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

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  • Hiroshi Shiraishi

    (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)

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    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.

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    File URL: http://hdl.handle.net/10.1002/for.1053
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    Bibliographic Info

    Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

    Volume (Year): 27 (2008)
    Issue (Month): 3 ()
    Pages: 193-215

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    Handle: RePEc:jof:jforec:v:27:y:2008:i:3:p:193-215

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    Web page: http://www3.interscience.wiley.com/cgi-bin/jhome/2966

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