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

Author

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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)

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.

Suggested Citation

  • Hiroshi Shiraishi & Masanobu Taniguchi, 2008. "Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 193-215.
    • Handle: RePEc:jof:jforec:v:27:y:2008:i:3:p:193-215
    DOI: 10.1002/for.1053
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    References listed on IDEAS

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    1. Yoshihide Kakizawa, 1999. "Note on the Asymptotic Efficiency of Sample Covariances in Gaussian Vector Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 551-558, September.
    2. Yoshihide Kakizawa & Masanobu Taniguchi, 1994. "Asymptotic Efficiency Of The Sample Covariances In A Gaussian Stationary Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 303-311, May.
    3. 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(2), pages 185-204, June.
    4. 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.
    5. 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.
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    Cited by:

    1. Shiraishi, Hiroshi & Taniguchi, Masanobu & Yamashita, Takashi, 2018. "Higher-order asymptotic theory of shrinkage estimation for general statistical models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 198-211.

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