
 FixedIncome Portfolio Selection by Kay Giesecke of Stanford University, and 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 fixedincome portfolio of corporate and government bonds, industrial loans and credit derivatives, is less wellunderstood. The fixedincome 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 fixedincome portfolio. We optimize the total marktomarket 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 survivalcontingent market value of these positions at the horizon. The selection problem is cast as a polynomial goal program that involves a twostage constrained optimization of preference weighted moments of the portfolio marktomarket. The decision variable is the vector of contract notionals. A capital constraint guarantees the solvency of the investor. The multimoment formulation takes account of the nonGaussian distribution of the portfolio marktomarket. It is also computationally tractable, because we succeed in developing analytical expressions for the moments of the portfolio marktomarket, which are given in terms of nested expectations under riskneutral and actual probability measures. The expressions are valid for a broad class of intensitybased, doublystochastic 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. Books Referenced in this paper: (what is this?) 