Liquidity Risk of Corporate Bond Returns

Transcription

1 Liquidity Risk of Corporate Bond Returns Viral V. Acharya, Yakov Amihud and Sreedhar Bharath May 2008 Preliminary and incomplete: Do not quote without permission Abstract We examine the unconditional and conditional sensitivity of monthly U.S. corporate bond returns to liquidity factors over the period 1973 to We find that while investment grade bond returns are little affected by either stock- or treasury bondmarket liquidity, these liquidity factors significantly affect returns on sub-investment grade bonds. This latter effect arises due to liquidity betas of sub-investment grade bonds occasionally switching to a regime with extremely high values. This nature of liquidity risk of corporate bond returns is robust to controlling for other systematic risks (term and default), as well as changes in volatility and expected loss over time, none of which seem to exhibit a regime-switching behavior in terms of their effect on corporate bonds. Overall, the findings are consistent with a flight to quality phenomenon during stress periods whereby investors prefer more liquid and safer assets to less liquid and riskier ones when market liquidity deteriorates. Keywords: quality. credit risk, credit spreads, default, recession, flight to JEL CLASSIFICATIONS: G12, G13, G32, G33. Viral Acharya is Professor of Finance at London Business School and a Research Affiliate of the Center for Economic Policy Research (CEPR). Yakov Amihud is Professor of Finance at Stern School of Business, New York University. Sreedhar Bharath is Assistant Professor of Finance at University of Michigan. We thank Jason Sturgess and Yili Zhang for diligent research assistance. We are grateful to Banque de France grant for this study, to Moody s KMV for giving us the Expected Default Frequency (EDF) data, and to Ruslan Goyenko for sharing with us his illiquidity series for the US treasuries. All errors remain our own. Contact address: Viral V. Acharya, London Business School, Regent s Park, London - NW1 4SA, U.K. vacharya@london.edu, tel: +44 (0) , website: 1

2 Liquidity Risk of Corporate Bond Returns Abstract We examine the unconditional and conditional sensitivity of monthly U.S. corporate bond returns to liquidity factors over the period 1973 to We find that while investment grade bond returns are little affected by either stock- or treasury bondmarket liquidity, these liquidity factors significantly affect returns on sub-investment grade bonds. This latter effect arises due to liquidity betas of sub-investment grade bonds occasionally switching to a regime with extremely high values. This nature of liquidity risk of corporate bond returns is robust to controlling for other systematic risks (term and default), as well as changes in volatility and expected loss over time, none of which seem to exhibit a regime-switching behavior in terms of their effect on corporate bonds. Overall, the findings are consistent with a flight to quality phenomenon during stress periods whereby investors prefer more liquid and safer assets to less liquid and riskier ones when market liquidity deteriorates. Keywords: quality. credit risk, credit spreads, default, recession, flight to JEL CLASSIFICATIONS: G12, G13, G32, G33. 2

3 1 Introduction The effects of expected illiquidity and liquidity risk (unpredictable variations in illiquidity) on asset prices have been at the center of a large body of recent academic research. 1 While these studies have made substantial progress in enhancing our understanding of how liquidity affects asset prices, they all have one common feature which is that their analysis has been unconditional in nature. In contrast, casual empiricism suggests that effects of liquidity on asset prices are felt most in an episodic fashion. 2. By and large, such a conditional or episodic role of liquidity in affecting asset prices has not been investigated before, the exception being a recent study by Watanabe and Watanabe (2007) who find evidence supportive of there being a regime switch in the nature of liquidity risk of stock returns. In this paper, we investigate the liquidity risk of corporate bond returns, focusing on the conditional effects during stress times and on the difference in such conditional effects between high-rated and low-rated bonds. Our novel contribution is to document that the liquidity risk of corporate bonds is highly conditional in nature, especially for junk bonds, and arises primarily during periods of economy-wide stress. In fact, during such periods, the effect of liquidity risk on junk bond returns can be as large as that of default risk itself in terms of economic magnitude. This nature of liquidity risk of corporate bond returns is robust to controlling for other systematic risks, as well as changes in volatility and expected loss over time. Specifically, we examine the unconditional and conditional sensitivity of monthly U.S. corporate bond returns to liquidity factors over the period 1973 to The two liquidity risk factors we employ are the price-impact motivated measure for aggregate stock market of Amihud (2002), as calculated by Acharya and Pedersen (2005), and the equally weighted quoted bid-ask spread of off-the-run treasuries, as in Goyenko (2005). In unconditional tests, we investigate the time-series beta of corporate bond returns on these liquidity risk factors, controlling for the effect of interest rate and default risk factors (as in Fama and French, 1 See, for example, Amihud and Mendelson, 1986, Amihud, 2002, Pastor and Stambaugh, 2002, and Acharya and Pedersen, 2005, for equity markets; Krishnamurthy (2002) for treasuries; and, Chen, Lesmond and Wei (2007) and de Jong and Driessen (2006) for corporate bonds. We discuss this literature further in Section 2. 2 Though it is not the focus of their paper, Acharya and Pedersen (2005) report that stocks that are illiquid in an unconditional sense also have the highest liquidity risk, in that their illiquidity rises when aggregate market return and illiquidity are high too. They document in Figure 1 of their paper and the related discussion that all significant (more than three standard deviation) illiquidity episodes in the US stock market during the period have been preceded by significant asset-side shocks: 5/1970 (Penn Central commercial paper crisis), 11/1973 (oil crisis), 10/1987 (stock market crash), 8/1990 (Iraqi invasion of Kuwait), 4-12/1997 (Asian crisis) and 610/1998 (Russian default, LTCM crisis). 3

4 1993). In conditional tests, our primary focus, we allow these liquidity betas to vary over time, specifically to be different in normal times versus stress times. We adopt a variety of definitions for stress times for the economy combining variables that capture incidence of recession in the real economy and its manifestation in stock markets. Results from our unconditional tests show that as rating declines, liquidity risk of corporate bond returns increases with respect to both stock-market and treasury liquidity factors, with a sharp increase at the cusp of investment grade and junk grade. Statistically, the liquidity risk of investment grade bonds is insignificant, that of junk bonds is significant, and importantly, the difference in liquidity risks between junk bonds and investment grade bonds is also significant. Overall, these results are consistent with those of de Jong and Driessen (2006). These unconditional estimates of liquidity risk, however, suggest that the economic magnitude of liquidity risk is small on average, especially when compared to the effect of interest rate and default risk. Our conditional tests are based on a regime-shifting model of betas of junk bond returns on interest rate, default and liquidity risks; there is no shift detectable for investment grade bonds. Data identifies two distinct regimes for junk bond betas, substantial difference across which arise only due to difference in liquidity betas and not in betas of other risk factors. The difference in liquidity betas across regimes is also large from an economic magnitude standpoint: liquidity risks magnify by a factor of three to ten from first to second regime, whereas interest rate and default risks are virtually unaffected. The probability of being in the high liquidity beta regime correlates with macroeconomic variables that one would generally employ to exogenously specify stress times, and this probability also captures some periods that are easy to identify with known stress episodes in the US economy and markets. In the stress regime, the economic magnitude of liquidity risk of returns is substantially large, almost comparable to that of default risk. A one standard deviation in either of the liquidity factors produces only about a tenth of a standard deviation shock in returns during normal times; during stress times, however, the effect is between one fifth to one third of a standard deviation and the overall effect of liquidity factors is magnified as the two liquidity risks become more correlated during stress times. In contrast, the economic contribution of interest rate and default risks is larger in absolute terms in either regime, but that of interest rate risk falls during stress times whereas that of default risk rises but the shifts in the two effects are smaller across the two regimes and also seem to offset each other. We show that the findings are robust. First, we allow for a change in expected cash flows (expected loss) on corporate bonds by employing a time-series of expected default 4

5 frequency and expected loss given default, and allow this change to have differential effect on investment grade and junk bonds in normal and stress times. Second, we control for changes in aggregate stock-market volatility as implied by realized index returns. Third, we replace the Fama and French (1993) model of systematic risk factors with the Mertonmodel inspired specification of Schaefer and Strebulaev (2006) that employs equity return corresponding to a corporate bond to proxy for default risk. In each of the three robustness checks, the two liquidity betas of junk bonds continue to exhibit a strong regime-switching pattern. What is the economic significance of these findings? We claim that the evidence is consistent with a flight-to-quality phenomenon during stress periods whereby investors prefer more liquid and safer assets to less liquid and riskier ones when market liquidity deteriorates. This preference manifests as a higher liquidity risk premium, so that the sensitivity of returns to liquidity factors rises. 3 We call it a liquidity risk premium and not a generalized risk premium, since we found that in the stress times we examine or identify in data, there is no such increase in the sensitivity of returns to traditional risk factors such as interest rates and default risk. To summarize, junk corporate bond returns exhibit liquidity risk that has a significant conditional component during stress times for economy and markets, and this conditional pattern is consistent with investor preference for safer and more liquid instruments during such times. Section 2 discusses related literature. Section 3 describes the data we employ. Sections 4 and 5 present results for our unconditional and conditional liquidity risk tests, respectively. Section 5.1 shows the regime-switching model estimates. Section 5.2 considers robustness checks and Section 6 provides an application of liquidity risk to bond returns around rating downgrades. Finally, Section 7 provides a flight-to-quality based interpretation for our results. Section 8 concludes. 2 Related literature Like other assets, bond yields reflect their liquidity characteristics. Amihud and Mendelson (1991) show that short-term Treasury notes and Treasury bills with the same time to maturity have different yields due to differences in their liquidity (measured by the bid-ask 3 Note that once we control for changes in expected cash flows, the realized return s sensitivity to risk factors arises due to the sensitivity of expected return, a sensitivity that thereby conveys information about the risk premium. 5

6 spread and broker fees): Bills, which are issued frequently, are more liquid and then notes and consequently their yield is lower. Kamara (1994) finds that the notes-bills yield spread is an increasing function of liquidity risk, measured as a product of the volatility of yield and the ratio of the bills-to-notes turnover. Elton and Green (1998) find that differences in trading volume between Treasury securities explain differences in their yields. Boudoukh and Whitelaw (1993) find that the designated benchmark bonds in Japan, which are more liquid than similar bonds without such designation, have lower yield to maturity. And, Longstaff (2004) finds that higher yield on RefCorp government-agency bonds (issued by the Resolution Funding Corporation) are higher than those on same-maturity Treasury bonds whose risk is the same, since the RefCorp bonds are less liquid. The effect of liquidity of corporate bonds on their yields is analyzed by Chen, Lesmond and Wei (2007). They measure illiquidity, or the implicit bid-ask spread, by the imputed value change that is needed to induce a transaction in the bond, assuming that if that value change is smaller than transaction costs, a trade will not take place. They also use the quoted bid ask spread is a measure of illiquidity. They find that illiquidity is greater for noninvestment grade bonds, and that after controlling for factors that affect yield, such as risk of default and maturity, the corporate yield spread over Treasury is an increasing function of illiquidity. The effect of illiquidity on bond yields is much larger for non investment grade bonds. Chen et al. also find in a time-series analysis that changes in illiquidity induce changes in yields in the same direction. Edwards, Harris and Piwowar (2005) and Goldstein, Hotchkiss and Sirri (2005) document corporate bond illiquidity using the TRACE data starting around Both papers employ a price-impact measure, and Goldstein et al. also employ bid-ask spread. Though their focus is the study of corporate bond transparency on its liquidity, their results suggest significant trading costs for corporate bonds. Chacko (2003) imputes a corporate bond liquidity by assigning liquidity to a bond according to the turnover of the fund that holds it. The idea flows from Amihud and Mendelson (1986) that in equilibrium, liquid asset are held by more frequently-trading investors. Chacko then constructs a liquidity factor by sorting bonds into high- and low-liquidity portfolios and taking the return difference between them. The return on the high-minus-low liquidity portfolio is then used to price bonds. The results show that bond returns are increasing in the exposure to the bond risk factor, after controlling for other factors. Downing, Underwood and Xing (2005) study a similar issue, but their measure of bond liquidity is a proxy of corporate bond price impact similar to that of Amihud (2002). They find that long-term corporate bonds have greater beta with respect to the bond illiquidity factor and that liquid- 6

7 ity shocks explain a sizable part of the time-series variation in bond returns. They further find that illiquidity risk is priced in a context of a linear APT model (with other factors: market, maturity and credit risk). While these studies linking corporate bonds liquidity to their returns or yields make a promising start, the data availability limits any significant time-series analysis, especially of conditional effects during times of economic stress, which is our primary focus in this paper. Hence, a number of papers including this paper have employed liquidity measures from treasury bonds (bid-ask spread or on-the-run to off-the-run spread) and stock markets (bid-ask spread or a price-impact measure). Longstaff, Mithal and Neis (2004) show that the basis between corporate bond spreads and credit default swap premia is explained by fluctuations in treasury liquidity. de Jong and Driessen (2005) follow Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) by estimating two liquidity betas of bond returns with respect to stock and bond liquidity shocks, using Amihud s (2002) ILLIQ for stock illiquidity and quoted bid-ask spreads on long-term U.S. Treasury bonds, as well as the beta on the S&P 500 index. They find that bonds with lower rating and longer maturities have more negative liquidity betas, implying that these bonds have higher illiquidity premium. The de Jong and Driessen study is the closest to our unconditional analysis (Tables 2 and 3), but they have a much shorter timeseries and do not isolate regime-switching behavior of liquidity betas as we do. Finally, the effect of bond liquidity transcends the bond market. Goyenko (2005) studies the cross-market effect of liquidity and finds that stock returns as well as Treasury bond returns are affected by both stock and bond liquidity shocks. Furthermore, the exposure of stocks to treasury bond liquidity appears priced in the cross-section of stock returns. 3 Data Our bond data are extracted from the Lehman Brothers Fixed Income Database distributed by Warga (1998) and supplemented by the National Association of Insurance Commissioners (NAIC) traded bond prices data. We follow closely the data extraction methodology outlined by Bharath and Shumway(2008). The Warga (1998) database contains monthly price, accrued interest, and return data on all corporate and government bonds from We use the data from the period when coverage becomes wide spread. This is the same database used by Elton et al.(2001) to explain the rate spread on corporate bonds. This database has also been used by Gebhardt et.al. (2005) in their study of cross section 7

8 of bond returns. In addition, the database contains descriptive data on bonds, including coupons, ratings, and callability. A subset of the data in the Warga database is used in this study. This is supplemented by data from the NAIC database for the period We employ several selection criteria. First, all bonds that were matrix priced rather than trader priced are eliminated from the sample 4. Employing matrix prices might mean that all our analysis uncovers is the rule used to matrix-price bonds rather than the economic influences at work in the market. Eliminating matrix-priced bonds leaves us with a set of prices based on dealer quotes. This is the same type of data as that contained in the standard academic source of government bond data: the CRSP government bond file. Next, we eliminate all bonds with special features that would result in their being priced differently. This means we eliminate all bonds with options (e.g. callable bonds or bonds with a sinking fund), all corporate floating rate debt, bonds with an odd frequency of coupon payments, and inflation-indexed bonds. In addition, we eliminate all bonds not included in the Lehman Brothers bond indexes, because researchers in charge of the database at Lehman Brothers indicate that the care in preparing the data was much less for bonds not included in their indexes. This also results in eliminating data for all bonds with a maturity of less than one year. The same selection criteria were used with the NAIC database as well. It should be noted that in the Lehman database all bonds have missing data on August 1975 and December Most bond issues are rated by both S&P and Moody s and agree with each other. We value weight the monthly returns of all eligible bonds in each rating class by the total amount outstanding of each bond. This also help us reduce significantly biases resulting from bad prices of particular bonds. The monthly corporate bond return as of time τ + 1, r τ+1 is computed as r τ+1 = P τ+1 + AI τ+1 + C τ+1 P τ AI τ P τ + AI τ, (1) where P τ is the quoted price at time t; AI τ is accrued interest, which is just the coupon payment scaled by the ratio of days since the last payment date to the days between last payment and next payment; and C τ+1 is the semiannual coupon payment (if any) at time t+1. Following Fama and French (1993), we use two risk factors for corporate bonds. Common 4 For actively traded bonds, dealers quote a price based on recent trades of the bond. Bonds for which a dealer did not supply a price have prices determined by a rule of thumb relating the characteristics of the bond to dealer-priced bonds. These rules of thumb tend to change very slowly over time and do not respond to changes in market conditions. 8

9 risk for corporate bonds arises from unexpected changes in the term structure of interest rates and from changes in default risk. Fama and French (1993) justify these choices by an ICAPM setting in which the these two factors are hedging portfolios. Following the suggestions by and the results in Gebhardt et al (2005), we do not include the market factor because empirically they found that the market factor has almost no explanatory power for corporate bond returns in the presence of default and term risk factors. Following Gebhardt et al (2005), we use TERM, as the difference in the monthly longterm government bond return (from Ibbotson Associates) and one month T-bill returns (from the Center for Research in Security Prices, CRSP), as a proxy for the unexpected changes in the term structure, and DEF, defined as the difference between the monthly return on a value-weighted market portfolio of all investment-grade corporate bonds (AAA to BBB) with at least ten years to maturity and the monthly long-term government bond return, as a proxy for default risk. Acharya and Pedersen (2005) predict market illiquidity by running a regression of the ILLIQ measure of Amihud (2002) using a AR(2) specification. The residual of this regression is interpreted as the stock market illiquidity innovation (illiqinnov). The bond market illiquidty innovation series construction is the first difference in the aggregate treasury bond illiquidity series constructed by Goyenko (2005). In particular, the aggregate treasury illiquidity is an equally-weighted average of quoted bid-ask spreads on off-the-run bonds of different maturities. We do not describe these measures here in full detail except refer the reader to Acharya and Pedersen (2005) and Goyenko (2005). Panel A of Table 1 provides summary statistics on the bond market factor portfolios. The average risk premium for the default factor (DEF) is % per month, while the average risk premium for the term factor (TERM) is 0.205% per month. The default premium is quite small in relation to its standard deviation of 1.41%. While this implies that we cannot reliably reject the null hypothesis of zero default premium, it was still found to be a factor explaining the cross section of bond returns by Gebhardt et al (2005). Figure 1 plots the standardized bond and stock market illiquidity innovations. The measured innovations in market illiquidity are high during periods that were characterized by liquidity crisis, for instance oil shock of 1973, the period of high interest rates, the stock market crash of 1987, the 1990 recession and the 1998 LTCM crisis. 9

10 4 Unconditional liquidity risk We first examine the unconditional effect of liquidity factors on corporate bond returns divided into categories by ratings, and then grouped into investment grade and sub-investment grade. 4.1 Methodology and results First, we estimate the following time-series specification: R j,t = α j + β j,t T erm + β j,d Def + β j,i Illiqinnov + β j,bi Bondilliqinnov + ɛ j,t, (2) for j {AAA,..., CCC & Below, Unrated}. Note that this specification resembles the Fama and French (1993) model to explain corporate bond returns, but we have augmented it with the two liquidity risk factors. Table 2, Panel A presents the coefficient estimates. For all ratings, the loadings on Term and Def are positive and statistically significant. The Term loadings seem higher overall for ratings of BBB and above compared to those for BB and below. In contrast, the Def loadings do not reveal any particularly strong pattern across different ratings. Of primary interest to this paper, the liquidity risk loadings are negative for all ratings and for both measures of liquidity risks. This implies that when stock-market and treasury illiquidity rises, corporate bond returns tend to fall. This effect is statistically insignificant for both liquidity risks for BBB and above (except for AA for which both are significant). For BB down to CCC and below, both liquidity risk betas are significant, whereas for Unrated bonds, only the stockmarket illiquidity beta is significant. Perhaps the most notable feature of the liquidity risk betas is that their magnitude is substantially higher for BB and below compared to bonds rated above, usually by factors between four to ten. Finally, the explanatory power of these models is reasonable for BBB and above (adjusted R-squared between 27% and 76%), but deteriorates substantially for BB and below (adjusted R-squared between 9% and 22%). It is worth mentioning that these results match those of de Jong and Driessen (2006), but there are some differences. In our Table 2, Panel A, β i and β bi are generally increasing in bond rating, whereas in de Jong and Driessen (Tables 4 and 5), β i is practically flat in rating, increasing only for BB and B and CCC ratings. In contrast, their β bi is increasing in rating. Note that they include S&P return on the right hand side whose beta is increasing 10

11 monotonically in rating, while we do not, and instead include Term and Def, following much of the corporate bond literature following Fama and French (1993). Indeed, when we include S&P return on the right hand side, we find little incremental effect beyond Term and Def, and even by itself, the market return shows up only weakly. Panel B reports the economic magnitudes of the different factor loadings. In particular, it reports for each factor loading and each rating class, how many standard deviation in returns arises from a standard deviation shock to the factor. The calculations employ the summary statistics reported in Table 1. For BBB and above, the liquidity risks are not too significant in an unconditional sense: a one standard deviation shock to liquidity risks produces a meagre 1% to 8% of standard deviation in returns for these rating classes. For BBB and above, the economic magnitude of Term and Def effects is far more significant, especially of Term. For BB and below, the economic magnitude of Term and Def is far smaller. While we expect Term to have a stronger effect on higher-rated bonds as they have longer maturity compared to lower-rated bonds, the lower economic magnitude of Def for lower-rated bonds is surprising. The economic magnitude of the two liquidity risks is higher for BB and below, with one standard deviation shock to stock-market illiquidity producing between 11% to 18% of standard deviation in bond returns, the corresponding range for treasury illiquidity being 6%to 15%. One point to note here is that while the maximum shocks to Term, Def and stock-market illiquidity innovations are of the order of four to five standard deviations, the maximum shock to treasury-market illiquidity innovation is around nine standard deviation. Thus, the realized economic impact of the latter innovation may be larger than Panel B suggests. Next, we group all bonds with ratings of BBB and above into investment-grade category (IG) and the rest into sub-investment grade category (Junk). While this classification is natural at one level for comparison of betas across different credit-risk categories, it is motivated primarily by the desire to improve the statistical power of any test making such comparison. As Table 2, Panel A revealed, there appears to be a significant breakpoint in beta estimates (especially for liquidity risk betas) at the BBB to BB cusp. However, on either side of these two ratings, the behavior of estimates is not monotone except for Term. It is, however, by and large the case that ratings above BBB have the same relative property in terms of beta estimates to ratings below BB. Hence, we estimate the following panel specification: R j,t = α IG + β IG,T T erm t + β IG,D Def t 11

12 + β IG,I Illiqinnov t + β IG,BI Bondilliqinnov t + ɛ j,t, and (3) R k,t = α Junk + β Junk,T T erm t + β Junk,D Def t + β Junk,I Illiqinnov t + β Junk,BI Bondilliqinnov t + ɛ k,t, (4) for j {AAA,..., BBB} and k {BB,..., CCC & Below, Unrated}. The estimation above can either be run by ordinary least squares regression (OLS). This would assume that there is homoscedasticity in residuals ɛ j,t and ɛ k,t. This may not however be the case. In particular, there is reason to believe that perhaps the residuals for lower-rated classes are more variable than those for higher-rated classes. Indeed, if we estimate the above specification by OLS and test for homoscedasticity of residuals, this is indeed what we find. Hence, we also estimate the specification using feasible generalized least squares regression (FGLS) of Greene (2003), which takes account of the heteroscedasticity and first order auto correlation in residuals (using the Prais-Whinsten method) and weighs data accordingly while arriving at coefficient estimates. Table 3 reports the estimations where we pool all rating classes into a single panel, where we separate into investment grade and junk but the method employed is OLS, and finally, where we separate into investment grade and junk but the method is FGLS. There are several patterns which tell in a more striking fashion the facts unearthed also from Table 2. First, both Term and Def loadings are significant for both investment grade and junk. However, while the Term loading is higher in magnitude for investment grade than for junk, the Def loadings are remarkably similar. Again, we find this failure of Def in producing different return exposures for investment grade and junk rather surprising. After all, the separation between these categories is (supposedly) primarily due to their different credit risks. Second, liquidity risk is higher for junk bonds than for investment grade bonds, both from a statistical as well as economic magnitude standpoint. In the OLS estimation, investment grade exposure to stock-market as well as treasury liquidity is insignificant; with FGLS, the exposure to stock-market liquidity is marginal whereas that to treasury liquidity is highly significant. The liquidity risk loadings of junk bonds are highly significant (p-values essentially being zero) for both liquidity risks and for both estimation methods. To formalize these observations, we compare the coefficients β IG and β Junk statistically. The results are also reported in Table 3 below coefficient estimates. Note that since OLS standard errors may be biased due to correlation of residuals between investment grade and junk (for example, due to omitted common factors), we also report comparison of coefficients based on the Seemingly Unrelated Regressions (SUR) approach of Zellner (1962). In case 12

13 of Term, investment grade beta is higher than junk beta with p-values of zero. In contrast, there is no statistically significant difference between Def betas. Indeed, based on OLS, FGLS or SUR method, the p-value for the test that the difference is zero is virtually close to one. Liquidity risk betas being the same between investment grade and junk for a given liquidity measure is rejected across all methods at conventional confidence levels (p-values being at most 6%). The test that both liquidity betas are identical between investment grade and junk is rejected even more strongly, as reported under the row heading Liquidity. To summarize, Tables 2 and 3 make it clear that there is unconditional liquidity risk in corporate bond returns, but that it is substantially higher for junk bonds than for investment grade bonds. 5 Conditional liquidity risk As discussed in introductory remarks, most of the current academic literature has focused on unconditional liquidity risk as we also analyzed thus far. However, from an economic perspective, there are sound reasons to believe that the effect of liquidity risk is episodically high but muted in many periods. This could be because investor aversion to risk in general or to liquidity risk in particular may exhibit time-variation. Of greater relevance to corporate bonds, financial institutions are usually the marginal price-setters in these markets. Such institutions may be far away from their funding or capital constraints during halcyon times but when hit by adverse shocks to funding liquidity may reflect an aversion to holding corporate bonds in lieu of treasuries. The case for conditionality in liquidity risk is thus strong and we investigate it next. 5.1 Regime-switching model of bond betas As a first step of our conditional analysis, we perform a regime-switching analysis of corporate bond betas on various risk factors, separately for investment grade and junk bonds. In essence, we let the data tell us whether there is a set of times when betas are substantially stronger than other times Methodology We estimate a Markov regime-switching model for corporate bond betas as follows where we allow alpha and all betas of bond returns of a given type (investment grade or junk) 13

14 to be potentially different between two regimes. Note that we collapse returns of all bonds that are in investment grade or junk category to a single time-series of bond returns for that grade using an equally weighted average. For investment grade bonds: Regime k (s t = k) for k {1, 2}: R IG,t = α k IG + β k IG,T T erm t + β k IG,D Def t + β k IG,I Illiqinnov t + β k IG,BI Bondilliqinnov t + ɛ k IG,t. (5) The state variable s t determines whether it is regime 1 or regime 2 and the Markov switching probability for state transition is specified as: P (s t = 1 s t 1 = 1) = p IG, and (6) P (s t = 2 s t 1 = 2) = q IG. (7) Similarly, for junk grade bonds: Regime k (s t = k) for k {1, 2}: R Junk,t = α k Junk + β k Junk,T T erm t + β k Junk,D Def t + β k Junk,I Illiqinnov t + β k Junk,BI Bondilliqinnov t + ɛ k Junk,t. (8) The state variable s t determines whether it is regime 1 or regime 2 and the Markov switching probability for state transition is specified as: P (s t = 1 s t 1 = 1) = p Junk, and (9) P (s t = 2 s t 1 = 2) = q Junk. (10) The model is estimated using maximum likelihood estimation. Since the estimation procedure is standard (Hamilton, 1994), we do not provide details here but only the results. Two points are in order before we proceed. One, the probabilities of state transition are assumed to be constant rather than varying with some exogenous condition. In this sense, the conditionality of this model arises purely from the regime switch rather than the likelihood of the regime switch being based on some economic variable. Second, the model also allows for residuals to be heteroscedastic between the two regimes. 14

15 5.1.2 Results We find that data do not support any regime switch for investment grade bonds whatsoever. The regime with high betas is one with high liquidity betas but it is based on an extremely small number of data points (all in the year 2003) and the probability of being in this regime versus the other switches directly between 0 and 1. 5 Identification of such regimes is usually considered as the estimation ending up with a local minimum when it fails to find any substantial regime switch. This is perhaps not too surprising given that the unconditional liquidity betas for investment grade bonds were found to be quite insignificant in Table 2 and 3. Hence, we focus attention for rest of the paper on regime switch in betas of junk bonds. Note that when we estimate a common regime switch for both investment grade and junk bonds, we again end up with a local minimum in estimation. The results in Table 4 for the regime switch in junk bond betas are striking. There are two clear regimes and importantly these are regimes in liquidity betas. Regime 1 is characterized by relatively low liquidity betas of junk bond returns, whereas Regime 2 is characterized by much higher liquidity betas. Note that all betas are significant individually in their respective regimes, but not so in terms of comparisons across regimes. Though the Term and Def betas are statistically different across the regimes, in terms of economic magnitude, the differences are inconsequential. In other words, the behavior of junk bond returns does not exhibit substantial variation in risk exposure to interest rate risk and default risk over our sample period. In contrast, while tests of difference in liquidity betas between the two regimes are also strongly significant for each liquidity factor, what is remarkable though is the relative magnitude. Stock-market liquidity risk in Regime 2 is seven to eight times higher than that during Regime 1, and treasury liquidity risk is about three times higher. Going forward, we call Regime 1 and Regime 2 as normal and stress regimes, respectively. Table 4 also reveals that the two regimes indeed have switching probabilities that correspond to the notion of normal and stress times. The probability of staying within normal regime is estimated to be 0.974, whereas that for staying within stress regime is much lower at In other words, the likelihood of a migration to stress regime from a normal regime is just 2.6%, whereas from stress regime to normal regime is 7.8%. Put another way, the probability of switching out of a normal regime within a year is 27%, whereas that for switching out of stress regime within a year is around twice as high 57%. To summarize, stress regime reflects high liquidity risk in junk bond returns, but is not expected to last very long. Table 5, Panel A reports the summary statistics for the risk factors and returns to 5 The details of this result is available upon request. 15

16 investment grade and junk bonds during normal and stress regimes. We classify dates into regimes based on whether the likelihood of being in Regime 2 is lower than 30% and greater than 70%, respectively. During stress times, Term and Def risk factors are more variable, especially Def. In contrast, stock-market illiquidity innovations are not more variable, but their median level is more negative in stress regime though they are more positively skewed in stress regime. That is, stock-market illiquidity is less variable in terms of standard deviation but more likely to be extremely high during stress regime. In contrast, treasury illiquidity innovations are somewhat more variable in stress times, but their median level is much the same as in normal times. Both investment grade and junk bonds have much higher mean return in stress regime and are also much more variable, both values for both sets of bonds being about twice as large in the stress regime. Interestingly, Table 5, Panel B shows that the negative correlation between Term and Def drops to a lower magnitude during stress times, whereas the positive correlation between the two liquidity risk measures rises. As in normal times, there is little correlation between liquidity risk measures and Term or Def, though treasury illiquidity innovations become more negatively related to Def during the stress regime. How economically significant is this conditional liquidity risk of junk rated bonds? Table 6 shows that the conditional liquidity risk effect in the stress regime can be of the same order of economic magnitude as the conditional effect of Term and Def on junk bond returns. The table reports how much of a standard deviation in returns is associated with a standard deviation shock to a risk factor, where both standard deviations are calculated separately for normal time and stress time and the corresponding normal time and stress time betas employed in the calculation. The effect of Term and Def is always greater than the liquidity risk factors in an absolute sense for junk bond returns, in normal times as well as in stress times. The stress times are however coincident with a significant rise in the explanatory power of liquidity risk. In particular, a one standard deviation shock in stock-market and treasury liquidity is associated by between one-fifth to one-third of a standard deviation shock in junk bond returns in stress times, and this is about thrice as large as their effect in normal times. Based on the standard deviation of returns in stress times (Table 5, Panel B), this effect is between 40 to 70 basis points and seems substantial. It should also be noted that Table 5, Panel B reveals that liquidity factors are more highly correlated during stress times, so that the net impact of liquidity risk on junk bond returns may be even greater than the individual effects we have reported in Table 6. Note that in either regime, Term and Def have a much higher effect on 16

17 junk bond returns in terms of economic magnitude. However, these effects are between 45% and 65% of a standard deviation in both regimes; that of Term falls in stress regime whereas that of Def rises and the two effects seem to offset each other. In other words, in terms of explanatory power across regimes, liquidity risks contribute the most significant change in pattern of junk bond returns Stress regime and macroeconomic factors In Figure 4, we plot the model-implied probability of being in the stress regime. The stress regime picks up most data points in 70 s (picking up the oil-price shock of mid 70 s and the high interest-rate regime of late 70 s and early 80 s), early 80 s (during the high interest-rate environment in the US) and The regime-switching model appears to pick up stress in 1989 leading up to the NBER recession of 1990 and 1991, but does not identify mid 90 s and the Russian default and LTCM episode of 1998 as being in stress regime. In order to understand more formally what times constitute stress periods we consider both economy wide and stock market wide factors. We identify recessions by various available methodologies in the literature and capture market conditions by the stock market return and the aggregate expected likelihood of default. Specifically, as for Tables 5 and 6, we first convert the model-implied probability of being in stress regime into a binary variable which is set to one if the probability is higher than 70% (which gives us about 25% of data as being in stress regime), and zero otherwise. We relate this stress dummy to dummy variables corresponding to five macroeconomic variables whose year-month values are shown in Appendix I. These five variables are: a) NBER recession dates; b) Mkt return (negative) which is a dummy in a given month if there have been three consecutive months of negative market return including the given month, where market return is measured as the CRSP Value weighted return with dividends; c) Moody s KMV EDF, which is the value-weighted average of firm-level expected default frequency (EDF) supplied to us by Moody s KMV, where the value weights are based on equity market capitalization of firms; d) Prob(Recession) - Hamilton, a dummy variable if the probability of recession estimated from a Hamilton (1989) model on US GNP growth rates is greater than 70 percent (see Appendix II for its construction, also employing a regime-switching model); and, e) The Chicago Fed s CFNAI index (a follow up measure of the Stock and Watson (2001) recession index) is lower than the fifth percentile. Table 7 shows the relationship between regime-switching model based Stress and these macroeconomic notions of stress times. Though we present the OLS regression results with 17

18 discrete variables, the probit estimates provide similar evidence. All correlations have the expected sign, which is positive and statistically significant. When all five variables are used to employ the model-implied probability of being in the stress regime of liquidity risk of corporate bond returns, the negative stock market return, Hamilton probability of being in low regime of GNP growth rate and CFNAI index being low are significantly and positively correlated. Though the R-squared is low at 6%, this is typical of such associations between variables that describe the relatively rare stress periods of the economy. Figure 4, in fact, illustrates the positive even if imperfect relationship between the model-implied probability of stress and NBER recession months. This provides a measure of confidence that our regimeswitching results on liquidity betas of junk bonds (Table 4) have some underlying economic foundation. We will elaborate more on this foundation later. 5.2 Robustness checks In our robustness checks as well, we restrict attention to the regime switch only for junk bond betas. This is because investment grade betas show no regime switch at all even with the changes we make below Variation in expected loss If we assume that expected cash flows on corporate bonds do not change over time (for sake of argument), then any realized return must be due to changes in expected return and a small duration effect over a month. Since cash flows on corporate bonds are promised, their expectation does not change as sensitively to new information as it does for cash flows of equities. The implication is that the regime switch in liquidity risk we have uncovered could be interpreted to mean that during stress times, the expected return on junk bonds increases substantially more (compared to normal times) when stock-market and treasury bond illiquidity rise. To complete this argument though, we must check that the starting assumption that changes in expected cash flows are controlled for is legitimate. To this end, we construct an aggregate time-series measure of expected loss on corporate bonds. We proxy for expected likelihood of default by the value-weighted average of firmlevel expected default frequency (EDF) supplied to us by Moody s KMV, where the value weights are based on equity market capitalization of firms. We proxy for loss given default using the logarithmic specification of Altman, Brady, Resti and Sironi (2003) who relate aggregate recovery (one minus loss given default) to aggregate default rate. The specific 18

19 function form we employ is as follows: aggregate recovery = ln(aggregate def ault rate) (11) where the aggregate default rate is substituted by the value-weighed EDF described above. Multiplying the aggregate EDF with aggregate loss given default gives us our proxy for expected loss (Loss t ) over time. We calculate the change in expected loss Loss t as (Loss t Loss t 1 ). The time-series of this change is plotted in Figure 6. We augment the regime-switching model to allow junk bond returns to have exposure to expected loss changes ( Loss t ) that differs across the two regimes. Table 8 reports the estimations. Throughout, we find that changes in expected loss have little effect on our earlier conclusions. Regime 2 is distinct from Regime 1 primarily due to it having higher liquidity betas, the effect of stock liquidity risk being magnified almost fifteen times in Regime 2 compared to Regime 1 (compared to about seven to eight times in Table 4); Term and Def betas now exhibit even less difference between the two regimes. Note also that the probabilities of staying within the regime are slightly larger than those in Table 4, for both regimes. Overall, this lends us confidence that the liquidity risk effects we uncovered indeed correspond to an increase in expected return of junk bond returns in stress times when illiquidity rises. The effect of change in expected loss is itself generally as per economic priors. An increase in expected loss produces a lower contemporaneous return, an effect that is statistically significant and also somewhat larger in magnitude in the stress regime Variation in market volatility One criticism often leveled against liquidity measures is that high illiquidity is coincident with volatile market periods. In the case of corporate bond returns, this criticism has more bite as not capturing volatility fully could imply having an omitted variable bias in our specifications and liquidity factors may be picking up an omitted effect. To this end, we add to our unconditional and conditional specifications changes in the monthly volatility (Vol) of daily returns on value-weighted CRSP index with dividends. 6 The time-series of this change 6 A somewhat related idea is to control for changes in VIX, a measure of index options-implied volatility published by the CBOE and considered by many researchers and practitioners as a gauge for global risk appetite of financial institutions. When VIX rises, the risk appetite is supposedly lower as reflected by financial institutions in their pricing of index options. However, VIX time-series starts only 1986 and this rules out almost half of our sample period, seriously limiting the ability of data to identify significant regime shifts in liquidity betas. 19

20 is also plotted in Figure 6. As such, we do not find any evidence of overwhelming correlation between changes in Vol and our other risk or liquidity factors. 7 The changes in Vol are positively correlated with stock-market illiquidity innovations, but they seem to have little association with treasury illiquidity innovations. Table 9 shows the result for regime switch in betas of junk bond returns, where we add changes in Vol as a risk factor along with Term, Def and the two liquidity risks. Overall, our conclusions remain unaffected but there are some noticeable facts. First, Term and Def betas are now somewhat higher in normal regime than stress regime. Second, there is no effect of volatility changes on junk bond returns in normal regime, but in the stress regime, they have a negative effect on returns in stress regime (though statistical significance is marginal). And third, the shift in liquidity betas across regimes and the regime-switching probabilities are again similar to Table 4 (unlike Table 9 where there were some quantitative differences) Other choices for Term and Def In Table 10, we employ a different set of interest rate and default risk factors. These are based on the recent paper by Schaefer and Strebulaev (2006) who demonstrate that sensitivities of corporate bond returns to interest rates and default risk are summarized well by the corresponding hedge ratios with respect to treasuries and equity in Merton (1973) model. They regress excess returns of a corporate bond of a firm on TERM (as defined earlier) and excess equity return of the firm, where all excess returns are measured relative to the onemonth T-bill return. They show that the resulting coefficients from the time-series regression match well the Merton-model implied hedge ratios. Their evidence is suggestive that the residual risk unexplained by these systematic risk factors, and this residual risk tends to be substantial, is not linked to interest rate or default risk. One advantage of their approach is that controlling for default risk using firm s equity return may be far superior to an aggregate default risk factor such as Def. We adopt the approach of Schaefer and Strebulaev and verify that our conclusions on regime switch in liquidity risk of corporate bond returns remain unaffected. This entails a few changes. First, we calculate an equally-weighted portfolio of all corporate bonds in investment grade and junk categories. Second, we employ as the dependent variable the excess return on this corporate bond portfolio over the one month T-bill return. And third, we substitute Def factor by an equally weighted average of equity returns of firms 7 The exact numbers are available upon request. 20