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

Hiroshi Shiraishi, Masanobu Taniguchi

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)193-215
Number of pages23
JournalJournal of Forecasting
Volume27
Issue number3
DOIs
Publication statusPublished - 2008 Apr 1
Externally publishedYes

Keywords

  • Asymptotic efficiency
  • Non-Gaussian linear process
  • Optimal portfolio
  • Prediction error
  • Return process
  • Spectral density

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research

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