Olivier Gueant

In recent years, interest has grown for portfolio construction methods that do not rely on expected returns. Among risk-based methods, the most popular ones are minimum variance, maximum diversification, and risk budgeting (especially equal risk contribution, aka. ERC). Risk budgeting is particularly attractive because of its versatility: based on the Euler decomposition of positively homogeneous functions, it can be used with a large range of risk « measures », from volatility to expected shortfall/CVaR and beyond. The goal of this talk is to present new mathematical results about the construction of risk budgeting portfolios for a very wide spectrum of risk « measures » and to show that, in many cases, stochastic optimization techniques can be used to build risk budgeting portfolios.