Risk Budgets

Abstract

In a previous issue, George Chow and Mark Kritzman discussed the relationship of risk budgeting and asset allocation. A risk budget is defined as the conversion of optimal allocations from mean–variance optimization into value at risk assignments. This comment identifies an error in the formula for the sensitivity of portfolio value at risk with respect to asset weights. The authors demonstrate how to derive VaR sensitivity correctly and extend the analysis to more than three assets.