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Title: Testing for the Sharpe ratio under a family of GARCH models Authors:  Yifan Zhang - Renmin University of China (China) [presenting]
Zhenya Liu - Renmin University of China (China)
Shixuan Wang - University of Reading (United Kingdom)
Abstract: The asymptotic properties of the Sharpe ratio estimator under a family of GARCH models are investigated. For financial time series, especially asset return, the stylized facts of left-skewed distribution and heteroscedasticity are often observed. In such circumstances, the limit behavior of the Sharpe ratio estimator is derived for the general GARCH(1,1) return. Additionally, we develop a strongly consistent estimator for the obtained asymptotic variance. A zero Sharpe ratio $t$-type test is proposed based on the theoretical results. Simulation studies demonstrate that the test has a good finite-sample performance under several specific examples. We illustrate the test in applications to explore the cross-sectional distribution of managerial skills measured with the Sharpe ratio in U.S. mutual funds.