# A test for the equality of multiple Sharpe ratios

## John Alexander Wright, Sheung Chi Phillip Yam and Siu Pang Yung

#### Abstract

ABSTRACT

This paper provides a test for the equality of multiple Sharpe ratios. First we extend the multivariate Sharpe ratio statistic of Leung and Wong for the case when excess returns are independently and identically distributed. We then provide a test that holds under the much more general assumption that the excess returns are stationary and ergodic, making use of the generalized method of moments and heteroscedasticity and autocorrelation consistent estimation of covariance matrixes. We repeat Leung and Wong's testing for equality of the Sharpe ratios of 18 iShares using our new tests and conclude that the hypothesis of equality cannot be rejected at the 1% level.