Integrating Market Risk and Credit Risk: A Dynamic Asset Allocation Perspective

Abstract

This paper investigates how investors who face both market risk (interest rate risk) and credit risk in addition to equity risk would optimally allocate their financial wealth in a dynamic, no arbitrage, continuous-time setup. I model credit risk through a defaultable zero-coupon bond and solve the stochastic differential equation of it under the recovery to market value scheme. I obtain a closed-form solution to this investment problem, which enables me to analyze the impact on investors' decisions of various risk parameters. One interesting insight of this paper is that a non-zero recovery rate of the credit-risky bond affects investors' decision in a fundamental way. This is manifested in a dividend-like adjustment term in the drift of the stochastic differential equation (SDE) of the defaultable zero-coupon bond's return process. The optimal asset allocation involves the separation effect and effect. As a result, the relation between myopic demands for bonds and market prices of risk becomes relatively complicated compared with that in the traditional setup. In addition, I show the cross-markets correlation is an important factor in the asset allocation decision. In particular, it affects investors' ability to hedge against or speculate on the stochastic risk premium of the defaultable bond. Numerical examples show that the inclusion of credit markets significantly enhances investors' welfare. I also find modeling interest rate as a stochastic process greatly reduces model risk, giving investors more realistic prospects in their investment decisions. Key Words: integration of market risk and credit risk, asset allocation, welfare analysis, corporate bond, model risk