How Expected Shortfall Can Simplify the Equally-Weighted Risk Contribution Portfolio

Abstract

In recent years both equity and bond markets have been afflicted by high volatility. In order to build up a conservative portfolio 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, that is equally-weighted risk contribution portfolio. This kind of procedure leads not to equalize the portfolio weights but the risk weights. The only thing to understand is how we can measure risk. While many authors focus on volatility, in this paper we shall present an alternative and coherent risk measure, that is Expected Shortfall estimated by Filtered Bootstrap Approach. We shall show how to use the ES properties to derive an easy way to equalize risk contribution, and we shall also present some empirical examples using different models. A model presented in S. Colucci, D. Brandolini "A Risk Based Approach to Tactical Asset Allocation" to compare results will also be introduced. In the end, the empirical result will show that ERC portfolio, ES Stable portfolio and minimum variance portfolio have roughly speaking the same performance risk and distribution, but if turnover and its costs are taken into account, the result changes in favor of ES Stable.

Keywords: Risk Parity, Expected Shortfall, Equally weighted Porfolio, Asset Allocation

JEL Classification: G11, G23, C15