Quantifying Tail Risk in Hedge Funds

42 Pages Posted: 16 May 2013

See all articles by Mattia Landoni

Mattia Landoni

Southern Methodist University (SMU) - Finance Department

Ravi Sastry

University of Melbourne - Department of Finance

Date Written: February 21, 2020

Abstract

We evaluate popular measures of hedge fund tail risk such as maximum drawdown (MDD) and worst one-period loss, and prove theoretically that realized tail risk is a downward-biased estimator of true tail risk. The bias can be almost 100% using a reasonable calibration. That is, true tail risk can be twice as large as its conventional estimator (realized tail risk). Kelly and Jiang (2013) show that tail events are systematic rather than idiosyncratic, so tail risk cannot be eliminated via diversification. Accurate measurement of fund-level tail risk is therefore essential for loss-averse investors and redemption-averse asset managers. We propose a simple, efficient parametric estimator that needs only short return histories as input and predicts future tail event probabilities and magnitudes with surprising precision. Additionally, we note that using sample standard deviation to estimate volatility is also biased, as originally observed by Miller and Gehr (1978) who provide a correction when returns are normal. The same technique employed in this paper to estimate tail risk can be used to improve estimation of the Sharpe ratio and other measures based on volatility for any return distribution, and in particular when returns (or simply the tails) follow power laws (Gabaix et al., 2006).

Keywords: hedge funds, tail risk, worst-case loss, extreme value theory

JEL Classification: C58, G11, G23

Suggested Citation

Landoni, Mattia and Sastry, Ravi, Quantifying Tail Risk in Hedge Funds (February 21, 2020). Columbia Business School Research Paper No. 13-35. Available at SSRN: https://ssrn.com/abstract=2265691 or http://dx.doi.org/10.2139/ssrn.2265691

Mattia Landoni

Southern Methodist University (SMU) - Finance Department ( email )

United States

Ravi Sastry (Contact Author)

University of Melbourne - Department of Finance ( email )

Level 12
198 Berkeley Street
Victoria 3010
Australia

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