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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

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  • Lucio De Capitani

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. Copyright Springer-Verlag 2012

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  • Lucio De Capitani, 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, Springer;Società Italiana di Statistica, vol. 21(4), pages 517-537, November.
    • Handle: RePEc:spr:stmapp:v:21:y:2012:i:4:p:517-537
    DOI: 10.1007/s10260-012-0198-z
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    6. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    7. Jobson, J D & Korkie, Bob M, 1981. "Performance Hypothesis Testing with the Sharpe and Treynor Measures," Journal of Finance, American Finance Association, vol. 36(4), pages 889-908, September.
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    Cited by:

    1. Lucio Capitani & Leo Pasquazzi, 2015. "Inference for performance measures for financial assets," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 73-98, April.

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