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Fixed-Income Portfolio Selection

by Kay Giesecke of Stanford University, and
Jack Kim of Stanford University

June 2, 2010

Abstract: The equity portfolio selection problem is the subject of a substantial literature. Though equally important in practice, the selection problem for a fixed-income portfolio of corporate and government bonds, industrial loans and credit derivatives, is less well-understood. The fixed-income portfolio problem presents unique challenges: the risk of issuer default induces skewed return distributions, the correlation of defaults influences the tail of the portfolio return distribution, and credit derivative positions have complex risk/return implications. This paper addresses the static selection problem for a fixed-income portfolio. We optimize the total mark-to-market value of the portfolio at the investment horizon, which incorporates the intermediate premium and default cash flows of long and short cash and derivative positions, and the survival-contingent market value of these positions at the horizon. The selection problem is cast as a polynomial goal program that involves a two-stage constrained optimization of preference weighted moments of the portfolio mark-to-market. The decision variable is the vector of contract notionals. A capital constraint guarantees the solvency of the investor. The multi-moment formulation takes account of the non-Gaussian distribution of the portfolio mark-to-market. It is also computationally tractable, because we succeed in developing analytical expressions for the moments of the portfolio mark-to-market, which are given in terms of nested expectations under risk-neutral and actual probability measures. The expressions are valid for a broad class of intensity-based, doubly-stochastic models of correlated default timing that are widely used in portfolio credit risk and derivatives pricing. A numerical analysis illustrates the implications for portfolio selection of idiosyncratic default risk and default correlation. It also indicates the robustness of the optimal policies with respect to estimation errors.

Keywords: credit swap, credit derivative, default risk, point process, intensity, moments, nested expectation, measure change, polynomial goal program, portfolio optimization.

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