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Reconciling mean-variance portfolio theory with non-Gaussian returns

Author

Listed:
  • Lassance, Nathan

    (Université catholique de Louvain, LIDAM/LFIN, Belgium)

Abstract

Mean-variance portfolio theory remains frequently used as an investment rationale because of its simplicity, its closed-form solution, and the availability of well-performing robust estimators. At the same time, it is also frequently rejected on the grounds that it ignores the higher moments of non-Gaussian returns. However, higher-moment portfolios are associated with many different objective functions, are numerically more complex, and exacerbate estimation risk. In this paper, we reconcile mean-variance portfolio theory with non-Gaussian returns by identifying, among all portfolios on the mean-variance efficient frontier, the one that optimizes a chosen higher-moment criterion. Numerical simulations and an empirical analysis show, for three higher-moment objective functions and adjusting for transaction costs, that the proposed portfolio strikes a favorable tradeoff between specification and estimation error. Specifically, in terms of out-of-sample Sharpe ratio and higher moments, it outperforms the global-optimal portfolio, and also the global-minimum-variance portfolio except when using monthly returns for which estimation error is more prominent.

Suggested Citation

  • Lassance, Nathan, 2021. "Reconciling mean-variance portfolio theory with non-Gaussian returns," LIDAM Reprints LFIN 2021013, Université catholique de Louvain, Louvain Finance (LFIN).
    • Handle: RePEc:ajf:louvlr:2021013
    Note: In: European Journal of Operational Research
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    Cited by:

    1. Khashanah, Khaldoun & Simaan, Majeed & Simaan, Yusif, 2022. "Do we need higher-order comoments to enhance mean-variance portfolios? Evidence from a simplified jump process," International Review of Financial Analysis, Elsevier, vol. 81(C).

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