Is Default Risk Priced in Equity Returns? Caren Yinxia G. Nielsen * Abstract Size and book-to-market equity (BM) strongly explain stock returns cross section; the risk they capture is the relative distress of small and value stocks. This study examines the default risk s pricing power, measured by U.S. firms market-revealed credit-default-swap premiums ( ), in average returns across stocks. It also explores whether the size and BM effects stem from proxying the default-risk effect. In the tests, size dominates the size default-risk effect, while BM and default risk work together. Therefore, size and BM partially proxy the default-risk effect. As expected, size is priced with a negative risk premium and BM is positive. However, higher default risk only engenders higher expected stock returns when BM is below a threshold and unpriced. Additionally, size indeed proxies sensitivity to the default-risk factor. Furthermore, the Fama French factors SMB (small-minus-big) and HML (high-minus-low) share some common information with the default-risk factor in assetpricing tests. Keywords: Asset Pricing; Equity Returns; Size Effect; Book-to-Market Effect; Default-Risk Effect; Credit-Default-Swap Premium JEL classification: G12 * Department of Economics, Knut Wicksell Centre of Financial Studies, Lund University, P. O. Box 7082, S Lund, Sweden. Tel.: ; Caren_Yinxia.Guo_Nielsen@nek.lu.se. I started this paper when I was a visiting student at Århus University in Denmark.

4 Is Default Risk Priced in Equity Returns? 2 The capital asset pricing model (CAPM) developed by Sharpe (1964) and Lintner (1965) has paved the way how people think about asset 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 SMB and HML 1 portfolios from Fama and French (FF; 1992, 1993, 1995 and 1996). Fama and French state that size or market equity (ME, stock price times number of shares) and book-to-market equity (BM, ratio of a common stock s book value to its market value) strongly explain the cross section of stock returns. Stocks with smaller ME and higher BM earn higher expected returns. As FF (1993) suggest, the reasons for these ME and BM effects lie in ME s and BM s association with financial distress. Therefore, small and value stocks (with high BM) should be compensated due to their high sensitivities to state variables, such as specific business-cycle factors. More aggressively, the three-factor model (the factors are the excess market return over the risk-free rate, SMB and HML) is an equilibrium pricing model, a three-factor version of Merton s (1973) intertemporal capital asset pricing model or Ross s (1976) arbitrage pricing theory (FF; 1993, 1995 and 1996). In this view, SMB and HML mimic combinations of two underlying risk factors or state variables of special hedging concern to investors. However, they could not identify these two state variables. The explanation of the ME and BM effects remain a puzzle. While some researchers, such as Lakonishok et al. (1994), Daniel and Titman (1997) et cetera, explore behavioral stories, others investigate whether the equity market prices a firm s financial distress with a positive premium in the framework of the rational pricing theory. However, the conclusions of the studies in the rational pricing field do not agree. Some find a positive value premium, a possible explanation of the ME and BM effects, with 1 SMB (HML) is small minus big (high minus low), referring to the difference in returns on portfolios of small (high book-to-market) stocks and large (low book-to-market) stocks.

5 Is Default Risk Priced in Equity Returns? 3 default risk as the proxy for the financial distress. 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 ME 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 ME and BM 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 ME and BM as control variables. However, others reveal a negative distress premium or mispricing argument of the BM 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 low-credit-risk than high-credit-risk firms. Griffin and Lemmon (2002) apply Ohlson s O- score as a proxy for distress risk, demonstrating BM effect reveals among firms with the highest distress risk; this BM premium is due to the mispricing of high distress risk rather than the risk-based explanation. The disagreement of previous research appears to result from using different proxies for financial distress. We consider default risk as the most intuitive proxy. However, how much of the default-risk information is of special hedging concern to investors varies with the

6 Is Default Risk Priced in Equity Returns? 4 state of the economy and government policies. Therefore, this study employs the default risk under the risk-neutral measure revealed from the credit-default-swap (CDS) market. This choice of the proxy for financial distress is also consistent with Ozdagli s (2010) theoretical argument that the positive value premium and the negative distress premium result from using the risk-neutral and real default probability, respectively. His model also predicts that firms with higher risk-neutral default probabilities, such as those revealed from credit default swap premiums (CDSP), should have higher stock returns. Additionally, the advantages of choosing the CDS market also lie in the properties of the CDS and its importance in financial markets. First, a CDS is a contract of protection against default. The protection buyer pays periodic premiums to the protection seller in exchange for compensation in the event of default by the reference entity. CDS isolates default risk from other risks faced by a firm. Therefore, it could be argued to be a clean measure of default risk. Second, the CDSP is market based, not accounting data as O-score and Z-score that suffer from being backward looking. The market-quoted CDSP directly reflect the market perceptions of the referred firms default risk. In this study, the default risk is the uncertainty surrounding a firm s ability to service its debts and obligations, rather than the risk of facing bankruptcy (Chapter 11) or liquidation. Even though these two concepts are correlated, in the view of the pricing power in equity returns, the risk of not paying debts is normally an earlier negative shock and more powerful in driving investors expectations compared to the risk of bankruptcy or liquidation. Furthermore, CDS is the most liquid default derivative and takes the biggest proportion of the market trading. Finally, 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)

7 Is Default Risk Priced in Equity Returns? 5 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). From the perspective of asset pricing, default risk could affect investors expectations of future wealth, consumption and investment opportunities, which are linked to state variables. During financial turmoil, the marginal utility of buying protection against default risk, such as a CDS contract, is much higher simply because the situation of other assets is very bad. This intertemporal shift of marginal utility could reveal changes in the state variables. Therefore, default risk could be systematically priced and even help price other assets. Furthermore, Ferguson and Shockley (2003) demonstrate that the true CAPM should include both equity and debt claims in the market portfolio. This theoretical model explains why the debt-related variables, such as ME and BM, have strong explanatory power for the cross section of average returns. Hence, default risk, proxied by the CDSP, has a relation to the ME and BM effects from the perspective of asset pricing. The purpose of this study is to investigate the pricing power of default risk, measured by the CDSP, in average stock returns and to determine whether the ME and BM effects are due to their proxying for the default risk. The overall analysis considers three aspects. First, it examines whether a default-risk effect exists for portfolios and individual stocks to demonstrate whether default risk is priced in equity returns. Second, it explores the relationship between the default-risk effect and the ME and BM effects for portfolios and individual stocks. Third, it tests whether ME and BM are related to the loadings on the default-risk factor, assumed to be one of the underlying common risks in stock returns. My contribution to the research is to use only the default risk of concern to the investors in the market, the default risk under the risk-neutral measure revealed from the CDS market, to investigate the pricing of firms financial distress. Additionally, this study

8 Is Default Risk Priced in Equity Returns? 6 specifically focuses on the explanation of the ME and BM effects. Furthermore, the CDSP data are for individual U.S. firms ( ), rarely used in studying equity returns, and hand picked to match existing data from accounting and the stock market. In brief, I find that there exists a joint effect of ME or BM with default risk on portfolio returns. Furthermore, the ME effect dominates its joint effect with default risk, while both BM and default risk co-work for their joint effect. Fama and MacBeth s (FM; 1973) regressions on individual firms prove that ME and BM have explanatory power for the variation of returns across stocks, but the BM effect is only significant when the default-risk term and an interaction term of BM and default risk are also in the regressions. ME is priced with a negative risk premium; BM is priced with a positive risk premium. Only when BM is below a certain level, and is not priced, is higher default risk priced with higher stock returns. Additionally, the factor loadings of portfolios show that ME does proxy sensitivity to the default-risk factor. Therefore, default risk could be the underlying risk factor of the ME effect. Although tests on the asset pricing models cannot provide strong evidence that DHML (high minus low for the default-risk factor) should be considered a significant factor in asset pricing, DHML does share common information with other factors and cannot be ignored. I process the analysis as follows. Section 1 describes the data. Section 2 investigates the relationship of the default-risk effect and the ME and BM effects by intuitive portfolio groupings. To analyze these relationships more formally, Section 3 applies FM regressions to individual stocks to examine the explanatory power of ME, BM and default risk in stock returns and their relationships. Section 4 examines the factor loadings and investigates whether ME and BM proxy for the sensitivities to the default-risk factor, which has been declared as one explanation for the ME and BM effects. Section 5 conducts the asset-pricing tests on the factors using discount-factor pricing models. Section 6 concludes.

9 Is Default Risk Priced in Equity Returns? 7 1. Data This study applies the analysis to all individual nonfinancial firms in the U.S. market with matched data from the equity market, accounting and credit-derivative market. The data set is the intersection of daily common stock files on major stock exchanges (NYSE, AMEX, NASDAQ) from the Center for Research in Security Prices (CRSP), balance-sheet data in COMPUSTAT s fundamentals quarterly file and CDS data from Credit Market Analysis (CMA) 2. Each firm s annual reports are checked to ensure the firms from the different data sets match. The data set consists of 467 firms with matched data. The market returns, T-bill rates and SMB and HML data are from Kenneth R. French s home page 3. Stock and accounting data are from January 2003 through September 2010 and CDS data are from January 2004 to September 2010 because more recent CDS data are more efficient due to the newness of the market, and we need one year preceding 2004 for stocks to estimate market βs used in the FM regressions. The study uses weekly data to minimize the microstructure effects of high-frequent data and also to maintain the tests statistical power. Firms weekly returns are holding-period returns adjusted for all distributions (such as dividends and splits) from the first to last trading date of a week (with Friday as the end of a week). The value-weighted returns of all stocks on the main exchanges (NYSE, AMEX and NASDAQ) proxy for market returns. The book equities (BE, book value of common equity plus balance-sheet deferred taxes) of stocks are quarterly data from COMPUSTAT because quarterly data reflect the performance of a firm more effectively and quarterly earnings lead trading activities. When calculating the BM ratio in each week, I use the ME on the last trading date before the BE recording date for comparison to ensure a stock s market information is publicly known 2 CMA data are collected through Thomson Datastream Navigator. 3

10 Is Default Risk Priced in Equity Returns? 8 before the accounting data are recorded. This ratio is influential only when ME and BE are comparable; therefore, it is updated when BE is updated. 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. Therefore, assuming a two-month lag on quarterly data (fiscal quarters 1, 2 and 3) and a three-month lag on annual data (fiscal quarter 4) 4 is reasonable. I measure a firm s ME by its weekly ME, which is a stock s price multiplied by the number of share outstanding on the last trading date of a week. The CDS data are the mid-premiums of 5-year senior CDSs from CMA. 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. Furthermore, Mayordomo et al. (2010) use the most liquid single-name 5-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. I use Veracity Code provided by CMA to control the quality of the data, eliminating all quotes with scoring higher than three, because three or lower Veracity Score verify that the quote is associated with an actual trade or that the quote is an indication provided by a market participant, not derived from a model. 2. ME, BM and Default Risk Portfolio Approach This section uses portfolio groupings to investigate the relationship between the ME or BM effect and the default risk effect as proxied by the CDSP. There are two hypotheses to test in this sample. One is whether each of these three effects exists. This is equivalent to whether ME, BM or CDSP explains the differences in average returns across stocks and whether 4 Standard & Poor s analysis also uses these lags (

11 Is Default Risk Priced in Equity Returns? 9 stocks with smaller ME, higher BM or higher CDSP are rewarded with higher expected returns. The other hypothesis concerns whether the ME or BM effect can be interpreted as the default-risk effect; whether a default-risk effect exists after controlling for ME or BM or a ME or BM effect exists after controlling for default risk. This test aims to explore the interaction between the ME or BM effect and the default-risk effect, the joint effect and the exclusive effect Correlations between ME, BM and CDSP Table 1 displays the time-series averages of the cross-sectional correlation coefficients between ME, BM and CDSP for all individual stocks and the corresponding p-values (for the null hypothesis that the correlation is zero). The data are weekly data for the period from January 2004 to September The average cross-sectional correlation between ME and BM is significantly negative at the 6% level. On average, CDSP is significantly negatively correlated with ME across stocks. These results are consistent with the story that smaller stocks tend to have higher BM, which results from their poor prospects, and smaller firms carry higher financial distress, which induces a higher CDSP. Thus, the ME effect may interact with the BM effect and proxy for a default-risk effect. The cross-sectional correlation between BM and CDSP does not provide any information because on average, the correlation is essentially zero. Table 1: Time-Series Average Correlation between ME, BM and CDSP ME BM Correlation p-value Correlation p-value BM * CDSP ** ME is size; BM is book-to-market equity; CDSP is credit-default-swap premium. This table shows the timeseries averages of the cross-sectional correlation coefficients. * and ** denote significances of the statistics at 10% and 5% levels, respectively.

12 Is Default Risk Priced in Equity Returns? Outline of the Analysis To help readers understand the concepts more easily, this section provides an overview of the analysis in the rest of Section 2 and brings up a summary of the results. Briefly, Section 2 examines the joint effect of ME and default risk, of BM and default risk, and the exclusive effect of ME or BM after controlling for default risk and of default risk after controlling for ME or BM. Joint effect here means the intersection of two effects, while exclusive effect indicates the relative complement of one effect in the other effect. These analyses are used to picture the interactions of the ME or BM effect with the default-risk effect. Section 2.3 analyzes the relationship between the ME effect and the default-risk effect. The results show that the ME effect dominates the joint effect of ME and default risk, there is a strong ME effect after controlling for default risk, but the default-risk effect after controlling for ME is very weak. The left picture in Graph 1 displays the overall relationship, where the intersection of the two ellipses stands for the joint effect of ME and default risk and the relative complement of one ellipse in the other stands for the exclusive effect represented by the other ellipse. The ellipses relative sizes represent the effects relative strengths. Section 2.4 explores the relationship between the BM and default-risk effects. The evidence suggests that both BM and default risk work for the joint effect, there is a BM effect after controlling for default risk, but there is no default-risk effect after controlling for BM. Additionally, compared to the case for ME, the exclusive effect of BM is weaker. The right picture in Graph 1 gives an overview.

13 Is Default Risk Priced in Equity Returns? 11 Graph 1: Interrelation of ME or BM Effect and Default-Risk Effect Size Effect Size Effect Default Risk Effect BM Effect BM Effect, Default Risk Effect The black ellipse represents the ME or BM effect and the grey one the default-risk effect. The intersection of the two ellipses stands for the joint effect of ME or BM and default risk. The relative complement of one ellipse in the other stands for the exclusive effect represented by the other ellipse. Furthermore, the relative sizes of the ellipses show the relative strengths of the effects. These findings provide evidence that part of the ME or BM effect could be interpreted as default risk, especially for the BM effect. This is consistent with FF s reasoning that small stocks and value stocks earn higher expected returns because they are under relatively higher financial distress. However, ME and BM contain more information than the financial distress regarding the explanatory power for cross-sectional stock returns. Furthermore, the default risk proxied by CDSP provides additional information about stock returns that cannot be explained by ME The ME Effect and the Default-Risk Effect Portfolios Formed on ME and CDSP Independently To focus on the relation between ME effect and default-risk effect, we perform an independent two-pass portfolio sort based on ME and CDSP. This sort is useful in exploring the joint ME and default-risk effect on expected equity returns and their interaction in the joint effect.

14 Is Default Risk Priced in Equity Returns? 12 Portfolios are formed quarterly 5. In the first week of each calendar quarter from January 2004 to September 2010, all stocks are allocated into three size portfolios according to the ME breakpoints determined using the market capitalizations of NYSE stocks 6. Then each ME tertile is subdivided into three CDSP portfolios based on CDSP breakpoints determined from all firms. Thereafter, we calculate the equal-weighted weekly returns, market capitalizations, BM and CDSP for the resulting nine portfolios for the rest of the quarter and the first week of the next quarter. Here, the values of ME and CDSP for each stock are the same across each calendar quarter. Table 2 shows the time-series average of the equal-weighted returns, ME, BM and CDSP, and the post-ranking market for each of the nine portfolios, as well as for each of the portfolios sorted on just ME or CDSP (All). The market is an estimator of the time-series slope of the portfolio s excess returns over riskfree rates on the excess market returns. Additionally, Panel B displays the average returns on some specific zero-investment portfolios to further explore the joint effect of ME and default risk. Panel A shows that for the whole sample (All), average stock return does increase monotonically as ME decreases or as default risk increases. Though the return differences are statistically insignificant, these effects are still considerable. The return difference between small- and big-stock portfolios (Small Big) is 0.126% weekly (6.552% annually) and that for high- and low-default-risk portfolios (High Low) is 0.058% weekly (3.016% annually). Additionally, the insignificance might result from the small cross-sectional sample used in this study. 5 Although forming portfolios more frequently might produce more significant results, this study applies quarterly formation because accounting data are updated quarterly. 6 Breakpoints are based on the NYSE because capitalization is closed relative to the stock exchange and NASDAQ stocks are mainly small. Robustness tests using all stocks to determine size breakpoints produced qualitatively similar results.

15 Is Default Risk Priced in Equity Returns? 13 Table 2: Portfolios Formed on ME and CDSP Independently All CDSP-Low CDSP-Medium CDSP-High High Low Panel A: Average Return All (0.28) ME-Small ( 0.01) ME-Medium ( 0.08) ME-Big ( 1.30) Small Big 0.126(0.78) 0.107(1.09) 0.118(1.57) 0.286(1.25) Panel B: Average Return of Zero-Investment Portfolio SH-ML 0.007(0.03) SH-BL 0.104(0.44) SH-BL 0.104(0.44) SH-BM 0.100(0.52) MH-BL 0.087(0.66) SM-BL 0.122(1.28) SL-MH 0.020(0.17) BH-SL 0.288( 2.06) SL-BH 0.288(2.06) BH-SM 0.304( 2.18) ML-BH 0.279(2.06) BM-SL 0.102( 1.23) Panel C: Average ME All ME-Small ME-Medium ME-Big Panel D: Average CDSP All ME-Small ME-Medium ME-Big Panel E: Average BM ratio All ME-Small ME-Medium ME-Big Panel F: Market All ME-Small ME-Medium ME-Big Portfolios are independently formed quarterly on size (ME) and credit-default-swap premium (CDSP) each with 6 to 66 stocks on average. This table shows the time-series average of the equal-weighted returns (in percent), ME (in billions of dollars), book-to-market equities (BM) and CDSP (in basis points), and the post-ranking market for each of the portfolios, as well as for each of the portfolios only sorted on ME or CDSP (All). Small Big and High Low indicate the return differences between small and big stocks and between high- and low-default-risk stocks, respectively. Corresponding t-statistics calculated from Newey-West standard errors are in parentheses. The rest of the analysis focuses on the nine portfolios displayed in the centers of Panels A, C to F and the specific portfolios in Panel B. Panel A provides evidence of an interaction between the ME and default-risk effects. First, an overview picture shows that there are ME and default-risk effects on stock returns. Among the nine portfolios, the average returns on small-stock portfolios (higher than 0.23% per week) are higher than those on big-

16 Is Default Risk Priced in Equity Returns? 14 stock portfolios (lower than 0.14% per week). There is also a sign of the correspondence between high default risk and high average return. The average returns on the high-defaultrisk portfolios, with small and medium ME, are higher than 0.21%, while the average return on the low-default-risk portfolio, with big ME, is 0.13% weekly. Second, there is a joint ME default-risk effect. Small- and high-default-risk stocks deliver quite high average return (0.23% per week) and big- and low-default-risk stocks deliver quite low average return (0.13% per week). Third, for the joint ME default-risk effect, the ME effect dominates the default-risk effect. This is the case because the average return on the portfolio of big stocks but with high default risk is negative ( 0.05% per week), and stocks with small or medium ME but low default risk earn average returns higher than 0.22% per week. To explore this joint effect, Panel B exhibits the average returns on some specific zero-investment portfolios. The first label of each portfolio is for ME (S, M and B for small, medium and big) and the second is for CDSP (H, M and L for high, medium and low). The upper part of Panel B explores the joint effect of ME and default risk. The upper-left part displays the return differences of high- and low-default-risk stocks with variant differences in ME (long positions in smaller stocks and short positions in bigger stocks). These three zeroinvestment portfolios show the joint effect of ME and default risk with a focus on the defaultrisk effect. The average returns are all positive although statistically insignificant. Similarly, the upper-right part presents the joint effect with a focus on the ME effect. The average returns of these portfolios are slightly higher, especially for the portfolio SM-BL on which the return has a high t-statistic. The positive average returns on these six zero-investment portfolios provide evidence that there is a joint ME default-risk effect. Which effect plays a more important role in this joint effect? What is the interaction of ME and default risk in this joint effect? The lower part of Panel B answers these questions where we perform a different investment strategy by emphasizing one effect and reversing

17 Is Default Risk Priced in Equity Returns? 15 the other one completely. The lower-left part presents the portfolios with long positions in smaller stocks but with low default risk and short positions in bigger stocks but with high default risk (emphasizing the ME effect and reversing the default-risk effect); the lower-right part shows the portfolios with long positions in higher default-risk stocks of big ME and short positions in lower default-risk stocks of small ME (emphasizing the default-risk effect and reversing the ME effect). The outcomes are used to distinguish the possible different strengths of the two effects in the joint effect. That the ME effect dominates the default-risk effect is obvious. Compared to the corresponding portfolios in the upper part, the portfolios with reversed positions implied by the default-risk effect (the lower-left part) exhibit stronger ME effect, but the portfolios with reversed positions implied by the ME effect (the lower-right part) show no sign of any default-risk effect. The rest of Table 2 presents the ME, CDSP, BM ratios and market s of the nine portfolios. There is only a large variation in ME or CDSP among the portfolios. This confirms that the variation of the average returns is due to the variations of ME and default risk. Furthermore, the ME and CDSP verify the results from Panel B that there is a joint effect of ME and default risk, but the ME effect dominates the default-risk effect. The portfolio with the smallest ME ($2.13 billion) and highest CDSP (553 basis points) has a high average return (0.234% per week); the portfolio with the largest ME ($60.4 billion) and lowest CDSP (33.5 basis points) has a relatively low average return (0.13% per week). However, the portfolio with the highest average return (0.252% per week) is the one with a small ME ($3.09 billion) but medium CDSP (85.2 basis points); the portfolio with the lowest average return ( 0.052% per week) is characterized with a big ME ($23.81 billion) but high CDSP (270.5 basis points).

18 Is Default Risk Priced in Equity Returns? 16 For the nine portfolios, the BM ratio tends to increase as ME decreases or default risk increases, but the relation is not monotonic and the variation of BM is not great. Notice that there is a strong relation between market and CDSP or ME. Except for the small-me medium-cdsp portfolio, market increases monotonically as ME decreases or CDSP increases within each ME or CDSP tertile. However, when we rank all nine portfolios together, this trend breaks down dramatically for ME, but remains strong for CDSP. Notably, the portfolios with high market s (higher than 1.2) are characterized with high default risk. This provides evidence that default risk is linked to market risk and should be priced in equity returns Portfolios Formed on ME and CDSP Sequentially In this section, stocks are sorted sequentially on ME and CDSP to examine the existence of one effect after controlling for the other, the exclusive effect. The sequential sorts are performed here because independent sorts applied in Section cannot separate the two effects completely; the ME and CDSP breakpoints derived from the whole sample are possibly correlated. For example, within each ME tertile, the default-risk effect might be related to ME because of the significant negative correlation between CDSP and ME for the whole sample. Another advantage of sequential sorts is that the number of stocks in each portfolio is even greater, which results in more reliable t-statistics. First, we perform a two-pass sort on CDSP and then ME to investigate the ME effect after controlling for default risk. Portfolios are formed quarterly. In the first week of each calendar quarter, all stocks are allocated to three CDSP portfolios according to the CDSP breakpoints for all firms. Then each CDSP tertile is subdivided into three ME portfolios by the ME breakpoints only for the stocks in the tertile. Table 3 shows the time-series average of the equal-weighted returns, ME, BM and CDSP, and the market for each of the nine resulting portfolios, as well as for each of the portfolios only sorted on CDSP or ME (All).

19 Is Default Risk Priced in Equity Returns? 17 Table 3: Portfolios Formed on CDSP and then ME All ME-Small ME-Medium ME-Big Small Big Panel A: Average Return All (0.78) CDSP-Low (2.51) CDSP-Medium (1.01) CDSP-High (0.75) Panel B: Average Size All CDSP-low CDSP-Medium CDSP-High Panel C: Average CDSP All CDSP-low CDSP-Medium CDSP-High Panel D: Average BM Ratio All CDSP-low CDSP-Medium CDSP-High Panel E: Market All CDSP-low CDSP-Medium CDSP-High Portfolios are formed quarterly on credit-default-swap premium (CDSP) and then size (ME) sequentially. On average, there are 32 to 35 stocks in each of the resulting nine portfolios. This table shows the time-series average of the equal-weighted returns (in percent), ME (in billions of dollars), book-to-market equities (BM) and CDSP (in basis points), and the post-ranking market for each of the portfolios, as well as for each of the portfolios only sorted on ME or CDSP (All). Small Big indicates the return difference between small and big stocks. In the parentheses are the corresponding t-statistics calculated from Newey-West standard errors. Is there any ME effect after controlling for default risk? Panel A shows that within the CDSP-low and CDSP-medium tertiles, average return is negatively monotonically related to ME, and the return difference is positive within each CDSP tertile. Especially within the CDSP-low tertile, the average return difference between the small and big stocks is 0.147% weekly (7.644% annually) and statistically significant. Therefore, after controlling for default risk, ME does capture some common risk factors in stock returns. The rest of the table confirms that the effect we found is due to the variation of ME not to variations in other variables. There is indeed a large variation in the market capitalizations of stocks within each CDSP tertile, especially within the CDSP-low tertile.

20 Is Default Risk Priced in Equity Returns? 18 Second, we examine the existence of any default-risk effect after controlling for ME. A two-pass sequential sort is performed on ME and then CDSP in the same way as in the previous part. Table 4 presents the properties of the resulting nine portfolios. Only within the ME-medium tertile is there a monotonic positive relationship between CDSP and average return. The rest of the table verifies that this variation of the average returns for stocks with medium ME is due to default risk. However, the return difference within the ME-medium tertile is very small with a low t-statistic. Therefore, this default-risk effect after controlling for ME is very weak. Table 4: Portfolios Formed on ME and then CDSP All CDSP-Low CDSP-Medium CDSP-High High Low Panel A: Average Return All (0.28) ME-Small (0.10) ME-Medium (0.10) ME-Big (0.30) Panel B: Average CDSP All ME-Small ME-Medium ME-Big Panel C: Average Size All ME-Small ME-Medium ME-Big Panel D: Average BM Ratio All ME-Small ME-Medium ME-Big Panel E: Market All ME-Small ME-Medium ME-Big Portfolios are formed quarterly on size (ME) and then credit-default-swap premium (CDSP) sequentially. On average, there are 32 to 34 stocks in each of the resulting nine portfolios. This table shows the time-series average of the equal-weighted returns (in percent), ME (in billions of dollars), book-to-market equities (BM) and CDSP (in basis points), and the post-ranking market for each of the portfolios, as well as for each of the portfolios only sorted on ME or CDSP (All). High Low indicates the return difference between high- and lowdefault-risk stocks. Corresponding t-statistics calculated from Newey-West standard errors are in parentheses.

21 Is Default Risk Priced in Equity Returns? BM Effect and Default-Risk Effect This section focuses on the relationship of the BM effect and default-risk effect and evaluates whether the BM effect captures the relative-distress effect, which results from the fact that the market judges the prospects of firms with high BM (value stocks) to be poor relative to firms with low BM (growth stocks). The methodology is the same as in Section Portfolios Formed on BM and CDSP Independently Analogously to Section 2.3.1, this section uses the intersection of independent sorts of stocks on BM and CDSP to investigate the joint BM default-risk effect on expected equity returns. Portfolios are formed quarterly as in Section The BM breakpoints are determined by the BMs for all stocks. The stocks with negative BM are separated and denoted BM-neg. Table 5 displays the results. For the whole sample (All) in Panel A, average stock return does increase monotonically as BM or default risk increases. The return difference of high- and lowdefault-risk stocks is 0.058% weekly (3.016% annually); the return difference of value and growth stocks is 0.086% weekly (4.472% annually). Therefore, the BM and default-risk effects are still considerable even though the return differences are not significant. The rest of the analysis focuses on the nine portfolios displayed in the center of Panels A, C to F and some specific portfolios in Panel B, and BM-Neg. An overview of Panel A verifies the existence of a BM default-risk joint effect. Value stocks with high default risk deliver a relatively high average return (0.176% per week), and growth stocks with low default risk have the lowest average return (0.082% per week). However, Panel A does not show a clear picture of the dominance of BM or default risk in the joint effect. The portfolios with returns above 0.2% per week hold low-default-risk value stocks and high-default-risk stocks with medium BM.

22 Is Default Risk Priced in Equity Returns? 20 Table 5: Portfolios Formed on BM and CDSP Independently All CDSP-Low CDSP-Medium CDSP-High High Low Panel A: Average Return All (0.28) BM-Neg BM-Low (0.33) BM-Medium (0.52) BM-High ( 0.23) High Low 0.086(0.71) 0.148(2.31) 0.005( 0.07) 0.039(0.29) Panel B: Average Return of Zero-Investment Portfolio HH-ML 0.039(0.18) HH-LL 0.094(0.40) HH-LL 0.094(0.40) HH-LM 0.061(0.31) MH-LL 0.124(0.79) HM-LL 0.028(0.37) HL-MH 0.024(0.16) LH-HL 0.094( 0.56) HL-LH 0.094(0.56) LH-HM 0.027(0.20) ML-LH 0.000(0.00) LM-HL 0.116( 1.26) Panel C: Average BM Ratio All BM-Neg BM-low BM-Medium BM-High Panel D: Average CDSP All BM-Neg BM-Low BM-Medium BM-High Panel E: Average ME All BM-Neg BM-Low BM-Medium BM-High Panel F: Market All BM-Neg BM-Low BM-Medium BM-High Portfolios are independently formed quarterly on book-to-market equity (BM) and credit-default-swap premium (CDSP) with 14 to 52 stocks on average in each of the nine resulting portfolios. This table shows the time-series average of the equal-weighted returns (in percent), sizes (ME, in billions of dollars), BM and CDSP (in basis points), and the post-ranking market for each of the portfolios, as well as for each of the portfolios only sorted on BM or CDSP (All). High Low indicates the return difference between value and growth stocks or between high- and low-default-risk stocks. Corresponding t-statistics calculated from Newey-West standard errors are in parentheses. As in Section 2.3.1, the average returns on some specific zero-investment portfolios in Panel B of Table 5 explore the interaction of BM and default risk in the joint effect. The first label of each portfolio is for BM (H, M and L for high, medium and low) and the second

23 Is Default Risk Priced in Equity Returns? 21 is for CDSP (H, M and L for high, medium and low). The upper-left part displays return differences of high- and low-default-risk stocks but with variant differences in BM ratios (long positions in higher BM stocks and short positions in lower BM stocks). These three zero-investment portfolios exhibit the joint effect of BM and default risk with a focus on the default-risk effect. The average returns are all positive, though not statistically significant. Similarly, the upper-right part demonstrates the interaction of the two effects with a focus on the BM effect. The average returns of these zero-investment portfolios are positive but generally slightly lower. Overall, there is a joint BM default-risk effect. The zero-investment portfolios in the lower part of Panel B assess the relative strength of each effect in the intersection of the two effects. The strategy is to emphasize one effect but reverse the other one completely. First, we buy higher BM stocks with low default risk and sell lower BM stocks with high default risk (the lower-left part) to detect the power of the BM effect with opposite positions for the default-risk effect. Second, we buy higher default-risk stocks with low BM and sell lower default-risk stocks with high BM (the lowerright part) to test the power of the default-risk effect with opposite positions for the BM effect. Compared to the portfolios in the upper part, the BM effect is weaker without the default-risk effect (the lower-left part), and the default-risk effect disappears or turns weaker without the BM effect (the lower-right part). These results suggest that both BM and default risk work for the join effect. The rest of Table 5 confirms that the variation of the average returns is due to the variations of BM and default risk. It is noteworthy that the average default risk of stocks with negative BM ratio is extremely high and the average return of these stocks is quite high. Panel E provides additional information that there is some variation of ME, which is negatively related to CDSP or BM, especially the former. This may result from the joint ME

24 Is Default Risk Priced in Equity Returns? 22 default-risk effect analyzed in Section 2.3. Notice that as in Section 2.3.1, market is strongly negatively related to ME and positively related to default risk Portfolios Formed on BM and CDSP Sequentially Analogously to Section 2.3.2, this section applies sequential sorts to examine the disjoint of the BM and default-risk effects, specifically one effect after controlling for the other. First, portfolios are formed quarterly on CDSP and then BM sequentially to reveal any BM effect after controlling for default risk. Table 6 displays the time-series average of the equal- Table 6: Portfolios Formed on CDSP and then BM All BM-Neg. BM-low BM-Medium BM-High High Low Panel A: Average Return All (0.71) CDSP-Low (2.25) CDSP-Medium ( 0.33) CDSP-High (0.35) Panel B: Average BM Ratio All CDSP-Low CDSP-Medium CDSP-High Panel C: Average CDSP All CDSP-Low CDSP-Medium CDSP-High Panel D: Average ME All CDSP-Low CDSP-Medium CDSP-High Panel E: Market All CDSP-Low CDSP-Medium CDSP-High Portfolios are formed quarterly on credit-default-swap premium (CDSP) and then book-to-market equity (BM) sequentially with 32 to 33 stocks on average in each of the nine portfolios. Stocks with negative BM are shown separately. This table shows the time-series average of the equal-weighted returns (in percent), sizes (ME, in billions of dollars), BM and CDSP (in basis points) and the post-ranking market for each of the nine portfolios, as well as for each of the portfolios only sorted on BM or CDSP (All). High Low indicates the return difference between value and growth stocks. Corresponding t-statistics calculated from Newey-West standard errors are in parentheses.

25 Is Default Risk Priced in Equity Returns? 23 weighted returns, ME, BM and CDSP, and the market for each of the resulting nine portfolios, as well as for each of the portfolios only sorted on CDSP or BM (All). Panel A shows that within the CDSP-low and CDSP-high tertiles, average returns tend to increase with BM. Further, within the CDSP-low tertile, the return difference between value and growth stocks is positive and statistically significant, about twice the whole-sample return difference. However, there is no sign of a BM effect in the CDSP-medium tertile. Does this variation of average return found result from the BM variation? Indeed, there is a substantial BM variation within each CDSP tertile, but the BM ratio cannot capture the returns variation for stocks with medium default risk. The rest of the table confirms that the effect on the average returns across stocks is due to the BM ratio, not other variables. Second, portfolios are formed on BM and then CDSP sequentially to reveal any default-risk effect after controlling for BM. Table 7 demonstrates the properties of the resulting nine portfolios. Within each BM tertile, the relationship between average returns and CDSP is not linear. Although, as expected according to a default-risk effect, high-default-risk stocks deliver higher average returns than low-default-risk stocks. The large variation of CDSP within each BM tertile cannot capture the variation of the portfolios average returns. Therefore, we declare here that there is no default-risk effect detected after controlling for BM. Notice that there is some variation of ME within each BM tertile, but this variation cannot explain the average stock returns either.

26 Is Default Risk Priced in Equity Returns? 24 Table 7: Portfolios Formed on BM and then CDSP All CDSP-Low CDSP-Medium CDSP-High High Low Panel A: Average Return All (0.28) BM-Neg BM-Low (0.30) BM-Medium (0.78) BM-High ( 0.03) Panel B: Average CDSP All BM-Neg BM-Low BM-Medium BM-High Panel C: Average ME All BM-Neg BM-Low BM-Medium BM-High Panel D: Average BM Ratio All BM-Neg BM-low BM-Medium BM-High Panel E: Market All BM-Neg BM-Low BM-Medium BM-High Portfolios are formed quarterly on book-to-market equity (BM) and then credit-default-swap premium (CDSP) sequentially with 32 to 33 stocks on average in each of the nine portfolios. Stocks with negative BM are shown separately. This table shows the time-series average of the equal-weighted returns (in percent), sizes (ME, in billions of dollars), BM and CDSP (in basis points), and the post-ranking market for each portfolio, as well as for each of the portfolios only sorted on BM or CDSP (All). High Low indicates the return difference between high- and low-default-risk stocks. Corresponding t-statistics calculated from Newey-West standard errors are in parentheses. With respect to the whole analysis in Section 2, it is important to notice that the first decile breakpoint for ME in our sample is about the 55 th and 40 th percentile breakpoint in 2004 and 2010, respectively for ME in the FF sample. This is the case because there are not that many CDS contracts written referring to very small firms. This property of our sample could be one of the reasons the default-risk effect interacts more with the BM effect than with