Efficient Portfolios and Extreme Risks: A Pareto-Dirichlet Approach

Annals of Operations Research, forthcoming

39 Pages Posted: 21 May 2019 Last revised: 19 Sep 2023

See all articles by Olivier Le Courtois

Olivier Le Courtois

EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control

Xia Xu

ESSCA School of Management

Date Written: March 12, 2019

Abstract

This paper solves the mean variance skewness kurtosis (MVSK) portfolio optimization
problem by proposing a general Pareto-Dirichlet method. We approximate the
feasible portfolio set with calibrated Dirichlet distribution, and a portfolio is MVSK efficient
if its profile of the first four moments is not dominated by any other portfolio. Compared to
existing higher order portfolio optimization methods, our Pareto-Dirichlet approach provides
a practical solution to MVSK efficient frontier adjusting for the estimation uncertainties of
preference parameters and return moments. Specifically, the previous methods are designed
to determine if one specific portfolio is efficient or not, and they can misclassify inefficient
portfolios as efficient. Using them for MVSK efficient frontier construction has implemental
difficulties, while the Pareto-Dirichlet method is particularly suitable for this goal. We
illustrate our approach with Fama-French 30 Industry Portfolios. Our study also compares
the results of the MVSK program to the results from the mean variance (MV) and mean
variance skewness (MVS) programs. To facilitate the optimal portfolio choice, we introduce
a generalized Sharpe ratio to synthesize the effect of the first four moments in ranking MVSK
efficient portfolios.

Keywords: Portfolio Selection, Efficient Portfolio, Extreme Risk, Dirichlet Distribution

JEL Classification: G11, D81, C63

Suggested Citation

Le Courtois, Olivier Arnaud and Xu, Xia, Efficient Portfolios and Extreme Risks: A Pareto-Dirichlet Approach (March 12, 2019). Annals of Operations Research, forthcoming, Available at SSRN: https://ssrn.com/abstract=3376921 or http://dx.doi.org/10.2139/ssrn.3376921

Olivier Arnaud Le Courtois

EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control ( email )

23, av. Guy de Collongue
69134 Ecully Cedex
France

Xia Xu (Contact Author)

ESSCA School of Management ( email )

1 avenue Lakanal
Angers, 49000
France

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