A Quick Introduction to Quantitative Models That Discard Estimation of Expected Returns for Portfolio Construction

Abstract

In recent years both equity and bond markets have been afflicted by high volatility. In order to build up a portfolio on a quantitative basis, several models may be used, such as minimum variance portfolio or equally weighted portfolio. In 2008/09 another way to deal with diversification came up, the equally-weighted risk contribution portfolio. We give an introduction of some quantitative models in which expected returns are not an input. Expected returns estimation is a challenging procedure and we want to figure out how models that discard it can perform. We, also, provide a way to achieve maximum diversification using Expected Shortfall as risk measure and Filtered Historical Simulation as a way to estimate it. We take as a benchmark procedure the evergreen 1/n portfolio, while other methods are minimum variance, minimum Expected Shortfall, Equally Risk Contribution, Maximum Diversification and risk parity portfolio as in Maillard-Roncalli-Teiletche in order to study their characteristics, properties and implementation problems. We use an evaluation methodology that consider risk adjusted return, Ulcer index, thickness of the tail and portfolio turnover. We test modelsperformances against the 1/n by using robust Sharpe Ratio proposed by Ledoit and Wolf. We notice that the benchmark model has a poor risk adjusted performance while the Minimum Variance and Minimum Expected Shortfall models have good results, although in equity markets none of models can produce a statistically different Sharpe ratio.

Keywords: equally risk contribution, risk parity, maximum diversification, asset allocation, mean variance, 1/N, VaR models, expected shortfall

JEL Classification: G10, G11, G23, C00, C10, C50