Extending Risk Budgeting for Market Regimes and Quantile Factor Models

Abstract

We combine several disparate avenues in the literature to create a novel, unified risk-based optimisation framework. Specifically, we extend the existing risk budgeting approach of Richard and Roncalli (2015) to allow for changing market regimes, factor dependence and nonlinear and asymmetric market structure. We show that the existing framework can be readily extended to include a factor-dependent return process using standard models available in the literature. Structural changes in market conditions are then incorporated into the framework through the use of a regime-switching turbulence index and the nonlinear and asymmetric market dependence structure is accounted for by using quantile factor models. Most importantly, this extended framework is only comprised of a series of linear models, and is thus simple to understand and implement. We consider two applications of the extended framework, namely scenario analysis and parameter uncertainty analysis, through means of a simple empirical case study. Finally, we introduce the concept of Risk Maps, which provide managers with a graphical approach for estimating and evaluating risk optimality in a multi-objective and multi-scenario setting.