Simple and Robust Risk Budgeting with Expected
Shortfall

Abstract

Portfolio managers who exploit diversified sources of alpha have traditionally allocated risk among these alpha sources using Markowitz’s mean-variance paradigm. While this paradigm works well when returns are normally distributed, it is far less effective when the strategies have significant tail risk, as is often the case in fixed income. In this article, the authors describe a new risk budgeting algorithm that allocates risk among fixed-income strategies in a way that takes into account both their tracking error and their tail risk, and which charts a pragmatic middle course between the elegant simplicity of mean-variance optimization and the computational complexity of most robust risk allocation algorithms. It is, to the best of the authors’ knowledge, the first robust risk budgeting algorithm that can be solved in closed form on the back of an envelope. The algorithm inherits its closed-form solvability from a pragmatic compromise the authors make—they keep one foot in the “old world” by beginning with using variance as the measure of risk, and then plant the other foot firmly in the “new world” by switching at an appropriate point to using expected shortfall as the measure of risk. It works well in practice in spite of its simplicity and yields fixed-income risk allocations that reflect both a portfolio manager’s and a risk manager’s intuition better than does a standard mean-variance risk budget.