Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets
This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector-valued non-Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ĝ for non-Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ĝ . First, it is shown that there are some cases when the asymptotic variance of ĝ under non-Gaussianity can be smaller than that under Gaussianity. The result shows that non-Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ĝ to be asymptotically efficient when the return process is Gaussian, which shows that ĝ is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g , which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one-step-ahead optimal portfolio return by the estimated portfolio based on ĝ and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.
Volume (Year): 27 (2008)
Issue (Month): 3 ()
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- Taniguchi, Masanobu & Puri, Madan L. & Kondo, Masao, 1996. "Nonparametric Approach for Non-Gaussian Vector Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 259-283, February.
- Jobson, J. D. & Korkie, Bob, 1989. "A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning, and Mean-Variance Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(02), pages 185-204, June.
- Basak, Gopal & Jagannathan, Ravi & Sun, Guoqiang, 2002. "A direct test for the mean variance efficiency of a portfolio," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1195-1215, July.
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