Analytical Methods for Hedging Systematic Credit Risk with Linear Factor Portfolios

This paper is part of a series explaining various methodologies for defining and measuring the contributions of systematic factors to economic capital as well as for hedging systematic risk in credit portfolios. Multi-factor credit portfolio models are used widely today for measuring and managing economic capital as well as for pricing credit portfolio instruments such as collateralized debt obligations (CDOs). Commonly, practitioners allocate capital to the portfolio components, such as individual sub-portfolios, counterparties, or transactions. The hedging of credit risk is generally also focused on the ”deltas” of the underlying names in the portfolio. In this paper, we present analytical results for hedging portfolio credit risk with linear portfolios of the systematic credit factors. Formally, we minimize the systematic variance of portfolio losses by using a linear combination of the systematic risk factors. We review the mathematical tools to solve these optimization problems within a multi-factor Merton-type (or probit) credit portfolio model, and then apply them to various cases. First, we focus on static hedges of homogeneous and inhomogeneous credit portfolios. We also apply the methodology to hedge the systematic credit default losses of CDOs. Finally we show the application of the methodology to dynamic hedging strategies. In each case, we discuss the hedging portfolios, the effectiveness of the hedges and provide numerical examples.