Inference for the Difference of Two Independent KS Sharpe Ratios under Lognormal Returns

J Qi,A Wong,M Rekkas,Dejian Lai

doi:10.1155/2020/6751574

Abstract

A higher-order likelihood-based asymptotic method to obtain inference for the difference between two KS Sharpe ratios when gross returns of an investment are assumed to be lognormally distributed is proposed. Theoretically, our proposed method has O n − 3 / 2 distributional accuracy, whereas conventional methods for inference have O n − 1 / 2 distributional accuracy. Using an example, we show how discordant confidence interval results can be depending on the methodology used. We are able to demonstrate the accuracy of our proposed method through simulation studies.

Highlights

Let Pt be the price of an investment at time t, and assume this investment does not pay out dividends. e net return Rt, of this investment between time t − 1 and time t is given as
We propose to use a higher-order likelihood-based asymptotic method to obtain inference for the difference between two independent KS Sharpe ratios. e proposed method provides an important indicator to practitioners who are interested in comparing the performance of two assets
Accuracy is important as sample sizes can be limited in practice. e proposed method is straightforward and easy to use in practice. e methodology can be applied to obtain inference for the ratio of two independent KS Sharpe ratios

Summary

Introduction

Let Pt be the price of an investment at time t, and assume this investment does not pay out dividends. e net return Rt, of this investment between time t − 1 and time t is given as. When data are given in terms of relative prices rather than returns, Knight and Satchell [2] propose the following extension to the Sharpe ratio: KS 􏽱E g t􏼁. It is common to assume that log returns (i.e., the rt) are identically and independently distributed as normal with mean μ and variance σ2. Liu et al [3] applied the standard likelihood method to obtain inference for the Sharpe ratio with independent data, and Ji et al [4] extended the methodology to obtain inference for this ratio with autocorrelated return data. We propose to use a higher-order likelihood-based asymptotic method to obtain inference for the difference between two independent KS Sharpe ratios. Accuracy is important as sample sizes can be limited in practice. e proposed method is straightforward and easy to use in practice. e methodology can be applied to obtain inference for the ratio of two independent KS Sharpe ratios

Likelihood-Based Inference

Inference for the Difference of Two Independent KS Sharpe Ratios

Method

Findings

Conclusion