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Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice

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  • Athayde, Gustavo M. de
  • Flôres Junior, Renato Galvão

Abstract

Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.

Suggested Citation

  • Athayde, Gustavo M. de & Flôres Junior, Renato Galvão, 2001. "Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 434, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    • Handle: RePEc:fgv:epgewp:434
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    References listed on IDEAS

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    1. Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 107-122, June.
    2. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    3. Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
    4. Ingersoll, Jonathan, 1975. "Multidimensional Security Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 785-798, December.
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