The Credit Market Handbook: Advanced Modeling Issues

CHAPTER 8

Implications of Correlated Default for Portfolio Allocation to Corporate Bonds

Mark B. Wise^a,* and Vineer Bhansali^b

This chapter deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Using a multivariate normal copula function for the joint default probabilities, we show that retaining the first few moments of the portfolio default loss distribution gives an extremely good approximation to the full solution of the asset allocation problem. We provide detailed results on the convergence of the moment expansion and explore how the optimal portfolio allocation depends on recovery fractions, level of diversification, and investment time horizon. Numerous numerical illustrations exhibit the results for simple portfolios and utility functions.

1. INTRODUCTION

Investors routinely look to the corporate bond market in particular, and to spread markets in general, to enhance the performance of their portfolios. However, for every source of excess return over the risk-free rate, there is a source of excess risk. When sources of risk are correlated, the allocation decision to the risky sectors, as well as allocation to particular securities in that sector, can be substantially different from the uncorrelated case. Since the joint probability distribution of returns of a set of defaultable bonds varies with the joint probabilities of default, recovery fraction for each bond, and ...