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Higher order moments of the estimated tangency portfolio weights

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Abstract

In this paper we consider the estimated weights of tangency portfolio. The returns are assumed to be independently and multivariate normally distributed. We derive analytical expressions for the higher order non-central and central moments of these weights. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed-forms. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns of eight nancial indexes listed in NASDAQ stock exchange.

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  • Javed, Farrukh & Mazur, Stepan & Ngailo, Edward, 2017. "Higher order moments of the estimated tangency portfolio weights," Working Papers 2017:10, Örebro University, School of Business.
    • Handle: RePEc:hhs:oruesi:2017_010
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    1. Olha Bodnar, 2009. "Sequential Surveillance Of The Tangency Portfolio Weights," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 797-810.
    2. Taras Bodnar & Stepan Mazur & Nestor Parolya, 2019. "Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 636-660, June.
    3. Andrew G. Glen, 2017. "On the Inverse Gamma as a Survival Distribution," International Series in Operations Research & Management Science, in: Andrew G. Glen & Lawrence M. Leemis (ed.), Computational Probability Applications, chapter 2, pages 15-30, Springer.
    4. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    5. Okhrin, Yarema & Schmid, Wolfgang, 2006. "Distributional properties of portfolio weights," Journal of Econometrics, Elsevier, vol. 134(1), pages 235-256, September.
    6. Mark Britten‐Jones, 1999. "The Sampling Error in Estimates of Mean‐Variance Efficient Portfolio Weights," Journal of Finance, American Finance Association, vol. 54(2), pages 655-671, April.
    7. Taras Bodnar & Yarema Okhrin, 2011. "On the Product of Inverse Wishart and Normal Distributions with Applications to Discriminant Analysis and Portfolio Theory," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 311-331, June.
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    Cited by:

    1. Mårten Gulliksson & Stepan Mazur, 2020. "An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 773-794, December.

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    More about this item

    Keywords

    Tangency portfolio; higher order moments; Wishart distribution;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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