Portfolio Construction for Practitioners: Sizing Strategies with Skewed Returns

Abstract

Mean-variance optimization (MVO) is a popular framework for portfolio allocation due to its tractability and intuitive concept. However, MVO has several pitfalls; in particular, it does not take into account characteristics of the strategies' returns beyond their means and volatilities/correlations, which makes it unsuitable for sizing strategies with for example significant left-tail (e.g. volatility selling strategies).

In this paper, we propose an extension to the MVO framework that makes it more appropriate for sizing strategies with skewed returns, but at the same time is still intuitive and simple to use in practice.

The portfolio manager specifies a penalizing factor for the tail events, and the framework determines the optimal risk allocation based on this specification.

The proposed framework has three important features: 1) it is intuitive, interpretable and simple to use in practice, 2) when returns of the underlying strategies are jointly normally distributed, the proposed framework outputs the exact same solution as the MVO, and 3) the formulation is in the form of a convex optimization, which guarantees a unique optimal solution that is easy to compute.

Keywords: Portfolio Construction, Portfolio Optimization, Skewed-Return Strategies, Mean-Variance Optimization, Expected Shortfall

JEL Classification: G11