Institute of Mathematical Statistics Lecture Notes - Monograph Series

Estimation errors of the Sharpe ratio for long-memory stochastic volatility models

Hwai-Chung Ho

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The Sharpe ratio, which is defined as the ratio of the excess expected return of an investment to its standard deviation, has been widely cited in the financial literature by researchers and practitioners. However, very little attention has been paid to the statistical properties of the estimation of the ratio. Lo (2002) derived the $\sqrt{n}$-normality of the ratio's estimation errors for returns which are iid or stationary with serial correlations, and pointed out that to make inference on the accuracy of the estimation, the serial correlation among the returns needs to be taken into account. In the present paper a class of time series models for returns is introduced to demonstrate that there exists a factor other than the serial correlation of the returns that dominates the asymptotic behavior of the Sharpe ratio statistics. The model under consideration is a linear process whose innovation sequence has summable coefficients and contains a latent volatility component which is long-memory. It is proved that the estimation errors of the ratio are asymptotically normal with a convergence rate slower than $\sqrt{n}$ and that the estimation deviation of the expected return makes no contribution to the limiting distribution.

Chapter information

Hwai-Chung Ho, Ching-Kang Ing, Tze Leung Lai, eds., Time Series and Related Topics: In Memory of Ching-Zong Wei (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 165-172

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Primary: 60G10: Stationary processes 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60F05: Central limit and other weak theorems

long memory stochastic volatility Sharpe ratio

Copyright © 2006, Institute of Mathematical Statistics


Ho, Hwai-Chung. Estimation errors of the Sharpe ratio for long-memory stochastic volatility models. Time Series and Related Topics, 165--172, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000001021.

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