Liquidity Risk Premia in Corporate Bond Markets

1. Liquidity Risk Premia in Corporate Bond Markets Frank de Jong Joost Driessen INQUIRE Hamburg, March 2006

2. Motivation Two important puzzles in corporate bond markets • Time-series variation of credit spreads • Integration/segmentation of equity and corporate bond markets? • Level of credit spreads versus observed default rates • ‘Credit spread puzzle’

3. 1: Time-series variation in credit spreads • Credit spread changes correlated with many factors • Equity returns (Kwan, JFE 96) • Equity volatility (Collin-Dufresne, Goldstein, and Martin, JF 01, Campbell & Taksler, JF 03, Cremers, Driessen, Maenhout & Weinbaum, WP 05) • Other factors: interest rates, macro factors, … • But… CGM find evidence for a separate corporate bond factor • To what extent are equity and corporate bond markets integrated?

4. 2: Credit spread puzzle • Yield spreads on corporate bonds are far higher than justified by historical default losses • Especially serious for high-grade bonds, which hardly ever default • For example, long-term AA bonds: • Historical default loss generates credit spread of 3 basis points • Average credit spread of 67 basis points in our sample

5. 2: Credit spread puzzle • Recent attempts to explain this puzzle have had mixed success • Taxes (Elton, Gruber, Agrawal & Mann, JF 01) • Debated (Amato & Remolona, WP 04) • We find similar results for Europe where tax effect is not present • Exposure to priced market risk factors • Equity risk premium (Elton, Gruber, Agrawal & Mann, JF 01) • Jump risk premium (Collin-Dufresne, Goldstein & Helwege, WP 05, and Driessen, RFS 05)

6. This paper • Do liquidity shocks in equity and government bond market spill over to corporate bond market? • Can premia on liquidity risk explain part of the credit spread puzzle?

7. Liquidity • Recent literature in asset pricing stresses the role of liquidity for asset prices • Amihud-Mendelson (1986) show that high transaction costs (low liquidity) must be compensated by higher expected returns • Evidence to support this theory is quite strong, both from equity and treasury bond markets • Recent developments to treat liquidity also as a priced risk factor

8. Liquidity risk • Hasbrouck-Seppi (2001) and Chordia et al. (2003) document commonality in liquidity • liquidity of individual stocks correlated with market-wide liquidity movements • Acharya and Pedersen (2004) and Pastor and Stambaugh (2004) add exposure to equity market liquidity shocks to a multifactor pricing model • They also include the three Fama-French factors (market, size and book-to-market ratio)

9. Evidence on liquidity risk premium • Acharya and Pedersen estimate an expected liquidity premium of 3.5% and a liquidity risk premium of 1.1% • Pastor and Stambaugh estimate 7.5% liquidity risk premium • Don’t include expected liquidity premium in the model • No research yet on pricing of liquidity risk for treasury or corporate bonds • Some exploratory research of effect of (expected) liquidity on spreads (Houweling, Mentink, Vorst, JBF 05) • Good testing ground for pricing models, though, as expected returns are easy to measure by yields (corrected for default losses) • Recent independent work by Chacko (WP, 05) and Chen, Cheng, and Wu (WP 05)

10. Remainder of presentation • Corporate bond data • Liquidity measures • Model • Results for US market • Results for European market

11. Data: Corporate bond returns • Lehman corporate bond returns, US, Jan 93-Feb 02 • Index level data, by rating class and maturity • AAA…CCC ratings; intermediate and long maturities • Construct expected returns by correcting yields for expected default and recovery rates E[rtT] = [πD(1-L) + (1- πD)](1+Yg+S)T –1

12. Historical default rates (85-03)

14. Expected corporate bond returns

15. Data (2) • Liquidity measures • Bid-ask spread for 10 year US T-bond from Fleming (2003) • ILLIQ for stocks (Datastream)

17. Liquidity measure for equity market • Intra-day data would be ideal to measure liquidity • But hard to obtain for long sample period • Hasbrouck (2001) shows that Amihud’s ILLIQ measure is a reasonable proxy when using daily data • ILLIQ measures slope of price/volume relation • Based on daily data of prices and volume • Ratio of absolute price return divided by volume, averaged over one month • Calculated for all S&P1500 stocks and averaged over cross-section to get market-wide liquidity measure

19. Model • APT style multifactor model • Equity market return, ILLIQ, Govt bond BAS • Implied equity volatility (VIX) turns out not to matter • Two-step regression approach Rit = ai + BiFt + bLi ΔLt + eit E[Ri] = Bi λF + bL λL • Equity risk premium fixed at several values • Hard to estimate, fix at 2% - 8%

20. Empirical results • Corporate bond returns have significant exposures to market and liquidity factors • Low ratings and long maturities are more exposed • Liquitity beta’s enter significantly in asset pricing equation • ILLIQ is significant by itself but looses significance when Govt bond BAS is included • Additional liquidity premium goes a long way in explaining credit spread puzzle • Only for high grade bonds, credit spreads remain too high • This can be solved by including tax effects

23. 4% equity risk premium

24. Equity risk premium estimated at 2.52%

25. 4% equity risk premium and tax effect

26. Results for European corporate bonds • Repeat analysis, now applied to European data • Euro-denominated corporate bond indices (Lehman) • 2000-2004 sample • Mainly focus on time series exposures • Hard to estimate risk premia using short sample

30. Conclusions • We explain part of credit spread puzzle by including liquidity as a priced risk factor • Most successful for long term and low-grade corporate bonds • Jumps may be necessary to explain short-term spreads • Corporate bond returns exposed to both equity and treasury bond market liquidity • Both priced, but quite strongly correlated in cross-section • Similar results for European bond market data