ALTERNATIVE METHODS FOR DERIVING STATISTICAL DISTRIBUTIONS OF SHARPE RATIO: REVIEW, COMPARISON, AND CRITIQUE

Lie-Jane Kao ； Cheng-Few Lee

《Advances in Quantitative Analysis of Finance and Accounting》 18期 (2021/12) Pp. 197-216

https://doi.org/10.6293/AQAFA.202112_(18).0007

摘要

This paper reviews three main distributional results of the estimated Sharpe ratio, including: (1) the exact non-central t and the asymptotic normal distribution under independently identically distribution (i.i.d.) normally distributed excess returns; (2) the asymptotic normal distribution under i.i.d. non-normally distributed excess returns; and (3) the asymptotic normal distribution under strictly-stationary-ergodic excess returns. Various statistical techniques are used to derive the asymptotic distributional results, including the central limit theorem and the generalized method of moment (GMM). This study further shows that either using the central limit theorem or GMM, a restrictive prerequisite that the 4th moment of the excess returns is finite, which excludes the often observed phenomena of fat-tailed excess returns, is required. Under such a condition, significant bias and sampling error could be associated with the estimated Sharpe ratio. A simulation study is given.

關鍵字

Central Limit Theorem ； Estimated Sharpe Ratio ； Fat-Tailed ； Generalized Method of Moment (GMM) ； Strictly-Stationary-Ergodic

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