Robust portfolio estimation under skew-normal return processes

Masanobu Taniguchi, Alexandre Petkovic, Takehiro Kase, Thomas DiCiccio, Anna Clara Monti

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    2 Citations (Scopus)

    Abstract

    In this paper, we study issues related to the optimal portfolio estimators and the local asymptotic normality (LAN) of the return process under the assumption that the return process has an infinite moving average (MA) (∞) representation with skew-normal innovations. The paper consists of two parts. In the first part, we discuss the influence of the skewness parameter δ of the skew-normal distribution on the optimal portfolio estimators. Based on the asymptotic distribution of the portfolio estimator ĝ for a non-Gaussian dependent return process, we evaluate the influence of δ on the asymptotic variance V(δ) of ĝ. We also investigate the robustness of the estimators of a standard optimal portfolio via numerical computations. In the second part of the paper, we assume that the MA coefficients and the mean vector of the return process depend on a lower-dimensional set of parameters. Based on this assumption, we discuss the LAN property of the return's distribution when the innovations follow a skew-normal law. The influence of δ on the central sequence of LAN is evaluated both theoretically and numerically.

    Original languageEnglish
    Pages (from-to)1091-1112
    Number of pages22
    JournalEuropean Journal of Finance
    Volume21
    Issue number13-14
    DOIs
    Publication statusPublished - 2015 Nov 14

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    Keywords

    • linear process
    • optimal portfolio
    • robust portfolio
    • skew-normal law

    ASJC Scopus subject areas

    • Economics, Econometrics and Finance (miscellaneous)

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