Estimated Sharpe ratio of asset returns with fat tails: theory and empirical evidence
本文推广了Lo(2002)的结果，允许资产收益分布存在厚尾（尾指数0<κ<4），发现估计的夏普比率有偏且收敛速度变慢，仅在收益有有限(4+ε)阶矩时无偏且正态，对ETF和共同基金的实证表明使用夏普比率比较投资绩效需谨慎。
Abstract This paper generalizes the results in Lo (2002) by allowing the distributions of asset returns exhibiting fat tails with the tail index 0 < κ < 4. We show that the asymptotic behavior of the estimated Sharpe ratio is biased and converges at a slower rate as 2< κ < 4. Therefore, the risk-return payoff information provided by the estimated Sharpe ratio can be misleading. It is also shown that the asymptotic unbiasedness and normality of the estimated Sharpe ratio can only be established as asset returns have a finite (4 + ε ) th moment with ε ≥ 0, i.e., κ > 4. Of particular interest are the cases as the tail index 2 < κ < 4, where the ex ante Sharpe ratio is well defined, and an inference method is developed. Empirical examples are used to illustrate the derived results, and an empirical study on major ETFs and mutual funds suggests caution in using the Sharpe ratio for comparing investment performance.