Portfolio Allocation with Skewness Risk: A Practical Guide

33 Pages Posted: 15 Jul 2018 Last revised: 8 Feb 2019

See all articles by Edmond Lezmi

Edmond Lezmi

Amundi Asset Management

Hassan Malongo

Amundi Asset Management; Université de Paris-Dauphine (Ceremade)

Thierry Roncalli

Amundi Asset Management; University of Evry

R Sobotka

Amundi Asset Management

Date Written: June 22, 2018

Abstract

In this article, we show how to take into account skewness risk in portfolio allocation. Until recently, this issue has been seen as a purely statistical problem, since skewness corresponds to the third statistical moment of a probability distribution. However, in finance, the concept of skewness is more related to extreme events that produce portfolio losses. More precisely, the skewness measures the outcome resulting from bad times and adverse scenarios in financial markets. Based on this interpretation of the skewness risk, we focus on two approaches that are closely connected. The first one is based on the Gaussian mixture model with two regimes: a normal regime and a turbulent regime. The second approach directly incorporates a stress scenario using jump-diffusion modeling. This second approach can be seen as a special case of the first approach. However, it has the advantage of being clearer and more in line with the experience of professionals in financial markets: skewness is due to negative jumps in asset prices. After presenting the mathematical framework, we analyze an investment portfolio that mixes risk premia, more specifically risk parity, momentum and carry strategies. We show that traditional portfolio management based on the volatility risk measure is biased and corresponds to a short-sighted approach to bad times. We then propose to replace the volatility risk measure by a skewness risk measure, which is calculated as an expected shortfall that incorporates a stress scenario. We conclude that constant-mix portfolios may be better adapted than actively managed portfolios, when the investment universe is composed of negatively skewed financial assets.

Keywords: Skewness, Volatility, Expected Shortfall, Stress Scenario, Market Regime, Drawdown, Risk Budgeting, Equal Risk Contribution, Gaussian Mixture Model, Jump-Diffusion Process

JEL Classification: C50, C60, G11

Suggested Citation

Lezmi, Edmond and Malongo, Hassan and Roncalli, Thierry and Sobotka, R, Portfolio Allocation with Skewness Risk: A Practical Guide (June 22, 2018). Available at SSRN: https://ssrn.com/abstract=3201319 or http://dx.doi.org/10.2139/ssrn.3201319

Edmond Lezmi

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Hassan Malongo

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

Université de Paris-Dauphine (Ceremade) ( email )

Place du Maréchal De Lattre De Tassigny
Paris, 75775
France

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

R Sobotka

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015
France

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