Sentiment and Corporate Bond Valuations Before and After the Onset of the Credit Crisis

Transcription

1 Sentiment and Corporate Bond Valuations Before and After the Onset of the Credit Crisis Jing-Zhi Huang Penn State University Yuan Wang Concordia University June 26, 2014 Marco Rossi University of Notre Dame Abstract This paper studies how stock market sentiment impacts corporate bond valuations. Using bond transactions from the Trading and Compliance Engine (TRACE), we find that sentiment is negatively related to bond yield spreads, with the impact being stronger after the onset of the recent credit crisis. After the crisis, the variation in sentiment also helps explain the extent to which the corporate bond market and the equity market are integrated. Our conditional analysis reveals that the negative effect of sentiment on yields is stronger when fundamental risk and liquidity frictions are higher pointing to a direct role of sentiment in the bond market whereby rational bond investors are unable in these high risk/high frictions scenarios to correct the mispricing generated by other bond investors. We also find that the sentiment effect is stronger when the returns to capital structure arbitrage are higher, suggesting that sentiment also spills over to the bond market through the activity of investors dedicated to correcting relative stock and bond value mispricings within the same firm. Keywords: sentiment, credit crisis, equity/bond market integration, capital structure arbitrage. We thank Stephen Brown, Zhi Da, Jean Helwege, Tong Yao, and Andrew Zhang for helpful comments. addresses: jxh56@psu.edu (Huang), marco.rossi@nd.edu (Rossi), and yuan.wang@concordia.ca (Wang).

2 1 Introduction Neoclassical finance has been able to rationalize many apparent equity return anomalies, but Keynes (1936) s animal spirits are not quite tamed yet. There is now a well established literature linking stock market sentiment to expected equity returns, both in the crosssection (Baker and Wurgler 2006) and over time (Lemmon and Portniaguina 2006). While the literature has mostly focused on equity, the hedging relation between debt and equity of the same firm suggests that stock market sentiment might also drive valuations in the bond market. This paper studies whether the effect of sentiment on stock prices spills over to corporate bonds and whether this spill-over is related to the credit crisis. Stock market sentiment could affect bond valuations directly through the behavior of bond investors or indirectly through the activity of dedicated arbitrageurs that exploit large discrepancies between equity and credit valuations. In the first case, equity market sentiment may proxy overall sentiment and be considered a state variable driving the pricing of different types of securities. 1 In this scenario, a mechanism similar to that described by Baker and Wurgler (2006) would be at work in the corporate bond market whereby investors overbid corporate bonds during periods of high sentiment and underprice such bonds during periods of low sentiment. This interpretation is particularly relevant after the onset of the recent credit crisis since both equity and corporate bond markets are no longer perceived as a safe harbor. In the second scenario, sentiment-driven noise traders only exist in the equity market, while corporate bond markets are dominated by institutional investors. When the two markets disagree about the true value of the firm, arbitrageurs (who need not have an opinion on the true firm value) enter the market. But because of capital structure arbitrage, the corporate bond market now becomes susceptible to sentiment. 1 The joint behavior of sentiment and systemic risk might also drive the comovement of security returns. Barone-Adesi, Mancini, and Shefrin (2011) show that systemic risk builds over time during periods of high sentiment and when sentiment starts to decline, as during the period between the demise of Bear Sterns and Lehman Brothers in 2008, we observe increased correlations of securities within a given asset class. 2

3 To differentiate between these alternatives, which are not mutually exclusive, we collect hedge fund data on fixed income arbitrage and capital structure arbitrage funds. Our strategy is to first identify time variation in the profitability of arbitrage and then interact this profitability with sentiment. The indirect spill-over hypothesis implies that the impact of sentiment should be stronger during periods of high profit opportunity since arbitrageurs are more likely to track and engage in short run relative value trading, thus inducing comovements of debt and equity at the lower frequency used in this study. Our empirical findings support both the direct and indirect effect of sentiment on corporate bond valuations. To further explore the channel through which equity sentiment propagates to bond prices, this study also investigates whether sentiment predicts the comovement of stock and bond returns of the same firm, a phenomenon that has gained a lot of attention in the literature (Kwan 1996; Downing, Underwood, and Xing 2009; Schaefer and Strebulaev 2008; Kapadia and Pu 2012; and Bao and Hou 2013). In the absence of arbitrage and under the standard conditions of structural credit risk models (Merton 1974), equity and bond returns are positively related in a deterministic, albeit non-linear, fashion (Schaefer and Strebulaev 2008). However, the integration between the equity and the corporate bond market is not perfect (Kapadia and Pu 2012) due to several factors such as limits to arbitrage and potentially lack of attention by investors in one market toward other related markets (Barone-Adesi, Mancini, and Shefrin 2011). We conjecture that the financial crisis has made the link between different asset classes more apparent, so it is possible that sentiment crashes affect the integration between equity and bonds since they are claims on the same assets. Another possibility is that the volatile crisis makes capital structure arbitrage more profitable, attracting more investors to the strategy making the bond market more sensitive to equity sentiment. We indeed find that after the onset of the credit crisis capital structure arbitrage is more profitable and that sentiment explains a much bigger fraction of the integration between equity and bonds of the same firm, lending support to both hypotheses. 3

4 To conduct our empirical analysis, we use bond transactions from the Trade Reporting and Compliance Engine (TRACE) over the period from 2002 to In general, we find that equity market sentiment explains the cross-section of corporate bond yield spreads, even after controlling for default risk, bond liquidity, and macroeconomic variables related to the business cycle. The impact of sentiment is strongly significant, both statistically and economically. Specifically, one standard deviation change in sentiment is associated with an overall decrease in yield spreads (equivalent to higher bond valuations) of approximately 17 basis points. In addition to running pooled regressions on the entire sample, we also partition the sample into subgroups based on credit quality and on the credit crisis. The rationale for dividing the sample into investment-grade and speculative-grade (or junk) bonds is that former look much more like Treasury bonds, whereas junk bonds are much closer to equity and sentiment should therefore play a bigger role. Consistent with this intuition, we find that the coefficient on sentiment for junk bonds is more than 85% larger than the relative coefficient for investment-grade bonds. In terms of economic significance, a one standard deviation increase in sentiment is associated with a decrease in speculative bond yield spreads of 28 basis points. We also find that the recent credit crisis represents a shift in the relation between sentiment and yield spreads. Regressions using pre- and post-crisis data show that the negative impact of sentiment on yield spreads comes from the post crisis data. This result is consistent with investors of the equity and bond markets sharing the same sentiment after the onset of the credit crisis. We also verify that capital structure arbitrage is more profitable, as measured by a substantially larger average strategy abnormal performance after the onset of the credit crisis. This last observation suggests that part of the effect of sentiment on corporate bond valuations might be explained by the trading of arbitrageurs. We explore these explanation by conducting a conditional analysis. To examine our findings from a different angle and to set the stage for the conditional 4

5 analysis, we analyze the sentiment effect on the market integration between the stock and the bond market. Kapadia and Pu (2012) propose a statistical measure of market integration that captures the comovement across firms equity and credit markets. The measure essentially computes the proportion of observations for which credit default swap (CDS) spread changes and equity returns have the same sign. We decompose this measure based on all the four possible combinations of the sign of equity and bonds returns. We find that before the crisis bond and stock returns are rarely both negative (positive) following periods of high (low) sentiment, which is inconsistent with the prediction of Baker and Wurgler (2006) that securities tend to be overpriced (underpriced) when sentiment is high (low). However, future negative corporate bond and equity returns are much more likely to occur after the crisis, with the proportion going from 19.06% to 29.36% (a 53% increase). Conversely, positive returns following high sentiment are much less likely after the crisis (dropping from 35.27% to 19.90%). We find a similar case when sentiment is low. The above findings from our disaggregated analysis of the comovement of debt and equity returns of the same firm still hold qualitatively even after controlling for other variables that are likely to affect bond returns and their covariation with equity returns. Since the response variable of interest has three outcomes (return disagreement; both positive returns; and both negative returns), we employ a multinomial logistic regression to conduct the multivariate analysis and find that sentiment has much stronger predicting power on the integration between equity and bonds after the onset of the crisis. Finally, in addition to looking at the overall impact of sentiment on yield spreads, we consider the conditional impact of several characteristics on spreads, where the conditioning is done by interacting these characteristics with sentiment. We find that the interactions of sentiment with equity volatility, a junk bond dummy, firm leverage, bond illiquidity, and the profit of capital structure arbitrage are always negative, strengthening the overall impact of sentiment on bond yields. Leverage and volatility represent fundamentals that are typically positively associated with credit risk. Therefore, the negative interaction shows that periods 5

6 of high sentiment are characterized by weaker connection of bond spreads with fundamentals whereas periods of low sentiment feature a stronger connection of bond spreads with fundamentals. A similar argument can be made for ratings and liquidity. These conditional tests are consistent with the notion that securities that are harder to value and arbitrage will be affected more by sentiment (Baker and Wurgler 2006). On the other hand, the negative interaction between sentiment and the profit of capital structure arbitrage suggests that arbitrage opportunities indirectly lead to a stronger sentiment effect. The findings of our study complement the equity literature on sentiment by providing evidence that overall market sentiment is a state variable driving the pricing of other securities. The fact that debt and equity, which are both positive-delta claims on the same assets (Merton 1974) and have certain common risk factors (Fama and French 1993), are negatively affected by sentiment suggests that this variable directly explains overall asset valuations, rather than the valuation of just a particular security type. In addition, this direct information spill-over between equity and bond markets (Kwan 1996 and Downing, Underwood, and Xing 2009) suggest that sentiment might affect corporate bond prices even if these two markets are not perfectly integrated at short horizons (Kapadia and Pu 2012). Lastly, our tests on capital structure arbitrage suggests that arbitrageurs play an important role in the equity sentiment spill-over to the bond market through an indirect channel. The rest of the paper is organized as follows. Section 2 describes the data used in our analysis. Section 3 presents the base-line empirical analysis linking sentiment to yield spreads. Section 4 addressed the relation between sentiment and equity-credit market integration. Section 5 reports results on the conditional analysis. Section 6 provides some robustness checks. Section 7 concludes. 6

7 2 Data 2.1 Sentiment Measure We use the sentiment measure developed by Baker and Wurgler (2006) in this study. The Baker-Wurgler (BW) sentiment index spans over 45 years, from July 1965 to December As the purpose of our study is to investigate how equity market sentiment affects the corporate bond market, we consider the sub-period sample from July 2002 to December 2010 due to the availability of bond transaction data from TRACE. Baker and Wurgler (2006) construct two versions of equity market-based sentiment series. The first version of the sentiment measure is constructed by taking the first principal component of six measures of investor sentiment. The six measures include the closed-end fund discount, the number and the first-day returns of initial public offerings (IPOs), turnover of stocks traded on New York Stock Exchange (NYSE), the equity share in total new issues, and the dividend premium. The principal component analysis aims at filtering out idiosyncratic noise in the six measures and captures their common component. The second measure is the one where each of the six measures has first been orthogonalized with respect to a set of macroeconomic conditions. In Figure 1, the first (top) index shows that equity sentiment fell during 2002 and 2003 due to the burst of Internet bubble, but it picked up and reached a peak in early The onset of subprime crisis caused sentiment to fall again. The second sentiment measure (bottom) shows much less persistence because the measure is orthogonal to the market conditions. In order to differentiate the sentiment effect from the marcoeconomics effect on corporate bond spreads and to avoid the econometrics problems of a persistent regressor, we focus on the orthogonalized measure in our empirical tests. However, all the conclusions of the paper are robust to the choice of sentiment measure used in the empirical analysis. 7

8 2.2 Corporate Bond Data Our corporate bond data come from two major sources: TRACE of the Financial Industry Regulatory Authority (FINRA) and the Mergent Fixed Investment Securities Database (FISD). Specifically, price and trade data of corporate bonds are from TRACE, and ratings and bond-specific characteristic information are from the FISD. Since January 2001 members of the FINRA have been required to report their secondary over-the-counter corporate bond transactions through TRACE. On July 1, 2002, TRACE began to report bond transactions, requiring that transaction information be disseminated for investment grade securities with an initial issue size of $1 billion or greater. TRACE was expanded in stages and was fully implemented in February 2005, covering essentially all publicly traded bonds. There appear to be a number of problematic trades during the early period of the database. Consequently, we eliminate canceled, corrected, and commission trades from the data. We also remove convertible bonds and bonds with time to maturity less than one year because of high pricing errors. Bond transactions under $100,000 are deleted to avoid the effects of retail investors. Finally, bonds issued by financial firms are removed. See Dick-Nielsen (2009) for more details on bond sample selection criteria. The FISD reports detailed information about corporate, U.S. Agency, U.S. Treasury, and supranational debt securities, including information about issue- and issuer-specific information such as coupon rate, maturity, issue amount, provisions, and credit ratings for all US corporate bonds maturing in 1989 or later. We merge the TRACE and FISD databases to create a panel of bond transactions and characteristics. Because the BW sentiment measure is a monthly index, we require monthly bond transaction data to match with the sentiment index. We first calculate the daily trading-volume weighted bond price and yield for all the bonds. And then we keep the last daily transaction yield and price at the end of each month to calculate the bond s monthly yield and return. If the transaction does not fall in the last trading day of the month, we 8

9 require the date be greater than the 25th of each month. The remaining data contain 2,160 bonds from 606 issuers. The total number of monthly observations is 54,080. Section 2.5 provides a more detailed description of the final sample of corporate bonds. 2.3 Macroeconomic and Firm-Specific Variables This study includes two major types of empirical tests. First, we are interested in the sentiment effect on corporate bond yield spreads. In order to obtain bond yield spreads, we compute credit yield spreads as the difference between the daily yield on the corporate bond (obtained by averaging the available yields on a given day) and the yield on the Treasury benchmark with the same time to maturity. The constant maturity benchmark yields are from Datastream and are for the following yearly maturities: 1/12, 1/4, 1/2, 1, 2, 3, 5,7, 10, 20, and 30 years. The control variables in this set of tests include three levels of control variables: bond specific characteristics, firm specific variables, and macroeconomic variables. Bond specific controls include time to maturity, coupon rate, S&P credit rating, bond issue size, and the Amihud (2002) illiquidity measure. Time to maturity is the number of years remaining until a bond matures. The S&P credit rating is computed using a conversion process in which AAA rated bonds are assigned a value of 1 and C rated bonds receive a value of 21. The Amihud measure is calculated using high-frequency transaction data from TRACE and is defined as the daily average of absolute returns divided by the trade size Q j (in million $) of consecutive transactions: Amihud t = 1 N t N t j=1 P j P j 1 P j 1 Q j (1) where N t is the number of returns on day t. At least two transactions are required on a given day to calculate the measure. We define a monthly Amihud measure by taking the median of daily measures within a quarter, and then assign the measure as the illiquidity for 9

10 the last month of the quarter. 2 The rest of the bond specific variables are directly available from FISD. Firm specific controls include leverage, income to sales, PPE, and stock volatility. Firm leverage, a proxy for financial health, is calculated as book value of debt divided by the sum of market value of equity and book value of debt. Income to sales is the earnings over the sales of the company. PPE is the ratio of property, plant, and equipment scaled by book value of assets. Stock volatility is the annualized standard deviation of 12-month daily returns, as in Campbell and Taksler (2003). Stock returns for calculating volatility are obtained from CRSP while other firm level variables are from Compustat. To identify if the sentiment effect on bond yield spreads is due to the business cycle or the irrationality of investors, we control for macroeconomic variables such as CPI growth, IPI growth, and U.S. unemployment rate. We choose business cycle variables based on previous literature and data availability. We start with macroeconomic variables: the CPI growth computed from CPI as in Fama and Schwert (1977); the growth rate of industrial production as in Chen, Roll, and Ross (1986); the U.S. unemployment rate (Unemp) as in Lemmon and Portniaguina (2006). Meanwhile, a few variables from the financial market have been frequently used as indicators for business cycle: the 3-month Treasury Bill rate as in Campbell (1987) and Hodrick (1992); the term spread (Term slope) defined as the yield difference between the 10-year Treasury bond and the 3-month T-bill as in Chen, Roll, and Ross (1986); TED spread computed as the Treasury Eurodollar spread; VIX defined as the Chicago Board Options Exchange Market Volatility Index. The second set of tests focus on the sentiment effect on bond portfolio returns. We first calculate monthly bond returns for each individual bond and then form bond portfolios by credit rating. Monthly bond returns are computed as: r t = (P t + AI t ) + C t (P t 1 + AI t 1 ) P t 1 + AI t 1 (2) 2 Helwege, Huang, and Wang (2013) find that Amihud-like liquidity proxies perform the best in explaining the liquidity component of bond spreads. 10

11 where P t is bond transaction price at the end the month t, AI t is accrued interest, and C t is the coupon payment, if any, in month t. Using monthly bond returns, we construct outstanding value weighted portfolios for the full bond sample, bonds rated from AAA to A, BBB rated bonds, and bonds with speculative grade rating. In the empirical tests, we try to understand wether sentiment predicts bond portfolio returns. Therefore, we use lag of sentiment as a return predictor. We define the rest of the controls following Fama and French (1993). There are six risk factors: the default premium (Default) is the difference between the monthly returns of long-term investment-grade bonds and long-term government bonds; the term premium (Term Slope) is the difference between the monthly returns of the long-term government bond and the one-month Treasury bill; Mkt Factor is the excess returns of the stock market over riskfree rate; SMB is the excess returns of small stocks over big stocks; HML is the excess returns of value stocks over growth stocks; Momentum Factor is the return on a portfolio of stocks with a high return from the previous 12 months, minus the return from a portfolio of stocks with a low return from the previous 12 months. The last four factors are downloaded from Ken French s website Hedge Fund Data We use data from Lipper TASS and the Center for International Securities and Derivatives Markets (CISDM) hedge fund database (formerly MAR Database). These databases collect quantitative and qualitative information on living and defunct hedge funds, funds-of-funds, and Commodity Trading Advisors (CTA) funds. We exclude fund of fund (from TASS) and keep only funds designated as Hedge Funds (CISDM). If a given fund reports to both databases, we keep the TASS version. Given our interest in the potential role played by arbitrageurs in the spill over of equity sentiment to the bond market, we only consider funds in the Capital Structure Arbitrage and Fixed Income Arbitrage trading strategies. Hedge fund databases are characterized by several biases (see Liang 2000 and Fung 11

12 and Hsieh 2000). First, to address the incubation (or backfill) bias, we drop the first 27 observations of each fund (Titman and Tiu 2011). To ensure some degree of statistical accuracy we keep only funds that have at least 24 consecutive monthly observations Descriptive Statistics Table 1 reports summary statistics for all variables considered in our empirical analysis. The bond- and firm-specific variables are winsorized at 1 and 99 percentiles to reduce the effect of outliers. The mean, median, and standard deviation of the yield spread is 267, 162, and 307 basis points, with upper and lower quartile values of 326 and 86 basis points, respectively. On average, the sample period has negative sentiment around , median sentiment of , with standard deviations of For the overall bond sample, the mean (median) bond rating variable equates to S&P ratings of BBB (BBB) with a standard deviation between A+ and BB-, indicating that a large portion of the sample is on the border between investment and non-investment grade debt. The mean traded debt has time to maturity of 9.1 years with a standard deviation of 7.78 years. The average bond offering amount is $592.8 million and the standard deviation is around $ millon. Coupon rates are more homogenous with a mean of 6.5% and a standard deviation of 1.4%. The median illiquidity of bonds is around 40 basis points with a standard deviation of 110 basis points which are comparable to Dick-Nielsen, Feldhütter, and Lando (2012). In terms of firm level variables, the mean and median leverage ratio is close to 34% with a standard deviation of 15%, which suggests that a large portion of the sample consists of firms with significant debt in their capital structure. The tangible assets (PPE) averagely account for 34% of firms book assets with a standard deviation of 23.8%. The annualized standard deviation of daily stock returns has a mean of 42% (3.5% per month 12), and the 3 From inspection of the data, we see that several funds report the same returns for many consecutive months. We thus eliminate the entire return time series for funds whose reported returns do not vary in any three-month sequence. 12

13 average firms income to sale is 4.2%. The market during the period has average term slope of 1.455%, three month treasury rate of 2.05%, Treasury Eurodollar (TED) spread of -70 basis points, VIX of 21.5%, CPI growth of 20 basis points, and 6.3% of unemployment rate. The average Industrial production index (IPI) growth is around zero. Table 2 presents descriptive statistics grouped by crisis period and credit rating. There are significant differences in several variables between pre- and post-crisis periods, and between investment- and speculative-grade bonds. First, we compare the difference in the statistics between pre and post crisis periods. Both the credit quality and illiquidity of corporate bonds become worse in post-crisis period. The median bond yield spread increases from 98 basis points to 232 basis points. The illiquidity measure of Amihud rises from 20 basis points to 50. Other bond-specific variables such as time to maturity, coupon rate, credit rating, and bond size, are persistent before and after crisis. Similarly, there is not much difference in firm level variables before and after crisis. Most market level variables change dramatically after the onset of the crisis. The average BW sentiment index rises from to , and the sentiment becomes more volatile with an increase in standard deviation by 22%. We observe similar pattern of changes for TED spread, VIX, and Unemployment, that both the level and standard deviation move up significantly. Term slope becomes steeper by 56% whereas three month treasury rate goes down by 52% on average. Finally, the CPI growth rate is stable and the Industrial production index (IPI) growth shows a dramatic drop in level and a substantial increase in standard deviation. We also observe significantly different bond- and firm-specific features between investment and speculative grades. Speculative-grade bonds show much higher yield spreads than investment-grade bonds. The average spread for high-yield bonds is 506 basis points whereas investment-grade bonds have a mean of 156 basis points. However, these high-yield bonds 13

14 show much shorter time to maturity and lower offering size. More specifically, the average time to maturity of high-yield bonds is about 3.4 years shorter and the mean issue size is $115 million lower than those of investment-grade bonds. We find that investment-grade bonds are relatively less liquid, indicating that investors are more likely to buy and hold those bonds. Regarding firm level variables, firms with speculative ratings has higher stock volatility, leverage, and tangible assets (PPE) than those of firms with investment rating. Furthermore, the average income to sales ratio of speculative rated firms is much lower than that of investment-grade firms. 3 Sentiment and Corporate Yield Spreads In this section we test whether sentiment affects corporate bond yield spreads. Because the sentiment measure without orthogonality to macroeconomic conditions is in part explained by macro factors related to the business cycle (Sibley, Xing, and Zhang 2012), we take two steps to differentiate the sentiment effect from macroeconomics effect on corporate bond spreads. First, we use a version of sentiment index which is constructed with six sentiment related measures that has first been orthogonalized with respect to a set of macroeconomic variables. Then we also included these macro factors as controls in most of the regression specifications considered in the empirical analysis. 3.1 Full Sample Analysis Table 3 presents estimates of three regressions of corporate bond yield spreads on sentiment and other bond-specific, firm-specific, and macro variables. We include progressively more macro variable controls as we move from Model 1 to Model 3. Because yields constitute a one-to-one mapping with respect to prices, sentiment and yields are contemporaneous in the regressions specification. This choice is consistent with including lagged sentiment when the 14

15 dependent variable is a return (see Baker and Wurgler (2006)). Results from all the specifications considered show that sentiment co-varies strongly with spreads even after controlling for macro variables. For instance, a one standard deviation change in sentiment (equal to 0.33, as reported in Table 1) is associated with a reduction in yield of approximately 32 basis points (Model 3). Considering the inverse relation between prices and yields, the negative coefficient on sentiment means that bond prices are overpriced when sentiment is high. Finally, consistent with other studies in the corporate bond literature, results shown in the table confirm that volatility, leverage and bond liquidity are strong determinants of observed corporate yield spreads. One may notice that some macroeconomic variables have wrong signs on their coefficients in predicting bond yield spreads. For instance, unemployment ratio should be positively related to bond yield spreads whereas the correlations reported in Table 3 are negative. This is because we control for year dummies in almost all our models, and the dummies may have collinearity with macroeconomic variables. If we remove year dummies, then regression coefficients have the sign as expected. 3.2 Investment-Grade versus Speculative-Grade Bonds In this subsection we divide the full sample into two subsamples based on bond ratings. The results reported in Table 4 indicate that sentiment has a greater impact on yield spreads of low-rated bonds. More specifically, as can be seen from the table, the coefficient on sentiment goes from (Model 2) to (Model4) representing an increase in absolute terms of approximately 86%. Since the volatility of sentiment is not affected by this partition, the increase in the coefficient represents an increase in economic significance. Noting the stock market nature of sentiment, the higher sensitivity of speculative-grade bonds with respect to sentiment is consistent with these bonds being more similar to equity. The other control variables are generally estimated with the correct sign even though their significance is mitigated somewhat by the partition. For instance, volatility plays an 15

16 even bigger role with junk bonds, but its impact on investment-grade bonds is diluted by the partition of the sample. The time to maturity coefficient is positive for investment grade bonds and negative otherwise. It is not unusual to observe such behavior in empirical studies and there is not full agreement on the sign of the slope of the term structure of credit risk (see Helwege and Turner 1999). Our result with respect to maturity is in line with Han and Zhou (2011) who document a negative slope of the term structure of CDS spreads for names with very low rating. 3.3 Sentiment Before and After the Onset of the Credit Crisis In this subsection we present several regression models estimated with two sub-periods: in the first sample we include observations taking place before the crisis up until March 2007; in the second sample we use data from April 2007 to December This partition of the data is consistent with Dick-Nielsen, Feldhütter, and Lando (2012). We report the results in Table 5. Note first from the table that the impact of sentiment is positive before the crisis and negative after the onset of the crisis. The flipping in the sign on sentiment before and after the crisis can be explained with the better predicting power of sentiment on the integration of the equity and bond markets after the crisis. Relative to the pre-crisis period, the volatile crisis makes both equity and debt investors more likely to share the same sentiment. The control variables included in the regressions continue to have the appropriate sign and economic significance. In terms of statistical significance, we observe that equity volatility appears to have lost its significance. The reason for this finding is twofold. First, partitioning the sample with respect to the crisis eliminates some of the time-series variation that the crisis event would convey in a longer sample period. Second, the use of the historical equity volatility based on twelve months of past equity returns might not give an accurate description of the currently underlying business risk of the company (Zhang, Zhou, and Zhu 2009 and Rossi 2012). Consistent with the second point raised, the VIX, which is a forward 16

17 looking measure of market volatility that is constantly updated, is strongly significant in all specifications. 4 Sentiment and Equity/Bond Market Integration If the equity-market sentiment has a stronger impact on the bond market after the onset of the crisis, that is, there is more information spill-over from the equity market to the bond market, sentiment should play a more important role in explaining equity/bond integration after the onset of the crisis. The hedging relation between debt and equity of the same firm might contribute to the enhanced predicting power of sentiment on the integration of the two markets because of the existence of capital structure arbitrageurs. Capital structure arbitrageurs may have more incentives to hedge their corporate bond positions using stocks issued by the same firm or the other way around when the firm becomes riskier. Schaefer and Strebulaev (2008) report the sensitivity of the bond return for a given stock return (the hedge ratio) in their Table 5. The sensitivity of the bond return increases rapidly as the bond gets riskier. For an investment-grade firm with quasi-leverage of 0.20 and asset volatility of 20%, the authors report a sensitivity of 0.70, compared with for a firm with quasi-leverage of 0.50 and asset volatility of 40%. That is, the bond position required to hedge a given stock position, changes rapidly as the bond gets riskier. Table 6 compares the hedging incentives for capital structure arbitrages in the pre- and post- crisis periods. As we can see, asset volatility and bond risk (return) increased dramatically from the pre-crisis period to the post-crisis period. At the same time, the hedge ratio and the magnitude of equity returns also increased rapidly in the post-crisis period. Consequently, in order to hedge an equity position, a much larger correction on bond prices is required in the post-crisis period than in the pre-crisis period. 17

18 4.1 Univariate Analysis of Integration Kapadia and Pu (2012) propose a statistical measure of market integration that captures the comovement across firms equity and credit markets. The measure essentially computes the proportion of observations for which CDS spread changes and equity returns have the same sign. Because this study investigates the sentiment effect on the equity/bond market, we focus on how sentiment predicts the integration of the two markets. We therefore extend the KP measure by looking at all the four possible combinations of the sign of equity and bonds returns. We then explore the behavior of these four components during periods of high and low sentiment within the crisis time partitions used in the paper. Table 7 shows the percentage of monthly equity/bond return pairs that fall in a given bin, e.g. both negative, or both positive. Panel A reports results for the whole sample and the last column ( Integration ) is similar to the integration measure proposed by Kapadia and Pu (2012). Looking at the different components of the integration measure in conjunction to the variation in sentiment reveals the important role played by the crisis in shaping the comovement of bonds and stocks. Baker and Wurgler (2006) suggest that sentiment negatively predicts stock returns, especially after periods of high sentiment if stocks are hard to arbitrage. However, as can be seen from Table 7, before the crisis, about 20% of the observations both stocks and bonds display negative returns when lagged sentiment is low, which is inconsistent with behavioral theory. Furthermore, high sentiment is followed by both positive bond returns and positive equity returns for around 20% of the observations. The crisis seems to have produced an equity and bond market that move more in sync with the predictions of Baker and Wurgler (2006). After the onset of the crisis, sentiment plays a much stronger role in predicting the equity/bond comovement. We see that following periods of low sentiment, negative bond and equity returns take place in only 13% of the observations as opposed to 20% in the pre-crisis period, which is a 35% reduction in the wrong direction. Conversely, both positive equity and positive bond returns go from 35.64% 18

19 to 44.18% of the observations. When it comes to high sentiment, future negative bond and equity returns are much more likely after the crisis, with the proportion going from 19.06% to 29.36%, which represents a 53% increase. Conversely, positive return following high sentiment are much less likely after the crisis (going from 35.27% to 19.90%). In addition, market integration is higher during periods of low sentiment both before and after the crisis. This result is consistent with findings in the rational inattention literature that investors pay more attention to fundamentals and the mechanics of payoffs during periods of economic depression. 4 While in good times rational investors might not find it profitable to carefully monitor the connection between debt and equity of the same firm, during periods of depression investors are more likely to carefully consider the connection between securities of different asset classes. 4.2 Multivariate Analysis of Integration Lastly, we wish to ensure that the impact of sentiment on the comovement of debt and equity returns is still there when we control for other variables related to sentiment and that are also likely to be driving the covariation of stocks and bonds. Because the response variable of interest has three outcomes (return disagreement; both positive returns; and both negative returns), a logistic regression is not appropriate since it can only handle binary dependent variables (two responses). Therefore, to conduct the multivariate analysis, we employ a multinomial logistic regression in which the independent variable explains the probability of going from one outcome to the other. We choose return disagreement as the reference outcome and report probabilities of moving from this reference state to the either both positive returns or both negative returns. Table 8 reports three specifications of the multinomial logistic regression. For each model the two columns represent the impact of the regressors on the probabilities of going from disagreement to both negative returns and both positive returns respectively (the odds ratios 4 See Tutino (2011) and Huang and Liu (2007) for some application of the theory of rational inattention to financial decision making. 19

20 are in squared brackets). For instance, looking at the first specification (Integration 1), we see that, before the crisis, periods of high sentiment are 18% more likely (relative to disagreement) to be followed by both positive returns, whereas there is no impact on the probability of having both negative returns. Consistent with the univariate analysis, sentiment significantly predicts the integration of the equity/bond market after the onset of the crisis. That is, both negative returns are much more likely to follow periods of high sentiment, while the opposite is true for both positive returns. The impact of sentiment goes in the same way as the univariate analysis even when we consider more general specifications. We also note that all specifications reveal that integration is much higher for speculative-grade bonds. 5 Conditional Sentiment Baker and Wurgler (2006) show that the mispricing induced by sentiment is more pronounced for stocks that are harder to arbitrage or to evaluate. In particular, they find that the mispricing is more prevalent for more illiquid stocks and for stocks characterized by a higher idiosyncratic risk. Using regression with sentiment interacted with bond and firm characteristics, we verify if the mechanism similar to that of stocks is at work for bonds as well. 5.1 Direct Effect: Market Frictions and Fundamentals The first four columns of table 9 report several regression models with sentiment entering both alone and interacted with variables related to bond characteristics and firm s fundamental. All four models estimated reveal that the impact of sentiment is stronger for bonds that are less liquid, or closer to default. With regard to illiquidity, proxied by the Amihud Measure, we see that for a mean level of illiquidity (from Table 1, equal to 0.01) the impact of sentiment on spreads is increased by an additional 20 basis points. A similar story can be said for the other interactions. For instance, the coefficient on sentiment jumps from

21 to when going from investment grade bonds to junk bonds. We thus confirm the findings of Baker and Wurgler (2006) that the pricing of harder-to-value securities is more likely to be affected by sentiment. A complementary interpretation of the Table 9 can be reached if we fix sentiment and let the characteristics vary. For instance, the negative interaction on leverage or volatility suggests that, when sentiment is high, bond spreads are less driven by firms fundamentals, whereas when sentiment is low, the effects of firms fundamentals on bond spreads are aggravated. A similar argument applies to ratings and liquidity. 5.2 Indirect Effect: Arbitrageurs and Sentiment Spillover Some of the interactions of sentiment and market frictions reported in Table 9, suggest that bond investors are behaviorally similar to equity investors in that they tend to overbid bonds during periods of high sentiment and underprice bonds when sentiment is low, and that the mispricing is more pronounced for bonds that more difficult to arbitrage. A concurrent explanation for the role played by sentiment in driving bond valuations could be that sentiment spills over to the bond market because of the trading activity of dedicated investors engaged in exploiting relative mispricing of securities within firms capital structure. For this alternative explanation to be consistent with our finding that sentiment drives high bond valuations mainly after the onset of the crisis, it is necessary that fixed income arbitrage strategies, especially capital structure arbitrage, are more profitable during and after the crisis. We collect hedge fund return data for fixed-income arbitrage funds from TASS and CISDM to analyze the time-variation of these funds abnormal performance. Table 10 reports average abnormal performance (regression α) for fixed-income arbitrage funds before and after the crisis. The abnormal performance is obtained by regressing the fund returns on seven risk factors know to drive hedge fund return. 5 As can be see from 5 It is well known that hedge fund returns are often smoothed resulting inflated αs and deflated βs (Getmansky, Lo, and Makarov, 2004). To address this problem, we also obtain α from regressions that included lagged risk factors (see Asness, Krail, and Liew (2001)) and the results do not change. 21

22 the table, the abnormal returns to arbitrage are substantially higher (about twice as much) after the onset of the financial crisis. Having established that capital structure arbitrage is more profitable after the onset of the crisis, we proceed to a more direct test by interacting a measure of time varying measure of arbitrageurs abnormal performance with sentiment (see Table 9, Model 5). We obtain this measure, by estimating rolling funds αs using a 24-month rolling window (each month) and then averaging across funds in a given month. The larger negative effect of sentiment during periods of high arbitrage profitability (Model 5) offers support to the alternative explanation that an indirect channel between equity and bond investors created by arbitrageurs is also driving the sentiment spill-over. While we identify a new channel for indirect sentiment spill-over, 6 we note that both explanations can coexist. 6 Robustness Checks The results so far are based on regressions having the level of yield spreads as the dependent variables and explanatory variables often included as levels. To ensure that the strong statistical significance obtained in the previous section is not due to the persistence of both regressand and regressors, we also conduct regression analysis using yield spread changes and corporate bond returns. 6.1 Sentiment and Credit Spread Changes We follow Collin-Dufresne, Goldstein, and Martin (2001) and estimate regression models with changes in credit spreads on the left hand side and changes in sentiment and other state variables related to credit risk on the right hand side. The estimated models also include lagged regressors as controls. As it can be seen from Table 11, sentiment is strongly significant in all the specifications. Other variables related to credit risk, such as leverage and 6 We are grateful to an anonymous referee for pointing out this alternative channel to us. 22

23 the VIX, are also highly significant. The R 2 is smaller compared to the R 2 of regressions using yield levels, but this is to be expected and it is consistent with results in Collin-Dufresne, Goldstein, and Martin (2001). 6.2 Changes in Sentiment and Integration To rule out the possibility that the persistence in the level of sentiment is driving some of our results in the integration analysis, in Table 7 (Panel B) we present integration statistics based on changes in sentiment. We note that since returns and sentiment changes are contemporaneous the relation between these two variables should be flipped compared to the case when sentiment is expressed in levels. Panel B of the table reveals that the finding reported in Panel A are robust to alternative definitions of sentiment. 6.3 Sentiment and Corporate Bond Returns In addition to considering changes in spreads, we also look at the closely related bond returns. In Table 12, we report equally-weighted bond portfolio return regressions on sentiment and six other factors known to explain corporate bond returns. In particular, we augment the Fama-French and momentum factors with two bond specific factors. These factors are the default spread and the term slope spread. The table shows that when lagged sentiment is high bond returns tend to be lower in the future. As can be seen, the negative impact of sentiment is significant overall, but the significance comes mostly from lower rated bonds. We also estimate bond portfolio regressions before and after the crisis. Table 13 shows that the sentiment effect on bond returns comes mostly during and after the crisis period. Consistent with the results on yield spreads, before the crisis, sentiment enters the regression with a positive coefficient for investment grade bonds and a negative coefficient for junk bonds. In all cases the coefficients are statistically insignificant. Overall, the analysis using both credit spreads changes and bond returns shows that the findings of the previous section are not due to the use of yield spread levels or persistent 23

24 regressors. In all the regressions implemented, the impact of sentiment on bond prices is consistent showing that the finding of this paper are robust. 7 Conclusion The current research links equity market sentiment to corporate bond valuations focusing on the levels of credit spreads, the changes in credit spreads, and corporate bond returns. Overall, this study provides evidence that sentiment is negatively related to corporate bond spreads. The analysis also reveals that the sentiment effect on bond valuations shows different patterns before and after the financial crisis. The integration between the equity market and the corporate bond market is more affected by sentiment after the financial crisis, consistent with the intuition that the crisis has changed this relation with bond and stock valuations moving in the same direction as sentiment changes. The conditional analysis shows that when sentiment is high, corporate bonds are overvalued and investors tend to ignore fundamental risks associated with credit rating, illiquidity, leverage, and stock volatility; whereas when sentiment is low, corporate bonds are undervalued and investors tend to exaggerate fundamental risks. The test with the interaction between sentiment and arbitrage profit shows that the sentiment effect is stronger when the arbitrage profit is higher, indicating that capital structure arbitrageurs also play an important role in the sentiment effect on bond valuations. 24