Bonds, Stocks, and Sources of Mispricing

Transcription

1 Bonds, Stocks, and Sources of Mispricing Doron Avramov 1, Tarun Chordia 2, Gergana Jostova 3, Alexander Philipov 4 Abstract Market-wide sentiment and firm-level financial distress jointly drive asset overpricing. The intersection of high sentiment and financial distress characterizes episodes of inflated bond and stock prices, to the extent that these securities are correctly priced otherwise. Overvaluation is attributable to sentiment-driven investors, both retail and institutional, who underestimate the severe implications of financial distress for a firm s future prospects. Anomalous patterns in the cross-section of stock and bond returns emerge as overpricing is corrected. JEL G10, G12, G14 October 18, 2017 We thank Jennie Bai, Junyoup Lee, Byoung-Kyu Min, Jiangfeng Shen, and seminar participants at the Aalto School of Business, Chinese University of Hong Kong (CUHK), Hong Kong University of Science and Technology (HKUST), University of Missouri, Vienna University, the 2017 Asian Bureau of Finance and Economic Research conference, the 2017 Asian Finance conference, and the 2017 European FMA for their helpful comments. 1 Finance Department, School of Business, The Hebrew University of Jerusalem, Jerusalem, Israel, phone: (02) , davramov@huji.ac.il and Chinese University of Hong Kong (CUHK) davramov@cuhk.edu.hk. 2 Department of Finance, Goizueta Business School, Emory University, 1300 Clifton Road NE, Atlanta, GA 30322, phone: , tarun.chordia@emory.edu. 3 Department of Finance, School of Business, George Washington University, Funger Hall Suite 501, 2201 G St. NW, Washington DC 20052, phone: , jostova@gwu.edu, corresponding author. 4 Department of Finance, School of Management, George Mason University, Fairfax, VA 22030, phone: , aphilipo@gmu.edu.

2 Canonical asset pricing theories prescribe that risk is correctly priced by rational agents in frictionless markets. However, to the extent that documented anomalous patterns in the cross section of average returns do not reflect compensation for risk, they could point to asset mispricing. 1 Indeed, equity overpricing could emerge in the presence of heterogeneous beliefs and short sale constraints (e.g., Miller (1977), Harrison and Kreps (1978), Scheinkman and Xiong (2003), and Stambaugh, Yu, and Yuan (2015)), when stock holders are able to extract value from other stakeholders during bankruptcy (e.g., Garlappi, Shu, and Yan (2008)), or when investors overweight low-probability windfalls (e.g., Barberis and Huang 2008). The empirical evidence is largely supportive of equity overpricing. Stambaugh, Yu, and Yuan (2012) [henceforth SYY] show that when market sentiment is high, investors overprice a subset of stocks. Independently, Avramov, Chordia, Jostova, and Philipov (2013) [henceforth ACJP] show that investors overprice financially distressed stocks. In both studies, overpriced stocks display extreme values of firm characteristics, such as high idiosyncratic volatility, high dispersion in analysts earnings forecasts, high trading frictions, high credit risk, and large negative earnings surprises. Such stocks are thus placed in the short leg of anomaly portfolios. Anomaly payoffs emerge from shorting overpriced stocks. While SYY trace anomalies to investor sentiment, ACJP point to firm-level financial distress. This paper identifies common sources of mispricing among stocks and corporate bonds and reconciles the puzzling dichotomy between the impact of market-wide sentiment and firm-level distress on anomalies. We show that equity and bond overvaluation emerges as sentiment-driven investors (both retail and institutions) underestimate the severe implications of financial distress for a firm s future prospects. It is the intersection of high sentiment (market level) and financial distress (firm level) that characterizes episodes of inflated bond and stock prices to the extent that such securities are correctly priced otherwise. 1 Anomalies reflect predictable cross-sectional patterns unexplained by canonical asset pricing models. Examples of predictive firm characteristics include: past stock returns (Jegadeesh and Titman, 1993), unexpected earnings (Ball and Brown, 1968), size and book-to-market ratio (Fama and French, 1992), accruals (Sloan, 1996), credit risk (Dichev, 1998; Campbell, Hilscher, and Szilagyi, 2008; Avramov, Chordia, Jostova, and Philipov, 2009), dispersion in analysts earnings forecasts (Diether, Malloy, and Scherbina, 2002), capital investments (Titman, Wei, and Xie, 2004), asset growth (Cooper, Gulen, and Schill, 2008), and idiosyncratic volatility (Ang, Hodrick, Xing, and Zhang, 2006), among others. Avramov, Cheng, Schreiber, and Shemer (2017) find that portfolio returns based on anomaly strategies are also predictable. 1

3 We thus provide an additional dimension to the sentiment-related mispricing of SYY: during high sentiment, only distressed stocks appear overpriced. Likewise, we identify an additional dimension of the financial distress related mispricing: distressed stocks are mispriced only during high sentiment periods. Throughout this paper, financial distress is captured via credit rating downgrades, especially of low-rated firms, and our overpricing measure employs the SYY methodology. The sentiment variable is the one proposed by Baker and Wurgler (2006) albeit the results are robust to considering two alternative sentiment measures: the University of Michigan Consumer Sentiment index and the Consumer Confidence Index. Beyond US equities, the evidence here applies to a vast universe of corporate bonds. While asset pricing theories deliver predictions that apply to both asset classes, corporate bonds are under-researched by academic scholars even when the outstanding capitalization of such bonds exceeds 8.5 trillion dollar as of December, There are several reasons to study stocks and bonds in a unified framework. The obvious one is that bonds provide out-of-sample tests for overpricing. In addition, studying bonds allows us to assess the appeal of various rationales for mispricing, including lottery type preferences of investors, transfer of wealth, market frictions, and institutional trading. Kumar (2009), Bailey, Kumar, and Ng (2011), and Conrad, Kapadia, and Xing (2014) attribute equity overpricing to lottery-type preferences among individuals. However, while equities have an unlimited upside, corporate bonds, under best circumstances, pay coupons and the principal. Moreover individuals are less active in trading bonds. 3 In addition, Garlappi, Shu, and Yan (2008) and Garlappi and Yan (2011) attribute the overpricing of distressed stocks to the ability of stock holders to extract value from other stakeholders during bankruptcy. These papers implicitly argue against bond overpricing among firms with overpriced equities because bondholders yield value to stockholders during financial distress, leading to bonds being undervalued. Finally, an examination of mispricing in bonds could also provide fresh insights on whether sentiment affects institutions who dominate 2 See 3 Fed Stats table indicate that institutions dominate the corporate bond market while individuals hold less than 10% of U.S. corporate bonds (source: the Federal Reserve Statistical Release: Z.1 Financial Accounts of the United States, September 21, 2017.). For high yield bonds, the share of institutional holdings is even larger (source: Bloomberg). 2

4 bond trading. 4 A caveat about studying corporate bonds is in order. As Merton s (1974) model imposes a tight relation between equity and bond prices, it is unclear whether corporate bonds really represent a new asset class. However, the empirical evidence shows that structural models of default mostly understate credit spreads. Moreover, equity and bond markets may not be fully integrated. 5 Thus, corporate bonds do seem to represent an independent asset class. We also run our battery of tests using stock-adjusted bond returns. We turn to describe our findings in more detail. First, we detect no evidence of underpricing among either stocks or bonds. Consistent with SYY, we detect no overpricing in bonds or stocks during low sentiment periods. However, on a stand-alone basis, investor sentiment cannot uniquely identify overpricing as there is no overpricing among stocks or bonds of low credit risk firms even during high sentiment periods. Consistent with ACJP, we also show that overpricing prevails among financially distressed firms. However, high credit risk firms do not give rise to anomalies during low sentiment periods. Interestingly, downgrades are neither larger in size nor more likely to occur during high versus low sentiment periods. Moreover, downgrades are associated with substantially elevated trading frictions but similarly so during high versus low sentiment. However, the price reaction of stocks and bonds to downgrade events is dramatically different following high versus low sentiment. Retail and institutional investors appear to be too optimistic about the consequences of financial distress when sentiment is high, but correctly price distress risk absent episodes of high sentiment. Overall, market-wide sentiment and firm-level financial distress jointly drive equity and bond overpricing. That is, overpricing emerges only during periods of high investor sentiment, among bonds and stocks of high credit risk firms, and only for those firms that experience deteriorating credit conditions. 4 Barber, Lee, Liu, and Odean (2009) suggest that institutions are more sophisticated than individuals. However, institutions may also be affected by biases. See, for instance, Haigh and List (2005), Locke and Mann (2005), Devin G. Pope (2011), Jin and Scherbina (2011), and Cici (2012). 5 Collin-Dufresne, Goldstein, and Martin (2001) find that changes in default probabilities and recovery rates have modest explanatory power for credit spread changes. Schaefer and Strebulaev (2008) show that while Merton s model hedge ratios match empirically observed stock-bond elasticities, structural models are poor predictors of bond prices. Kapadia and Pu (2012) argue that this failure of credit risk models is due to lack of integration between stock and bond markets caused by limits of arbitrage and illiquidity. 3

5 We further show that bonds of firms with overpriced equity deliver significantly lower raw, risk-adjusted, and stock-adjusted returns following periods of high sentiment. This calls into question the transfer-of-wealth hypothesis, which implicitly rationalizes the credit risk effect among equities through a negative relation between overpricing in stocks and bonds. This evidence also sheds light on a research controversy. In particular, Bhojraj and Swaminathan (2009) and Chordia, Goyal, Nozawa, Subrahmanyam, and Tong (2015) suggest that variables identifying mispricing in equities also identify similar-direction mispricing in bonds. They therefore imply bond overpricing among distressed firms. In contrast, Garlappi, Shu, and Yan (2008) and Garlappi and Yan (2011) implicitly argue against bond overpricing, as noted earlier. Our evidence is consistent with the former studies. The evidence also suggests that institutions are susceptible to waves of sentiment. They are the major holders of distressed bonds and they hold a large stake of distressed stocks. On the other hand, institutions significantly decrease their stock holdings of distressed firms prior to credit rating downgrades and only during high sentiment periods, thereby lending support to the notion that institutions are, after all, more sophisticated. Individual investors, who are on the other side of the trade, could increase their stock holdings during financial distress due to preferences for stocks with lottery-like characteristics, such as low price, high idiosyncratic volatility, and positive return skewness. However, as noted earlier, lottery-type preferences are less likely to explain overpricing in bonds. Focusing on distressed bonds only, the 80-th, 90-th, 95-th, and 99-th percentile of the monthly bond return distribution record payoffs of 1.89%, 2.88%, 4.14%, and 13.95%. The corresponding figures for distressed stocks are 7.71%, 12.41%, 17.59%, and 33.93%. The limited upside potential of bonds should make them less attractive for skewness preferring investors. Overall, the corporate bond results do not support rationales for overpricing related to investor preferences for skewness or the transfer of wealth hypothesis. The asset pricing models of Fama and French 2015 and Hou, Xue, and Zhang 2015 do not explain the low returns on distressed high credit risk firms. Risk-based explanations are further challenged because distressed firms do not provide higher returns following recessions and rating downgrade events are firm-specific and not clustered. 4

6 Trading frictions and information risk also do not lead to overpricing. When distressed firms are downgraded, trading frictions, information uncertainty, idiosyncratic volatility, and credit risk become equally extreme in both high and low sentiment states. As pricing errors emerge only during high sentiment, they are unlikely to reflect impediments to trading or increasing firm uncertainty. While trading frictions and firm uncertainties do explain why overpricing cannot be easily arbitraged away, they do not explain the appearance of overpricing in the first place. Our overall findings are consistent with the notion that investors, both institutional and retail, do not realize the severe implications of financial distress for a firm s prospects. Indeed, (Miller, 1977, p.1158) argues that in the presence of heterogenous beliefs and trading frictions, investors should realize that risky assets are overpriced and hence trade to correct the overpricing. In low sentiment periods, we observe just that investors display realistic views about financial distress and they price distressed (among other) assets properly. However, in high sentiment periods, investors make one particular type of pricing error: they underestimate the severe implications of financial distress for high credit risk firms. Even when market sentiment is high, there is no evidence of other pricing errors beyond investors optimism about financial distress as there is no evidence of stock or bond overpricing upon excluding observations around credit rating downgrades. 1. Data Our analysis combines data from equity and corporate bond markets employing a variety of vendors. We start by describing the individual bond data Individual bond data Our corporate bonds sample contains 3.94 million dealer-quote (from Lehman and DataStream) and transaction-based (from TRACE) bond-month return observations from 69,788 US corporate bonds (an average of 10,585 per month) from January 1986 to December Individual corporate bond data are obtained from three databases (coverage in paren- 5

7 theses): the Lehman Brothers Fixed Income Database [Lehman] ( ), DataStream ( ), and TRACE ( ). 6 DataStream and TRACE provide the majority of recent observations. From the Lehman database, we obtain monthly returns and ratings from January 1986 to March While most prices in the Lehman database are dealer quotes, some are matrix prices, derived from bonds with similar characteristics. Jostova, Nikolova, Philipov, and Stahel (2013) [henceforth JNPS] and Gebhardt, Hvidkjaer, and Swaminathan (2005) show that their results are unaffected by the exclusion of matrix prices. Monthly returns from DataStream are computed from the monthly total return index. 8 While Lehman and DataStream provide prices based on dealer quotes, TRACE is trade-based. TRACE is introduced in 2002 and by February 2005 covers more than 99% of the OTC activity in US corporate bonds. 9 While quote-based databases provide month-end prices and returns, trade-based databases provide intraday clean prices, from which returns are calculated as described below. From TRACE, we collect trade prices and coupon rates, payment dates and frequencies from July 2002 to December 2016 and follow the data cleaning procedure of Bessembinder, Kahle, Maxwell, and Xu (2009), eliminating canceled, corrected, and commission trades. Bond Return Calculation To compute monthly returns for TRACE, we first compute daily prices as the trade size-weighted average of intraday prices. 10 is the last available daily price from the last five trading days of the month. 11 month-end price, we compute monthly holding period returns as: The month-end price Using this r i,t = (P i,t + AI i,t + Coupon i,t ) (P i,t 1 + AI i,t 1 ) P i,t 1 + AI i,t 1 (1) 6 Individual bond return data from these databases have been used by Jostova, Nikolova, Philipov, and Stahel (2013) and Chordia, Goyal, Nozawa, Subrahmanyam, and Tong (2015). 7 While the Lehman database starts in 1973, comprehensive issuer-level rating data in COMPUSTAT start in Prior to 1986, bonds in Lehman are mostly investment grade and there are fewer bond issues. 8 As noted in JNPS, most US corporate bond prices are dealer quotes. These data are augmented with trading prices when available. DataStream starts extensive coverage on individual bond returns in See FINRA news release 10 This approach is consistent with findings in Bessembinder, Kahle, Maxwell, and Xu (2009) that a daily price based on trade-size weighted intraday prices is less noisy than the last price of the day. 11 Using the 5-day end-of-month window instead of the last day helps increase the number of non-missing monthly observations. If there are no trades in the last five trading days, the trade-based return is missing for that month. The conclusions of the paper are robust to extending/contracting this month-end window. 6

8 where r i,t is bond i s month t return, P i,t is its price at month-end t, AI i,t is its accrued interest at month-end t, and Coupon i,t is any coupon paid between month-ends t 1 and t. Computing accrued interest relies on the bond s first coupon date, coupon size, coupon frequency, and day count convention. If information on these cannot be found in any of the databases, we make the following assumptions. If the first coupon date is missing, we assume that coupons start accruing from the bond s issuance date, and if the payment frequency is missing, we assume that the bond pays interest semi-annually. If there is no available information on the day count convention used for coupon accrual, we assume that it is 30/360. Our findings remain unchanged when limiting the sample to the subset of observations having all required information. The overlap between databases is low over 90% of observations come from a single data source. When there are returns available from several sources, we take the return in the following sequence: TRACE, Lehman, and DataStream, giving precedence to trade-based returns. We include only US corporate fixed-coupon bonds denominated in US dollars. We filter out bonds that are convertible, putable, backed by mortgages or other assets, bonds with warrants, bonds with unusual coupons (e.g., step-up, increasing-rate, pay-in-kind, and splitcoupons), bonds that are part of unit deals, and preferred shares. We also collect issue date, maturity date, amount outstanding, duration, rating, coupon rate, payment dates, and frequencies. We eliminate observations that are obvious data entry errors, e.g., with negative prices, with maturity dates prior to issuance or trade dates, etc. We also eliminate return outliers above the 99.9th percentile as they appear to be data errors Firm-level bond data We aggregate bond returns at the company level. Individual bonds are matched to their corresponding equity using historic and current cusips. Only bonds matched to common equity in CRSP (share code: shrcd=10 and 11) are used. Each month, firm-level bond returns are obtained by equally weighting the returns of all outstanding bonds issued by the firm. This firm-level aggregation produces firm-level bond returns for a total of 3,147 firms (847 per month on average) listed on CRSP. More than half of the public bonds in 7

9 our individual bond sample are issued by private firms or do not have publicly traded equity listed on CRSP these are excluded from the analysis. Our analysis is based on firm-level bond returns as we study the impact of equity and firm-level overpricing on stock and bond prices. For robustness, we have implemented our major analyses with individual bonds. The overall results are qualitatively similar Equity returns and other firm-level data Equity data on monthly returns, trading volume, shares outstanding, and month-end prices are extracted from CRSP for all US common stocks listed on NYSE, Amex, and Nasdaq. Delisting returns from CRSP are used whenever stocks are delisted. Stocks priced less than one dollar at the beginning of the month are excluded from the analysis. In addition, the asset-pricing anomalies used to assess overpricing (see below) require accounting observations from COMPUSTAT and analyst data from I/B/E/S Credit risk proxies Our measure of credit risk is based on the firm s Standard & Poor s long term issuer credit rating, provided by Credit ratings in COMPUSTAT. We use the credit rating, rather than alternative proxies for credit risk, because ratings are publicly available and not model specific. As defined by S&P, the long-term issuer credit rating is the current opinion of an issuer s overall creditworthiness, apart from its ability to repay individual obligations. This opinion focuses on the obligor s capacity and willingness to meet its long-term financial commitments (those with maturities of more than one year) as they come due. We transform the S&P ratings into numeric scores: 1 represents a AAA rating and 22 reflects a D rating. 12 Hence, a higher numeric score reflects higher credit risk. Numeric ratings of 10 or below (BBB or better) are investment grade (IG), and ratings of 11 or higher (BB+ or worse) are high-yield or non-investment grade (NIG). 12 The entire list of ratings is as follows: AAA = 1, AA+ = 2, AA = 3, AA = 4, A+ = 5, A = 6, A = 7, BBB+ = 8, BBB = 9, BBB = 10, BB+ = 11, BB = 12, BB = 13, B+ = 14, B = 15, B = 16, CCC+ = 17, CCC = 18, CCC = 19, CC = 20, C = 21, D = 22. 8

10 The S&P long-term issuer rating relates to a firm, not to an individual bond issue. While the results in the paper use this issuer rating, robustness tests using firm-level average bond ratings produce similar results. Credit ratings provides both issue-specific and issuer-specific ratings. These ratings are supplemented with any additional ratings available in the bond databases. As with firm-level bond returns, firm-level average bond ratings are obtained each month by equally weighting the ratings of all outstanding bonds issued by the firm Overpricing measure Our measure of overpricing is based on anomalies studied by Stambaugh, Yu, and Yuan (2012) and Avramov, Chordia, Jostova, and Philipov (2013). Our list of anomaly-based conditioning variables includes price momentum, earnings momentum (SUE), idiosyncratic volatility, analyst dispersion, asset growth, investments, net operating assets, accruals, gross profitability, return on assets, and two variables for net issuance. 13 As in Stambaugh, Yu, and Yuan (2015) we compute a composite measure per firm as follows. Each month, we sort firms into deciles using the anomaly variables specified above. The composite overpricing measure is an equally weighted average of the firm s portfolio rankings based on the individual anomalies, where a high (low) ranking indicates relative overpricing (underpricing). As noted by Stambaugh, Yu, and Yuan (2015), while each anomaly variable is a noisy proxy for overpricing, the composite measure is likely to reduce measurement noise. As we examine the interaction between credit risk and overpricing, our overpricing composite measure excludes three credit risk variables used in SYY and ACJP, namely, failure probability, O-score, and credit rating. While the overall findings in this paper are based on our overpricing measure, in the internet appendix (Table IA.I) we report results using instead the Stambaugh, Yu, and Yuan (2015) overpricing measure, available from the authors 13 Price momentum uses cumulative returns over months t 2 to t 7, SUE is calculated as in Chordia and Shivakumar (2006) as the latest quarterly EPS announced over the previous 4 months minus the quarterly EPS 4 quarters ago, scaled by the standard deviation of these changes over the past 8 quarters. Analyst dispersion is calculated as the standard deviation of analysts earnings forecasts for the next fiscal year divided by the absolute value of the consensus forecast, subject to at least 2 analysts following the firm. Idiosyncratic volatility is calculated from the squared daily residuals from regressions of daily stock returns on the Carhart (1997) four factors. The remaining variables are calculated as in Stambaugh, Yu, and Yuan (2012). All accounting-based variables are lagged relative to returns as in Fama and French (1992). 9

11 websites. The two measures produce qualitatively similar findings Investor Sentiment We study the impact of investor sentiment on the profitability of anomalies using the Baker and Wurgler s monthly sentiment index available on Jeff Wurgler s webpage. In particular, SENTm t 1 is the month t 1 orthogonalized sentiment index, originally proposed in Baker and Wurgler (2006) and Baker and Wurgler (2007). 14 As noted in the introduction, robustness tests based on two alternative sentiment proxies, the University of Michigan Consumer Sentiment index and the Consumer Confidence Index, produce similar results. A stock s overpricing during high and low sentiment is assessed by examining whether its price subsequently corrects, i.e., whether the subsequent monthly return is relatively lower Descriptive statistics Our final sample consists of firm-month observations that have data on bond returns, stock returns, and Standard & Poor s long term issuer credit rating. The overall filters result in 266,742 firm-month observations for a total of 2,594 firms over the 31-year period from January 1986 to December 2016 (372 months). Our sample consists of bond and stock returns for an average of 717 firms per month with a minimum of 158 firms (in January and November 1998) 15, and a maximum of 975 firms (in March 2005). As the sample is limited by the availability of bond returns and issuer credit ratings, it comprises of firms that are more liquid and with higher market capitalization. The market capitalization of our sample of firms is, on average, 65% of the market capitalization of all firms listed on CRSP in a given month. In a given month, about 70% (91%) of our sample firms are above the 50th (20th) NYSE size percentile, i.e., qualifying as big ( big or small but not micro ) stocks according to the Fama and French (2008) classification The current sentiment index is based on first principal component of five (standardized) sentiment proxies where each of the proxies has first been orthogonalized with respect to a set of six macroeconomic indicators. The original sentiment index was based on six sentiment proxies. 15 Around this period, there are only limited databases offering bond data: Lehman ends in 1998, TRACE starts in 2002, and the coverage from DataStream is limited. 16 Market capitalization NYSE breakpoints are obtained from Professor Kenneth French s website. 10

12 Table 1 provides descriptive statistics of our final sample sorted on prior month S&P issuer credit rating. All numbers in the table represent the time-series mean of cross-sectional average characteristics. Our sample has firms from the full spectrum of ratings, from 1=AAA to 22=D, with an average of 9=BBB. The best-rated quintile of firms, C1, has an average rating of 4.90 (A+), all rated as IG, while the worst, C5, has an average rating of (B) with 95% of the firms rated NIG. In addition, 73% of the firms in C4 are rated NIG. Alternative measures of default risk show monotonically increasing default likelihood along the C1 to C5 groups with a sharper jump in C5. For example, the Failure Probability of C1 to C4 firms ranges between 0% and 0.11%, while that in C5 is 1.72%. Similarly, Altman s (1968) Z-score drops monotonically from 3.09 in C1 to 2.34 in C4 and then to 1.90 in C5. High credit risk firms tend to be smaller, more volatile, less liquid, value firms, with smaller institutional ownership, and covered by fewer analysts who tend to disagree more about their future earnings. Specifically, the market capitalization of C5 firms is $1.35 billion on average, while it is $30 billion for C1 firms. C5 firms have a book-to-market ratio of 1.18, while that of C1 is The Carhart (1997) four-factor idiosyncratic volatility of C5 firms is 2.72% per month, more than twice that of C1 firms of 1.13%. C5 firms Amihud (2002) illiquidity is 33 times larger than that of C1 firms (19.01 versus 0.58). Institutional ownership increases from 55.62% of shares outstanding in C1 firms to 60.45% in C3, to 60.27% in C4, then drops sharply to 50.63% in C5 firms. Analyst coverage monotonically decreases from analysts per firm in C1 to 7.61 analysts in C5. The cross-sectional dispersion in analysts EPS forecasts is over 10 times higher in C5 than in C1 firms: 0.58 versus High credit risk firms are much more likely to be on the short side of anomaly portfolios, a point consistent with SYY that the short side drives anomalies, and ACJP that high credit risk stocks drive anomalies. For example, C5 firms have the lowest standardized unexpected earnings; SUE is 0.03 in C5 versus 1.00 in C1. In fact, 45% of earnings surprises are negative in C5 versus 29% in C1. Moreover, as noted above, C5 firms have the highest idiosyncratic volatility and analyst dispersion. Strategies based on these anomalies would recommend shorting the lowest rated stocks. High credit risk stocks tend to be overpriced. Our overpricing measure (OV) ranges 11

13 from the most underpriced (OV=1) to the most overpriced (OV=10) rank based on the 12 conditioning variables noted earlier. C1 firms have an average OV of 4.79, namely they tend to be relatively underpriced with only 24% of C1 firms having OV above 5.5 (the median). In contrast, C5 firms have an average overpricing measure of 6.12 and 74% of them are overpriced (above the median). High credit risk stocks subsequently earn lower returns, offering additional evidence of overpricing. Returns average 1.08% per month in C1 firms and 0.68% in C5 firms. The portfolio alphas of C5 firms are 0.54% (for the CAPM) and 0.67% (for the Fama and French (2015) five-factor model) as compared to 0.25% and -0.04% for C1 firms. Firms typically have more than one bond issue. We average the characteristics across all bond issues of a firm, before averaging across firms and then across months. Notice that the average bond (or issue) rating is very similar to the firm-level (issuer) rating reported at the top of the table. While C5 firms have fewer public bond issues outstanding in a given month (2.60 on average) than C1 firms (11.05 issues per firm), the amount outstanding per issue does not differ much across ratings it is about $200 million per issue across C2-C5 firms. Higher credit risk firms tend to issue bonds with lower maturity (possibly because investors are unwilling to lend long-term to riskier firms), which translates into C5 firms having bonds with lower age (4.12 versus 5.78 years), lower time to maturity (4.63 versus 7.04), and lower duration (4.36 versus 6.52 years) than C1 firms. Like equities, bonds of C5 firms are more volatile their monthly standard deviation is 4.55% versus 1.94% for C1 firms. Bond returns of C5 firms are the lowest and also the most volatile. Bond returns increase with credit risk from C1 through C4 categories but then decrease for the C5 firms. Monthly returns average 0.62%, 0.64%, 0.68%, 0.71%, and 0.58%, respectively, for C1 to C5 firms. Similarly, alphas with respect to the Fama and French (2015) five-factor model are 0.30%, 0.32%, 0.30%, 0.28%, and 0.11%, respectively. 12

14 2. Results 2.1. Mispricing in stocks and bonds We first assess the overpricing-return relation among stocks and bonds. We construct ten overpricing portfolios. Each month t, we sort firms into decile portfolios, P1 to P10, based on the overpricing measure, with P10 (P1) denoting the portfolio of most (least) overpriced stocks. We then compute for each portfolio equally weighted month t + 1 returns for both stocks and bonds. Table 2 reports the time-series average of portfolio returns, along with their t-statistics. It does so for the overall sample as well as for investment-grade [IG] and noninvestment grade [NIG] subsamples (keeping the portfolio cutoffs fixed across subsamples). Starting with stocks, Table 2 confirms that the anomalies-based composite measure captures overpricing: stocks identified as most overpriced earn significantly lower future returns. The portfolio of most overpriced stocks, P10, earns an insignificant 32 basis points per month [bpm], while the most underpriced, P1, earns a statistically significant 128 bpm. The P10 P1 return differential is significant at 96 bpm (t-statistic of 2.95). Moreover, consistent with ACJP, the return spread between the most and least overpriced stocks is significant only among NIG stocks at 189 bpm, while for IG stocks the spread is statistically insignificant. Bonds of firms with overpriced equity are also overpriced. The P10 P1 return spread between the most (35 bpm) and least (66 bpm) overpriced bonds is 31 bpm (t-statistic of 3.47). As with stocks, the mispricing in corporate bonds is driven by NIG firms, where the P10 P1 spread is 62 bpm (t-statistic of 5.39). For IG firms the spread is virtually nonexistent. Unreported results using individual bonds, rather than firm-level average bond returns, point to similar bond overpricing Overpricing and downgrades ACJP show that asset pricing anomalies are driven by high credit risk firms during periods of financial distress. In particular, they show that mispricing in equities emerges in a specific group of stocks high credit risk stocks and in a specific time period when high credit 13

15 risk firms are in financial distress, i.e., around rating downgrades. They also show that mispricing is nonexistent among high credit risk firms during stable or improving financial conditions. Panel A of Table 3 verifies that mispricing, as measured by the composite index, is exclusively associated with high credit risk firms and only in periods of financial distress. Specifically, each month t, firms are sorted independently into 3 3 portfolios based on issuer credit rating and overpricing. Portfolio C1 (C3) contains the best (worst) rated firms. The table reports the time-series average of the equally weighted cross-sectional mean portfolio return for month t + 1. Each panel has four subpanels subpanels 1 and 2 report firmlevel average bond returns, while subpanels 3 and 4 report stock returns. Subpanels 1 and 3 consider all available return observations, while subpanels 2 and 4 exclude return observations from 12 months before to 12 months after an issuer rating downgrade. This 25-month period around a ratings downgrade will be designated as the financial distress period. Starting with stocks, observe from Panel A.3 that the high-minus-low overpricing spread increases monotonically as credit risk rises. Equity mispricing is indeed driven by stocks belonging to C2 and C3 groups. For instance, among the highest credit risk tercile, C3, the most overpriced stocks underperform the most underpriced stocks by 96 bpm (t-statistic of 4.21) in the subsequent month. Among the tercile of firms with the lowest credit risk, C1, stocks with the lowest and highest overpricing measure earn virtually identical returns. However, such mispricing among high credit risk stocks occurs only during downgrade periods. Panel A.4 shows that after excluding financial distress periods, firms with low and high values of the overpricing measure do not earn statistically different returns. This is true for all rating groups. Hence, mispricing is limited to high credit risk stocks and only during financial distress. Not surprisingly, upon excluding observations around rating downgrades, all nine portfolio returns in Panel A.4 become higher than those reported in Panel A.3. Mispricing in bond markets follows similar patterns it is limited to high credit risk firms and only in periods of financial distress. Observe from Panel A.1 that among C3 firms, bonds of overpriced firms underperform bonds of underpriced firms by 27 bpm (t-statistic of 4.41). This mispricing is absent or negligible among the better quality C1 and C2 firms. 14

16 Among C1 firms, bonds with low and high values of the overpricing measure have about the same future returns: 64 versus 63 bpm. Even among C3 firms, mispricing is absent outside episodes of financial distress as evident from Panel A.2. Notice also from Panels A.1 and A.3 that when stocks are relatively underpriced, both the bond and stock returns of the low rated, C3 firms, are higher than those of the high rated, C1 firms, 83 versus 64 bpm in the case of bonds and 150 versus 112 bpm for stocks. This accords with the risk return trade-off that the riskier assets should command higher returns. The characteristic-adjusted return spreads between the most overpriced and the most underpriced stocks/bonds are similar to those based on raw returns (see Panel B). Specifically, the bond and stock return spreads are insignificant for C1 firms, while they are strongly significant among C3 firms at 28 bpm for bonds and 84 bpm for stocks. Stock returns are characteristic-adjusted by size and book-to-market. Bond returns are characteristic-adjusted by age and duration (results are virtually identical if the adjustment considers amount outstanding and duration). The characteristic-adjusted return of a stock (bond) is its month-t return minus the value-weighted average month-t return of stocks (bonds) belonging to the same characteristic group, determined by a 3 3 independent sort on the two characteristics. Results based on risk-adjusted portfolio returns produce similar conclusions: stock and bond mispricing is limited to high credit risk firms in financial distress. Considering the Fama and French (2015) five-factor model and focusing on C3 firms, the risk-adjusted return differential between overpriced and underpriced firms is 80 bpm for stocks and 31 bpm for bonds (see Panel C). 17 When the Hou, Xue, and Zhang (2015) four-factor model is used for risk-adjustment, the corresponding return differential between overpriced and underpriced C3 firms is 55 bpm for stocks and 29 bpm for bonds (see Panel D). 18 For both factor models, spreads turn small and insignificant when periods around downgrades are excluded. 17 Porfolio alphas are obtained by risk adjusting each portfolio s monthly stock or bond returns using the Fama and French (2015) factors MKT, SMB, HML, RMW and CMA, obtained from Professor Kenneth French s web-page. Conclusions remain unchanged if bond returns are risk adjusted using the five Fama and French (1993) factors, including the three equity factors MKT, SMB, and HML, and two bond factors, the term premium [TERM] and the default premium [DEF] factors. TERM is the monthly change in the yield spread between 10-year government bonds and the 1-month Treasury Bill. DEF the monthly change in the yield spread between BBB-rated corporate bonds and 10-year government bonds. Both yield spread series are obtained from the Federal Reserve Bank of St. Louis website. 18 We thank Professor Lu Zhang for providing the data on their four factors: MKT, ME, IA, ROE. 15

17 Panel E of Table 3 shows the Stambaugh and Yuan (2017) mispricing factor alphas. The four Stambaugh and Yuan (2017) factors (available from the authors websites) are MKT, SMB, MGMT, PERF the last two are their mispricing factors, calculated as the return differential between the most underpriced and most overpriced stocks based on two most correlated clusters of their 11 anomaly variables. Stambaugh and Yuan argue that these mispricing factors are intended to capture anomaly-based mispricing in equity markets. We find that these factors explain the return spreads between the most overpriced and most underpriced stocks in our sample as well (for all rating groups), indicating that such spreads are indeed due to mispricing. However, this return differential is still significant among C3 bonds at 23 bpm, indicating that equity mispricing may not fully capture bond mispricing, that bond markets may indeed be segmented, and that bonds do seem to represent a separate asset class. We would like to highlight two further noteworthy points from the raw and risk-adjusted returns in Panels A-D. The first relates to the puzzling credit risk effect in the cross-section of stock returns. 19 Specifically, the credit risk effect the low returns of high versus low credit risk stocks (an apparent violation of the risk-return paradigm) is present only among overpriced firms. In other words, not all high credit risk stocks underperform but only those identified by our measure as overpriced. Among overpriced firms, the credit risk effect is 73 bpm among stocks and 19 bpm among bonds (Panel C). Note that among underpriced firms, high credit risk bonds actually earn returns that are higher than those of low credit risk bonds by 22 bpm (Panel B.1), or by 11 bpm or 13 bpm (Panels C.1 and D.1). The second point is that mispricing is driven by overpriced high credit risk bonds and stocks (a point consistent with SYY and ACJP). Notice that returns of underpriced stocks are very similar across credit risk groups. Further, when downgrade periods are removed, the most affected portfolios are those of the high credit risk overpriced stocks and bonds. For instance, in Panel A the returns of the high credit risk portfolio of bonds (stocks) increase from 56 bpm (54 bpm) to 79 bpm (126 bpm). Thus, it is the high credit risk overpriced stocks and bonds that generate the trading profits from the short side of the 19 Dichev (1998), Campbell, Hilscher, and Szilagyi (2008), Avramov, Chordia, Jostova, and Philipov (2009). 16

18 strategy due to the considerable decline in asset prices around financial distress. When downgrade periods are removed, the overpriced high credit risk stocks and bonds earn returns that are indistinguishable from low credit risk stocks and bonds (see subpanels 2 and 4 in Panels A-C). The only exception is in Panel B.2 where amongst the most overpriced firms, the bond returns of the C3 firms are higher than those of the C1 firms by 17 bpm. Thus, consistent with the risk-return paradigm, bond returns of the low rated overpriced firms exceed those of the high rated overpriced firms in the absence of financial distress. Figure 1 reinforces the evidence that mispricing in equity and bond markets exists due to overpricing amongst low rated firms during periods of distress. Subplots A-C (D-F) display, in event time, the returns of bonds (stocks) from 36 months before to 36 months after downgrades, where month 0 stands for the month of downgrade. Subplots A and D show that downgrades in C1 firms have very little impact on stock and bond returns (dashed line). In contrast, amongst C3 firms (solid line), both stocks and bonds experience negative returns for months prior to a downgrade and even more negative returns during the month of the downgrade. The large negative return in the downgrade month suggests that downgrade events among distressed stocks convey meaningful information possibly because customers, vendors, and employees abandon the firm, and the access to credit gets more limited. Dividing the sample into underpriced and overpriced firms at the time of downgrade, Plots B and E of Figure 1 show that downgrade events do not impact the returns of either the bonds or stocks of underpriced, high credit risk firms. For these underpriced firms, the information involving the downgrade appears to be already incorporated into asset prices. Note that the line appears more noisy because downgrade events are less frequent among underpriced firms (something that will become apparent in Table 5). The big impact of downgrades occurs in overpriced high credit risk bonds and stocks (Panels C and F) which experience a significant price correction around downgrades. As Table 3 Panels A-D show, once this negative price correction around downgrades is excluded, neither bonds nor stocks display any evidence of mispricing. 17

19 2.3. Sentiment-driven pricing errors and uncertainty SYY argue that high investor sentiment triggers overpricing, while ACJP argue that high credit risk stocks around downgrades drive the overpricing of the short leg, which as shown here holds true for bonds as well. We next reconcile these two findings. We examine the interaction between sentiment and mispricing in bonds and stocks around financial distress. Panels F and G of Table 3 report the evidence. Specifically, we repeat the analysis in Panel A, looking at stock and bond returns sorted on rating and the overpricing measure, but here Panel F (G) averages portfolio returns over months following low (high) monthly sentiment, SENTm t 1 < 0 (SENTm t 1 > 0). When sentiment is low (Panels F.1 and F.3), there is no mispricing in any credit risk group and subsequent difference in bond and stock returns across the high and low overpricing portfolios are indistinguishable from zero. When downgrade periods are excluded (Panels F.2 and F.4), there is still no return differential between stocks and bonds with high and low mispricing measure. The evidence suggests that when sentiment is low, the impact of downgrades across overpriced and underpriced securities is already incorporated into prices. Consistent with the risk-return trade-off, following low sentiment, bond and stock returns of the C3 portfolios always exceed those of the C1 portfolios across all mispricing groups, although not all differences are statistically significant. In contrast, when sentiment is high, both bond and stock investors appear to make pricing errors leading to overpricing of high credit risk stocks and bonds. Following high sentiment periods, the overpriced, high credit risk stocks and bonds realize low returns (Panels G.1 and G.3). The High Low overpricing-based return differential in C3 firms is 34 bpm for bonds and 131 bpm for stocks. The return differential across C2 firms is also significant, 57 bpm for stocks and 11 bpm for bonds. Overpricing disappears in both stocks and bonds, even during high sentiment and even among high credit risk firms when the financial distress periods are removed (see Panels G.2 and G.4). Figure 2 further illustrates the impact of downgrades on stock and bond returns following high and low sentiment. There is a clear difference in the market reaction to downgrades in 18

20 both stocks and bonds. When sentiment is low, the bond and stock price reaction is brief and mild. When sentiment is high, the negative market reaction around downgrades is much more pronounced and sluggish. For both stocks and bonds, the negative returns persist for months before and after the downgrade. Moreover, the well documented credit risk puzzle namely, the lower returns of high credit risk stocks appears to exist only following high sentiment and only among overpriced stocks (Panel G.3). The same is true for bonds (Panel G.1). The credit risk puzzle disappears once periods around downgrades are removed, even following high sentiment (Panels G.2 and G.4). In low sentiment states, equity investors appear to properly price the impact of distress (Panels F.3 and F.4) and bond investors earn higher returns from high credit risk than low credit risk bonds (Panels F.1 and F.2) in accord with the risk-return trade-off. We note that bonds corresponding to overpriced C3 firms also appear to be overpriced (Panel G.1), and they too earn negative returns around downgrades (Panel G.2). The evidence here suggests that the overpricing of high credit risk stocks in financial distress is unlikely to be due to wealth transfer from bondholders to shareholders, as suggested by Garlappi, Shu, and Yan (2008). While the wealth transfer story implies that bonds of overpriced equity should be underpriced, the evidence points to the contrary. What is the nature of pricing errors made by investors? Our results suggest that sentiment-driven investors make one particular type of pricing error in high sentiment states they underestimate the impact of financial distress on stock and bond returns. This appears to be the only pricing error they make as there is no mispricing beyond financial distress. And they only make this pricing error when sentiment is high. In other words, bond and stock investors are sluggish in reacting to financial distress when sentiment is high. The sentiment variable used throughout is that proposed by Baker and Wurgler (2006). To ensure that the documented overpricing is indeed related to investor sentiment, we replicate the results in Panels G and H of Table 3 using two alternative sentiment measures: the University of Michigan Consumer Sentiment c [UMCSENT] index and the Consumer Confi- 19

21 dence Index. 20 UMCSENT ranges between and 112 during our sample period, while CCI ranges between 96.7 and In both cases, we define values above and below median to represent high and low sentiment states, respectively. The results, presented in Table IA.II in the Internet Appendix, mirror those in Panels G and H of Table 3. Specifically, when sentiment is low, there is no evidence of mispricing in stocks and bonds of any credit risk group. When sentiment is high, the high-minus-low overpricing spread in stocks is 133 bpm for the UMCSENT index and 130 bpm for the CCI index, both highly statistically significant. The corresponding numbers for bonds during high sentiment are 38 bpm and 39 bpm, respectively. For both proxies, asset overpricing vanishes when periods around downgrades are excluded. One caveat about our analysis is in order. As the Merton s (1974) model of credit risk imposes a precise relation between stock and bond prices, it is unclear whether corporate bonds really represent a new asset class. However, if the markets are not fully integrated or if structural models do not fully explain credit spreads, then corporate bonds would indeed provide out-of-sample tests for overpricing. Indeed, Collin-Dufresne, Goldstein, and Martin (2001), Schaefer and Strebulaev (2008), and Kapadia and Pu (2012) argue that bond markets are at least partially segmented. To assess the extent to which bond mispricing is independent of stock mispricing, we use stock-adjusted bond returns. Specifically, we first regress firm-level average bond returns on stock returns and obtain the intercept and residuals over the entire time series. The sum of intercept and residuals establishes stock-adjusted bond returns. The internet appendix Table IA.III presents the results for stock-adjusted bond returns. For the high credit risk portfolio, the return spread in Panel A1, in the long-short overpricing portfolio, amounts to 15 bpm compared to 27 bpm in Panel A of Table 3. The corresponding portfolio return following high sentiment is 20 bpm compared to 34 bpm in Panel E of Table 3. Thus, bond overpricing is lower using stock-adjusted returns but it is still significant. The overall 20 The Surveys of Consumers, University of Michigan Consumer Sentiment c [UMCSENT] is based on telephone surveys of consumer expectations regarding the overall economy. The Consumer Confidence Index [CCI] is based on households plans for major purchases and their economic situation, both currently and their expectations for the immediate future (See 20