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Hedge Fund Tail Risk

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.

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Hedge Fund Tail Risk

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  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 27/28th, 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. Total Financial Assets as % of GDP

  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 management Brokers 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. Overview • Quantile Regressions – A Refresher • Bivariate tail exceeds average dependence (CoVaR vs. VaR) • Risk factors that identify tail dependence • Incentives to offload tail dependence • Robustness • Related Literature

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

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

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

  8. 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)

  9. Summary Statistics of Excess Returns

  10. Result 1a: CoVaRs > VaR

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

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

  13. Overview • Quantile Regressions – A Refresher • Bivariate tail exceeds average dependence (CoVaR vs. VaR) • Risk factors that identify tail dependence • Incentives to offload tail dependence • Robustness • Related Literature

  14. 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”

  15. 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

  16. OLS Alphas of Offloaded Returns

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

  18. CoVaR > VaR for OLS-offloading

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

  20. 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

  21. Result 3a: Hedging Tail Risk Lowers Returns

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

  23. Overview • Quantile Regressions – A Refresher • Bivariate tail exceeds average dependence (CoVaR vs. VaR) • Risk factors that identify tail dependence • Incentives to offload tail dependence • Robustness • Related Literature

  24. 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

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

  26. Garch-covariances measure dependence over time

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

  28. 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.

  29. 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)

  30. 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

  31. 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

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