In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study is performed in order to evaluate the minimum sample size for reaching a good coverage accuracy of the asymptotic confidence intervals
DE CAPITANI, L. (2012). Interval estimation for the Sharpe Ratio when returns are not i.i.d. with special emphasis on the GARCH(1,1) process with symmetric innovations. STATISTICAL METHODS & APPLICATIONS, 21(4), 517-537 [10.1007/s10260-012-0198-z].
Interval estimation for the Sharpe Ratio when returns are not i.i.d. with special emphasis on the GARCH(1,1) process with symmetric innovations
DE CAPITANI, LUCIO
2012
Abstract
In this paper, assuming that returns follows a stationary and ergodic stochastic process, the asymptotic distribution of the natural estimator of the Sharpe Ratio is explicitly given. This distribution is used in order to define an approximated confidence interval for the Sharpe ratio. Particular attention is devoted to the case of the GARCH(1,1) process. In this latter case, a simulation study is performed in order to evaluate the minimum sample size for reaching a good coverage accuracy of the asymptotic confidence intervals
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