Quantifying Tail Risk in Hedge Funds

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)