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Higher order moments of the estimated tangency portfolio weights

Author

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  • Farrukh Javed
  • Stepan Mazur
  • Edward Ngailo

Abstract

In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order non-central and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments.

Suggested Citation

  • Farrukh Javed & Stepan Mazur & Edward Ngailo, 2021. "Higher order moments of the estimated tangency portfolio weights," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(3), pages 517-535, February.
    • Handle: RePEc:taf:japsta:v:48:y:2021:i:3:p:517-535
    DOI: 10.1080/02664763.2020.1736523
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    Citations

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    Cited by:

    1. Javed, Farrukh & Mazur, Stepan & Thorsén, Erik, 2021. "Tangency portfolio weights under a skew-normal model in small and large dimensions," Working Papers 2021:13, Örebro University, School of Business.
    2. Drin, Svitlana & Mazur, Stepan & Muhinyuza, Stanislas, 2023. "A test on the location of tangency portfolio for small sample size and singular covariance matrix," Working Papers 2023:11, Örebro University, School of Business.
    3. Wang, Chou-Wen & Liu, Kai & Li, Bin & Tan, Ken Seng, 2022. "Portfolio optimization under multivariate affine generalized hyperbolic distributions," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 49-66.
    4. Gulliksson, Mårten & Oleynik, Anna & Mazur, Stepan, 2021. "Portfolio Selection with a Rank-deficient Covariance Matrix," Working Papers 2021:12, Örebro University, School of Business.
    5. Lassance, Nathan & Vanderveken, Rodolphe & Vrins, Frédéric, 2022. "On the optimal combination of naive and mean-variance portfolio strategies," LIDAM Discussion Papers LFIN 2022006, Université catholique de Louvain, Louvain Finance (LFIN).

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