Efficient Portfolios and Extreme Risks: An Extended Dirichlet Approach

26 Pages Posted: 21 May 2019 Last revised: 23 Nov 2020

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 using a new approach based on the Dirichlet distribution. To obtain efficient portfolios,
we generalize the Dirichlet distribution using the student copula to produce an increased
proportion of portfolios concentrated on a subset of the index. We illustrate our approach
using the forty stocks of the French index. Our study also compares MVSK efficient portfolios
with the efficient portfolios that are obtained in a reduced three-dimensional setting, such as
a mean-variance-skewness or mean-variance-kurtosis setting. To incorporate the preferences
of decision-makers and to determine an optimal portfolio within the efficient set, we introduce
and illustrate a new indicator called the generalized Sharpe ratio that groups variance,
skewness, and kurtosis into a single quantity.

Keywords: Portfolio Choice, Efficient Frontier, Extreme Risk, Dirichlet Distribution

JEL Classification: G11, D81, C63

Suggested Citation

Le Courtois, Olivier Arnaud and Xu, Xia, Efficient Portfolios and Extreme Risks: An Extended Dirichlet Approach (March 12, 2019). 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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
62
Abstract Views
463
rank
420,474
PlumX Metrics