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Better portfolios with higher moments

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  • Jarrod Wilcox

    (Wealthmate, Inc.)

Abstract

A toolset beyond mean–variance portfolio optimization is appropriate for those instances where higher return moments might need to be taken into account, either for individual decisions or for pricing studies. Maximizing expected log surplus utility is superior for compounding returns in excess of financial obligations. Here, it is matched with a more flexible scenario representation of the investor’s joint probability distribution of returns and with an agnostic optimization engine. We show simple examples based on extrapolating historical stock and bond returns and then extended using hypothetical option prices. We clarify how Black–Scholes implied volatility anomalies can arise in a portfolio context.

Suggested Citation

  • Jarrod Wilcox, 2020. "Better portfolios with higher moments," Journal of Asset Management, Palgrave Macmillan, vol. 21(7), pages 569-580, December.
    • Handle: RePEc:pal:assmgt:v:21:y:2020:i:7:d:10.1057_s41260-020-00170-5
    DOI: 10.1057/s41260-020-00170-5
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    References listed on IDEAS

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    1. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. "Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    2. Rubinstein, Mark, 1976. "The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets," Journal of Finance, American Finance Association, vol. 31(2), pages 551-571, May.
    3. Hakansson, Nils H, 1971. "Multi-Period Mean-Variance Analysis: Toward A General Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 26(4), pages 857-884, September.
    4. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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    Cited by:

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    2. Cui, Jinxin & Maghyereh, Aktham & Goh, Mark & Zou, Huiwen, 2022. "Risk spillovers and time-varying links between international oil and China’s commodity futures markets: Fresh evidence from the higher-order moments," Energy, Elsevier, vol. 238(PB).

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