%0 Journal Article
%T Inference for the Sharpe Ratio Using a Likelihood-Based Approach
%A Ying Liu
%A Marie Rekkas
%A Augustine Wong
%J Journal of Probability and Statistics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/878561
%X The Sharpe ratio is the prominent risk-adjusted performance measure used by practitioners. Statistical testing of this ratio using its asymptotic distribution has lagged behind its use. In this paper, highly accurate likelihood analysis is applied for inference on the Sharpe ratio. Both the one- and two-sample problems are considered. The methodology has distributional accuracy and can be implemented using any parametric return distribution structure. Simulations are provided to demonstrate the method's superior accuracy over existing methods used for testing in the literature. 1. Introduction The measurement of fund performance is an integral part of investment analysis. Investments are often ranked and evaluated on the basis of their risk-adjusted returns. Several risk-adjusted performance measures are available to money managers of which the Sharpe ratio is the most popular. Introduced by William Sharpe in 1966 [1], this ratio provides a measure of a fund¡¯s excess returns relative to its volatility. Expressed in its usual form, the Sharpe ratio for an asset with an expected return given by and standard deviation given by is given by the following: where is the risk-free rate of return. From this expression, it is clear to see how this ratio provides a measure of a fund¡¯s excess return per unit of risk. The Sharpe ratio has been extensively studied in the literature. The main criticism leveled against this measure concerns its reliance on only the first two moments of the returns distribution. If investment returns are normally distributed then the Sharpe ratio can be justified. On the other hand, if returns are asymmetric then it can be argued that the measure may not accurately describe the fund¡¯s performance as moments reflecting skewness and kurtosis are not captured by the ratio. To address this issue, several measures exist in the literature which integrate higher moments into the performance measure. The Omega measure is one such measure that uses all the available information in the returns distribution. Keating and Shadwick [2] provide an introduction to this measure. While various methods are available, they are also more complex and often very difficult to implement in practice. To gauge the trade-off between the attractiveness of such measures and their cost, Eling and Schuhmacher [3] compared the Sharpe ratio with 12 other approaches to performance measurement. Eling and Schuhmacher [3] focussed on the returns of 2,763 hedge funds. Hedge funds are known to have return distributions which differ significantly from the normal distribution
%U http://www.hindawi.com/journals/jps/2012/878561/