1. 1 Hedge Fund Tail Risk Tobias Adrian and Markus K. Brunnermeier Federal Reserve Bank of New York and Princeton University University of Arizona/Arizona State University September 27/28 th, 2007 The views expressed in this paper are those of the authors and do not necessarily represent those of the Federal Reserve Bank of New York or the Federal Reserve System

2. 2 Total Financial Assets as % of GDP

3. 3 Motivation Role of hedge funds: generate excess returns by  providing liquidity and bridging asynchronicities  providing market timing service  managing tail risk Co-movements across funds – spillover to banking sector  Financial stability Central banks  Counterparty credit risk managementBrokers and banks  Portfolio management Fund-of-Funds Hedge funds were key players in past financial crisis:  Asian financial crisis Global macro funds  LTCM crisis Fixed income arbitrage funds  GM downgrade Multi-strategy funds

4. 4 Overview 1.Quantile Regressions – A Refresher 2.Bivariate tail exceeds average dependence (CoVaR vs. VaR) 3.Risk factors that identify tail dependence 4.Incentives to offload tail dependence 5.Robustness 6.Related Literature

5. 5 Quantile Regressions – A Refresher OLS regression: min sum of squared residuals: Quantile regression: min weighted absolute values:

6. 6 Quantiles and Value-at-Risk Quantile regressions give an estimate of the quantile q of y as a linear function of x: where F -1 (q|x) is the inverse CDF conditional on x. So F -1 (q|x) = q% Value-at-Risk conditional on x. Note our sign convention!

7. 7 q-Sensitivity and CoVaR Return R i depends on return R j for quantile q: Definition: The q-sensitivity is  q which can be estimated using a quantile regression. Definition: We denote the CoVaR ij, the VaR of style i conditional on the (unconditional) VaR of style j by: Co since conditional measure captures contagion/comovement

8. 8

9. 9 Data Credit Swiss/Tremont Hedge Fund Strategies 1994/1-2007/08:  Hedge Fund index return  Returns of strategies  Advantage: Indexes capture large funds  Caveat: Survivorship bias, backfilling bias We check for robustness using other data sources Returns of Investment Banks, Commercial Banks, and Insurance Companies (from CRSP)

10. 10 Summary Statistics of Excess Returns

11. 11 Result 1a: CoVaRs > VaR

12. 12 Result 1b: 50%-sensitivities < 5 % sensitivities For hedge funds  Equally weighted  Value weighted For other financial institutions

13. 13 Result 1c: HF-VaR predicts I-Bank’s-VaR Quantile Granger Causality

14. 14 Overview 1.Quantile Regressions – A Refresher 2.Bivariate tail exceeds average dependence (CoVaR vs. VaR) 3.Risk factors that identify tail dependence 4.Incentives to offload tail dependence 5.Robustness 6.Related Literature

15. 15 6-Risk Factor Pricing Model Factors: Interpretation:  Repo - 3 Month Treasury : “Flight to Quality”  10 Year - 3 Month Treasury Return: “Business Cycle”  Moody's BAA - 10 Year Treasury Return: “Credit Indicator”  CRSP Market Excess Return: “Equity Market Risk”  VIX Straddle Excess Return: “Volatility Exposure”  Variance Swap Return: “Variation in Price of Risk”

16. 16 Offloaded Returns All factors are excess returns  We can offload systematic risk  Study CoVaR and q-dependence of offloaded returns 2 ways of offloading  Residual of 6-factor OLS regression  Residual of 6-factor 5%-quantile regression  Advantage of quantile regressions: Linearity allows portfolio choice interpretation! Focus on pricing errors after offloading risk-factors

17. 17 OLS Alphas of Offloaded Returns

18. 18 Result 2a: CoVaRs ~ VaRs for 5%-offloaded returns

19. 19 CoVaR > VaR for OLS-offloading

20. 20 Result 2b: Factors explain Increase in q-Sensitivities

21. 21 Incentives to hold Tail Risk Standard compensation (2 and 20)  20 % of profit (return, not alpha)  2 % from assets under management Flow-performance analysis  Reacts mostly to past returns, Sharpe ratio  Not much to alpha or information-ratio

22. 22 Result 3a: Hedging Tail Risk Lowers Returns

23. 23

24. 24

25. 25 Result 3b: Flows do Not React to Tail Risk

26. 26 Overview 1.Quantile Regressions – A Refresher 2.Bivariate tail exceeds average dependence (CoVaR vs. VaR) 3.Risk factors that identify tail dependence 4.Incentives to offload tail dependence 5.Robustness 6.Related Literature

27. 27 Robustness Analysis Alternative measure of sensitivities: GARCH covariances Alternative measure of tail risk: Expected Shortfall Other hedge fund indices: HFR and Altvest Other pricing factors

28. 28 q-Sensitivities measure dependence across states of the world

29. 29 Garch-covariances measure dependence over time

30. 30 Expected Shortfall ES Measures the average return below the Value-at-Risk The main result holds for Expected Shortfall

31. 31 Other Indices and Pricing Factors The main results go through with alternative hedge fund indices (HFR and Altvest) The key risk factors for tail risk is the Repo – Treasury spread, and the Volatiliy Swap.

32. 32 Related Literature Dependence / contagion: Boyson, Stahel, Stulz (2006), Chan, Getmansky, Haas, Lo (2006), Patton (2007), Adrian (2007) Hedge fund tail risk: Asness, Krail, Liew (2001), Agarwal & Naik (2004), Bali, Gokcan, Liang (2007), Liang & Park (2007), Bondarenko (2004) Pricing factors: Fung and Hsieh (2001, 2002, 2003), Hasanhodzic & Lo (2007) Finance applications of quantile regressions: Bassett and Chen (2001), Chernozhukov and Umantsev (2001)

33. 33 Summary Hedge funds have incentives to hold tail risk  Holding tail risk increases returns and flows do not react to tail risk There is spillover of tail risk among hedge funds and between hedge funds and banks (contemporaneous and lagged) The increase in CoVaR relative to VaR can be explained with liquid, tradable risk factors

34. 34 Future Research Focus on broader set of financial institutions Additional robustness checks: Autocorrelation, non-linear CoVaR, pricing factors Include out of the money option factor