Quantifying Tail Risk with Low-Frequency Data

31 Pages Posted: 16 May 2013 Last revised: 30 Jul 2015

See all articles by Mattia Landoni

Mattia Landoni

Southern Methodist University (SMU) - Finance Department

Ravi Sastry

University of Melbourne - Department of Finance

Date Written: September 5, 2013

Abstract

We document substantial practitioner interest in measures of the downside tail risk of hedge funds, such as maximum drawdown (MDD) and worst one-period loss, together with a general sentiment that volatility does not convey enough information about tail risk. We show that past observed extremes are inappropriate estimators of tail risk, and propose a better, parametric estimator that is simple to implement and needs only short return histories as input. In addition, we characterize the statistical properties of downside risk measures and show that they depend linearly on volatility. Together with evidence that tail shape does not change much across funds, this explains why extreme downside performance measures rank funds similarly to the Sharpe ratio. Finally, we note that using sample standard deviation to estimate volatility when returns have fat tails is problematic. We show that the same technique employed in the paper can be used to improve estimation of the Sharpe ratio and other measures based on volatility.

Keywords: hedge funds, maximum drawdown, tail risk, worst-case loss

JEL Classification: C58, G11, G23

Suggested Citation

Landoni, Mattia and Sastry, Ravi, Quantifying Tail Risk with Low-Frequency Data (September 5, 2013). 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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