A Shorter-Length Confidence-Interval Estimator (CIE) for Sharpe-Ratio Using a Multiplier k* to the Usual Bootstrap-Resample CIE and Computational Intelligence

by Chandra Shekhar Bhatnagar, Ashok Sahai, and Viswanadham Bulusu, .

Abstract: The population value of the Sharpe (1966) performance measure for portfolio i is defined as for i = 1, 2,..., n. It is simply the mean excess return over the standard deviation of the excess returns for the portfolio. The sample estimate of any of these portfolio measures is challenging not only because of the dynamic nature of this measure but also because of the statistical estimation issue involved therein. This paper has been motivated by the desire to meet the challenge of statistical estimation. A new estimator for Sharpe’s ratio is formulated using the optimal value defined as k*, which is used as a multiplier for the usual sample-counterpart estimator. This formulation has been pivotal to an efficient Confidence-Interval estimator (CIE). ‘Computational Intelligence’ has been deployed for the optimal mixing [using the optimal value of a design parameter, ?] of the proposed estimator and usual sample-counterpart estimator with the aim of achieving the shortest length of the proposed bootstrap-resample Confidence-Interval estimator (PBCIE) for Sharpe’s ratio. We have been successful in achieving a shorter length through the proposed Bootstrap-resample Confidence Interval Estimator [PBCIE] for Sharpe’s ratio vis-à-vis the Usual Bootstrap-resample Confidence Interval Estimator [UBCIE], without paying the usual cost in terms of a greater ‘Coverage Error’. An empirical simulation study has been used to bring forth the potential gain through a more efficient estimation in the context, with the limitation of the normal distribution being followed by the population for the portfolios. The empirical simulation study is modeled around the values of parameters in the study by Vinod and Morey (1999)

Key Words: Bootstrap resampling; Computational intelligence; Coverage error & the length of the confidence interval estimation; Empirical simulation study

Chandra Shekhar Bhatnagar, Chandrashekhar.Bhatnagar@sta.uwi.edu
Ashok Sahai, sahai.ashok@gmail.com
Viswanadham Bulusu, viswanadhambulusu1970@gmail.com

Editor: Ahmed H. Youssef,ahyoussef@hotmail.com

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