Nearly Unbiased Estimation of Sample Skewness

Abstract

In this paper we examine the finite sample bias of sample skewness estimator for financial returns. We show that the bias of conventional sample skewness comes from two sources: the covariance between past return and future volatility, known as the leverage effect, and the covariance between past volatility and future return, commonly referred to as the volatility feedback effect. We derive explicit expressions for this bias and propose a nearly unbiased skewness estimator under mild assumptions. Our simulation study shows that the proposed estimator leads to almost unbiased skewness estimates with a sightly elevated mean squared error, and can reduce the bias of the skewness coefficient estimates by 40%. In our empirical application, we find that bias-corrected average skewness can better predict future market returns comparing to the case without bias-correction. This leads to an improved performance of skewness-based portfolios in terms of Sharpe ratio, certainty equivalence and transaction cost.

Keywords: Skewness, bias, return predictability

JEL Classification: C13, C22.