Extending risk budgeting for market regimes and quantile factor models

We combine several disparate avenues in the literature to create a novel, unified risk- based optimization framework. Specifically, we extend an existing risk-budgeting approach to allow for changing market regimes and factor dependence as well as a nonlinear, 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 the market conditions are then incorporated into the framework via 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 comprised of a series of linear models only and is thus simple to understand and to implement. We consider two applications of the extended framework, namely, scenario analysis and parameter uncertainty analysis, by way 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 multiobjective, multiscenario setting.