Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets

Hiroshi Shiraishi and Masanobu Taniguchi
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Hiroshi Shiraishi: Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan, Postal: Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan
Masanobu Taniguchi: Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan, Postal: Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, Tokyo, Japan

Journal of Forecasting, 2008, vol. 27, issue 3, 193-215

Abstract: 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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:jof:jforec:v:27:y:2008:i:3:p:193-215

DOI: 10.1002/for.1053

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