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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

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    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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    File URL: http://hdl.handle.net/10.1007/s10260-012-0198-z
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    Bibliographic Info

    Article provided by Springer in its journal Statistical Methods & Applications.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (November)
    Pages: 517-537

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    Handle: RePEc:spr:stmapp:v:21:y:2012:i:4:p:517-537

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    Related research

    Keywords: Financial performance measures; Stationary and ergodic process; Central limit theorem for dependent data; Newey–West estimator;

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    3. 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, 09.
    4. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
    5. 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.
    6. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
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