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
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: Suggested Citation