Liquidity Risk of Corporate Bond Returns. Viral Acharya (NYU Stern), Yakov Amihud (NYU Stern) and Sreedhar Bharath (ASU) Forthcoming, JFE

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1 Liquidity Risk of Corporate Bond Returns Viral Acharya (NYU Stern), Yakov Amihud (NYU Stern) and Sreedhar Bharath (ASU) Forthcoming, JFE Sponsored by Centre for Advanced Financial Research and Learning (CAFRAL) and Fixed Income Money Market and Derivatives Association of India (FIMMDA) A short introduction: The effect of market liquidity on asset pricing The prevailing theory of asset pricing: Positive risk-return relation. However, the empirical evidence for the stock market is that on average, RM - Rf > 0. Across stocks, empirical evidence is scarce or non-existent, or higher risk lower average return. Problems in estimating risk. Our formal model assumes that Assets are characterized by dividend stream and trading costs. Investors need to trade occurs randomly. In equilibrium, we prove that 1. Asset returns are increasing function of trading costs. (The function is concave.) Or Asset prices are decreasing and convex function of trading costs. The theory of Amihud & Mendelosn (1986): Positive illiquidity-return relation. 2. Net returns too are an increasing function of trading costs.

2 The expected excess monthly return (or yield) on a stock as a function of the stock s bid-ask spread, reflecting clienteles (Amihud-Mendelson 1986) R i = β i ln(s i ) + year dummies 0.80% 0.70% 0.60% P/E ratio and liquidity (Loderer & Roth, JEF 2003) The effect of illiquidity (relative bid-ask spread) on the P/E ratio, controlling for (1) beta, (2) dividend payout, (3) current EPS growth and (4) expected earnings growth (from analysts reports). Excess Monthly Return 0.50% 0.40% 0.30% 0.20% 0.10% 0.00% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% Bid-Ask Spread (%) Result: discount of over 20% for a median-spread stock compared to zerospread stock ( ). Discount as a function of spread is observed for both Nasdaq and Swiss stocks. There is ample empirical support for this relation by independent studies. Restricted stock. Price discount of about 1/3. (Silber 1991). Why do small trading costs have a big price effect? Because they are incurred repeatedly, for ever. A quick calculation: Valuation of transaction cost of c PV = c / (r-g). It grows with the stock price, whose growth rate is r D/P. PV = c * P/D Assume that trading is once a year. Stock dividend yield, D/P, is now about 2%-2.5%. the price multiple of trading cost c is % trading cost leads to at least 4% discount in stock price. Liquidity is hard to observe, but we observe trading frequency, which by Amihud- Mendelson (1986) is affected by trading costs. Turnover = (volume /number of shares) proxies for trading frequency. More liquid stocks are traded more frequently. The effect of turnover on stock returns cross-section analysis Explanatory Variables: All months Excl. January Turnover: -.04 (8.58) -.04 (7.91) Book/Market:.14 (5.97).08 (3.29) log(size): -.05 (4.65).02 (1.60) β: -.37 (5.76) -.05 (6.84) Higher liquidity, or turnover lower expected returns.

3 Variable The effect of ILLIQ = avg( R /$Volume) on stock expected return (constant omitted), monthly, [From Amihud (2002)] All months Excl. January Liquidity changes over time: Evidence from the recent crisis U.S. trading costs as % of stock prices. Based on data from ITG. BETA ILLIQMA (0.64) (5.39) (0.79) (4.91) (0.59) (3.69) (0.30) (4.56) 1.8% 1.6% 1.4% Small Cap All Large Cap LnSIZE (3.50) (2.00) (3.51) (1.14) 1.2% 1.0% StdDev of Return (1.90) (2.89) (0.96) (1.77) 0.8% 0.6% DIVYLD (3.36) (4.28) (2.81) (2.11) 0.4% R (3.70) (6.19) (2.33) (2.92) 0.2% 0.0% Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1 Q3 Q1 RYR (3.40) (4.27) (2.04) (2.82) The effects of expected and unexpected illiquidity (illiquidity shocks) on excess monthly stock returns, Note: The (absolute) effect of liquidity declines in size. RM-Rf (EW) Constant (1.97) Excess returns on size-based portfolios RSZ 2 -Rf RSZ 4 -Rf RSZ 6 -Rf RSZ 8 -Rf RSZ 10 Rf (2.03) (2.12) (2.13) (2.05) (0.99) Current paper, Liquidity Risk of Corporate Bond Returns The yield spread on corporate bonds is considered a risk and default premium. Corporate bonds are usually less liquid than Treasury bonds, especially the high-yield ones. LnMILLIQ m (2.12) (2.11) (2.33) (2.36) (2.30) (1.18) Therefore, bond returns should respond to liquidity shocks (in addition to other LnMILLIQ U m (4.42) JANDUM m (4.20) (4.53) (5.03) (4.34) (4.08) (4.12) (3.45) (4.04) (2.64) (3.38) (1.47) R-squared D-W shocks that affect bond prices) because the required yield changes then. The yield spread reflects both risk\default premium and illiquidity premium. Chen, Lesmond & Wei (2007) pricing of the level of illiquidity. dejong & Driessen (2007), Lin, Wang & Wu (2011) pricing liquidity risk.

4 Liquidity and Treasury securities yields 1) Amihud-Mendelson (JF 1991): Treasury bills and Treasury notes with the same (short) maturity: Risk is the same. Bills are more liquid than bonds, bills have lower yield than notes. 2) On-the-run bonds are more liquid than off-the-run bonds, and have lower yield. Liquidity costs and corporate bond yields Yield spreads are known to exceed the expected cost of default, given data on default probability and recovery rate. The excess yield compensates for both risk and illiquidity. Lower rating lower liquidity (higher bid-ask spread and other measures of illiquidity) higher illiquidity premium. Chen, Lesmond & Wei (JF 2007) estimate the effect of the level of trading costs on the cross-section of bond yields, controlling for bond and firm characteristics, such as rating, leverage, risk. Results: Trading costs have a positive and highly significant effect on yield spread. Estimating the effect of Liquidity Risk on bond returns (current paper) R j,t = a j + β T,j TERM t + β D,j DEF t + β SI,j Silliq t + β BI,j Billiq t+ e j,t, R j, t = excess return on bond portfolio (over 30-day T-Bill rate) TERM t : Long-term govt (30yr) minus 30-day T-Bill return DEF t : Eq-wtd returns of all corporate bonds (maturity > 1 yr) average return on 1-yr and 30-yr govt bonds Silliq t, Billiq t : Innovations in stock and Treasury bond illiquidity (from AR(2) and AR(3) models). Research questions: Market liquidity changes over time. We study liquidity risk, the exposure of bond prices to liquidity shocks (the returns-liquidity shocks covariance). - Does the liquidity risk change over time? (risk in liquidity risk) - Is this change different for different rating classes of bonds? - Is the liquidity risk conditional? - If so is there an economic identification of changes in liquidity risk? A two-step approach: 1) Statistical analysis: Test for a pattern in changes over time in liquidity risk 2) If there is a pattern of such a change identify its economic determinants.

5 Related models and theories: Brunnermeier and Pedersen (2009): market liquidity can be adversely affected by funding liquidity. Because of margin constraints, a negative value shock causes a liquidity shock because of correlated liquidations. This lowers asset values and exacerbates the effect of the shock. He and Krishnamurthy (2010): Households invest through intermediaries. A negative wealth shock makes them allocate money away from risky to riskless assets, lowering intermediaries wealth and causing capital constraints and forced liquidation. Firm s policy-related model: Focus on incentives and endogenized constraint: Acharya and Viswanathan (2011): Adverse value shock affect financial firms\intermediaries greater firm s leverage incentive of firm s managers to risk-shift greater constraint on outside funding (rolling over debt) worsening funding liquidity need of firm to de-lever sale of assets worsening liquidity. This in turns affects asset prices. Sample period: , months. Bond data are from Lehman Fixed Income Database (Warga, 1998) for , and Merrill Lynch corporate bond index database (Schafer & Strebulaev, 2008) thereafter, incl Corporate bonds are largely held in institutional portfolios rather than in retail ones. Studying their return-liquidity relations is an appropriate setting to identify these liquidity effects. Returns are calculated from monthly prices and accrued interest. - We use actual prices, no matrix pricing. Bonds with no options (call, sinking funds). Excluded: bonds not in Lehman or Merrill indexes; with maturity < 1 year; not rated; non-identical S&P\Moody s rating; special features (call, sinking funds, floating rate). - Average # bonds in each month: 2,234 (between 245 and 9,286). - We construct indices of bond returns, VW, by rating class.

6 Illiquidity innovations Equity-market illiquidity: Amihud s (2002) ILLIQ, the equally-weighted monthly average of daily return /dollar volume, as modified by Acharya and Pedersen (2005). ILLIQ measures price impact, related to Kyle s (1985) λ. Stock illiq innovations Treasury bond market illiquidity: the monthly quoted % bid-ask spread of short maturity on-the-run treasuries (source: Goyenko (2006)). Was used by Longstaff, Mithal, Neis (2004), dejong and Driessen (2009). The innovations are residuals from an autoregressive model, AR(3) for stocks and AR(2) for bonds. The coefficients are adjusted for finite sample by Shaman and Stine s (1989) method. Bond illiq innovations Unconditional liquidity risk (red=significant) Coefficients Rating α ß T (all signif.) ß D (all signif.) ß SI ß BI Adj-Rsq AAA AA A BBB BB (Junk) B CCC & below TERM DEFAULT SILLIQ DEF Silliq Billiq

7 Time-varying betas Estimate a Markov regime-switching model in a two-equation model, for Investment Grade (IG) and Junk (Jnk) Regime-switching analysis, Hamilton (1994) Time-varying betas Estimate a Markov regime-switching model Regime-Dependent Variance-Covariance Matrix (s t = 1,2): R IG, t = a IG + β IG,T TERM t + β IG, D DEF t + β IG,SI Silliq t + β IG,BI Billiq t +e IG, t R JNk, t =a IG + β JNK,T TERM t +β JNK, D DEF t + β JNK,SI Silliq t + β JNK,BI Billiq t + e JNK, t Markov switching probability for state transition: P(s t = 1 s t 1 = 1) = p P(s t = 2 s t 1 = 2) = q Liquidity betas change substantially between regimes Regime 1 Investment G t-stat Junk Grade t-stat Parameters Constant P 0.96 TERM q 0.93 DEF Silliq ρ St = Billiq ρ St = σ i Regime 2 Investment G t-stat Junk Grade t-stat Constant TERM DEF Silliq Billiq σ i Wald tests for differences in coefficients Chi-sq tests Numbers are p-values Between regime 1 and 2 Between IG and Junk Investment G Junk Regime 1 Regime 2 TERM & DEF Liquidity TERM DEF Silliq Billiq

8 Stress regime linked to recessions Probability of stress regime. Pairs of estimates: (1) OLS, with logit transformation of prob(regime 2) (2) Logit estimation, with dummy = 1 if prob(regime 2) > 0.70 Variables lagged (1) (2) (3) (4) (5) (6) (7) (8) Const *** -1.03*** -1.11*** -.70*** -2.69*** -1.40*** -1.92*** -1.06*** NBER Recession 5.88*** 2.62*** Stock-Watson Index -1.69*** -.76*** Prob (Recession) -Hamiliton 4.71*** 2.01*** Negative Market Return dummy Business Conditions Index 3.12*** 1.78*** -1.81*** -.93*** Paper-Bill Spread.01**.004** TED Spread.03***.01*** Obs. Adj R 2 / PsedoR 2 (%) Variables lagged (9) (10) (11) (12) (13) (14) Const *** -2.50*** -4.69*** -2.54*** -4.75*** -2.62*** NBER Recession 1.43* 1.20* Stock-Watson Index Prof(Recession)-Hamilton ** 1.32** 1.21** Negative Market Return * Business Conditions -0.99*** -0.47** -1.13*** -0.60** Index Paper-Bill Spread TED Spread.03*** 0.01*** 0.03*** 0.01*** EE measure year growth *** *** *** *** *** *** Equity Volatility 93.82*** 53.44*** 80.39*** 49.93*** 80.53*** 50.01*** Equity Volatility * EE measure year growth *** *** *** *** *** *** Obs. Adj / Pseudo R 2 (%) 28 Probability of Regime Out of sample predictions of the stress regime Dep. Var = 1 if the actual prob(regime 2) > 70%, from statistical model Predicted prob(regime 2) is rolling monthly estimate from the economic prediction model (14), we start with estimates from (1/2 the sample), and predict for Regime 2 (as per Regime Switching Model ) Constant -1.78*** (.24) Predicted prob(regime 2) 5.77*** (.94) Obs. 216 Pseudo R 2 (%) 27

9 Junk-IG Return Junk-IG Return DEF Return -(T-Bill Yld -Fed Funds) -(T-Bill Yld -Fed Funds) Short Junk-IG Medium Junk-IG Long (Junk-IG) (1) (2) (3) (4) (5) (6) (7) (8) Const *** 26.02*** ** 48.57*** 24.24*** 28.43*** 24.13** Prob(Regime2) *** TERM -.07*** -.08*** *** -.47*** DEF.84***.77*** -.07** -.11**.55***.61***.62*** Silliq * ** * * Billiq ** 21.37** Prob(Regime 2)* TERM Prob(Regime 2)*DEF -.66*** -.67*** ** -.71*** -.82*** Prob(Regime 2)* Silliq Prob(Regime 2)* Billiq Obs. Adj R 2 (%) * ** * ** *** * ** 18 Flight to Liquidity Out-of-sample prediction of conditional bond returns for the financial crisis years, In each month, we calculate Prob(Regime 2) using our logit prediction model (column (14)). We calculate portfolio returns using the coefficients of each of the two regimes, conditional on the realized factors TERM, DEF, BILLIQ, SILLIQ for that month. Then, denoting p2 = Prob(Regime 2), Predicted return = (1-p2)*(predicted return using regime 1 coefficients) + p2*(predicted return using regime 2 coefficients) Predicting investment grade bond returns in Predicting junk bond returns in Actual Bond returns (bps) Actual Bond Returns vs. Predicted Bond Returns Investment Grade, Year RMSE (45 degree line) = RMSE (regression) = Actual = 0.84 Predicted t-stat (8.58) (0.11) R-Squared = 77% Regime Switching Model Prediction (bps) Data source: Regime Switching Model, Table 3 11 Actual Bond returns (bps) Actual Bond Returns vs. Predicted Bond Returns Junk Grade, Year RMSE (45 degree line) = RMSE (regression) = Actual = 0.86 Predicted t-stat (8.44) (0.77) R-Squared = 76% Regime Switching Model Prediction (bps) Data source: Regime Switching Model, Table 3

10 Out-of-sample predictions during the financial crisis Predicted value use estimated prob(regime 2) from the logit model, using the economic time series, the estimated coefficients of each regime and the current values of TERM, DEF, BILLIQ, SILLIQ (SE in parentheses) Dependent variable: Actual IG Returns Actual Junk Returns Constant 4.65 (42.93) (66.82) Predicted cond. IG return (0.098) Predicted cond. Junk return (0.102) R-sqr (%) p-value of F-test if slope = Obs The effects on stocks, classified by Book/Market Fama and French (1995): Firms with high BE/ME tend to be persistently distressed. They have low ratios of earnings to book equity for at least 11 years around portfolio formation. Conversely, low BE/ME is associated with sustained strong profitability. Recent studies (e.g., Chen, Noe & Tice, 2009) confirm that. We replicate the analysis for the high and low BE/ME quintiles. High and low BE/ME are taking the role of junk bonds and IG bonds, respectively. Liquidity betas change substantially between regimes Regime 1 Low BM t-stat High BM t-stat Parameters Constant P 0.96 Rm- Rf q 0.90 TERM DEF ρ St = Silliq ρ St = Billiq σ i Regime 2 Low BM t-stat High BM t-stat Constant Rm - Rf TERM DEF Silliq Billiq σ i Wald tests for differences in coefficients Chi-sq tests Numbers are p-values Between regime 1 and 2 Between High & Low BM Low BM High BM Regime 1 Regime 2 Rm-Rf TERM DEF Silliq Billiq

11 Probability of stress regime obtained from stock return estimates as a function of macroeconomic variables (1) OLS, with logit transformation of prob(regime 2) (2) Logit estimation, with dummy=1 if prob(regime 2) > 0.7 Variables lagged (1) (2) (3) (4) (5) (6) (7) (8) NBER Recession 2.73***.84*** Stock-Watson Index -1.09*** -.59*** Prob (Recession) -Hamiliton 3.48*** 1.62*** Negative Market Return Business Conditions Index 1.50*** *** -.61*** Paper-Bill Spread TED Spread.009*.001 Obs. Adj R 2 / PsedoR 2 (%) Variables lagged (9) (10) (11) (12) (13) (14) NBER Recession * Stock-Watson Index ** * Prof(Recession)- 1.91*** 1.06** 1.84***.89* Hamilton Negative Market Return Business Conditions Index Paper-Bill Spread TED Spread.01*** ***.004 EE measure yr growth ** *** *** *** *** *** Equity Volatility 62.53*** 36.41*** 55.85*** 36.99*** 55.81*** 36.21*** Equity Volatility t-1 *EE measure year growth *** *** ** *** ** * *** Obs. Adj / Pseudo R 2 (%) Probability of Regime 2 obtained from stock return estimates HMLDEF, returns on high-low default risk Stocks are classified into high and low default risk portfolios using Altman s (1968) Z-score as modified by Hillegeist et al. (2004). Z = Const *wcta *reta -0.1*ebitta -0.22*mvliab *sata. wcta = working capital / total assets. reta = retained earning / total assets. ebitta = earnings before interest and taxes/ total assets. mvliab = market value of equity / total liabilities. sata = sales / total assets. Portfolio construction: Every months, stocks are classified into a 5x5 matrix: 5 quintiles by daily return volatility, then into 5 quintiles by the modified Z-score. Each portfolio return is value-weighted. The return on low (high) default risk portfolio is the average return on the five stock quintiles with the highest (lowest) Z score. This lowers the effect of volatility on the default risk-return relation. Campbell et al. (2008): Corr (default risk, return volatility) > 0, Ang et al. (2006): volatility has negative effect on stock expected return. (This methodology follows Fama and French (1993) in neutralizing the effect of book-to-market effect from the size effect in portfolio construction.)

12 Relating HML to HMLDEF Regime 1 Regime 2 Coefficient t-stat Coefficiet t-stat Parameters Constant P HMLDEF q Silliq Billiq σ i Wald tests for differences in coefficients Chi-Sq p-value Constant HMLDEF Silliq Billiq Conclusion: Our paper -Focused on conditional liquidity risk of corporate bonds, which can be explained by economic factors associated with economic stress. -Shows evidence for time-varying liquidity betas for both Investment Grade and Junk bonds. -Shows that in times of stress, the effect of liquidity shocks on IG and Junk bonds takes opposite directions, consistent with flight to liquidity. The effects are similar for stocks classified by their BE/ME, related to likelihood of default.