Capital Allocation and Per-Unit Risk in Inhomogeneous
and Stressed Credit Portfolios

Abstract

This article considers the application of gradient allocation and portfolio optimization to credit portfolios. The assumption of linearity of risk that is implied by the use of gradient allocation is challenged in a setting of inhomogeneity and stress scenarios. To see the effects of mathematically derived portfolio optimization on real-life examples, we consider a number of insightful examples. This challenges mathematical results and enables a financial interpretation of the latter. The results reveal that per-unit risk is not disturbed by moderate inhomogeneity in most cases, whereas a change in portfolio composition as well as stress can influence the portfolio optimization decision significantly. The importance of incorporating sensitivity analysis and stress testing into reporting structures and optimization decisions is emphasized.