Abstract

Although bond portfolio optimization is one of the oldest applications of the mean-variance framework, it is considerably less developed and adopted than its equity and multi-asset counterparts. This paper presents a comprehensive framework for bond portfolio optimization applied to investment universes composed of individual securities. We first identify the challenges that distinguish bond portfolio optimization from equity portfolio optimization. We then develop a family of optimization problems with and without a benchmark under alternative risk factor models. In particular, we focus on a two-factor risk model based on interest rates and credit risk. We also distinguish between ℓ1-norm and ℓ2-norm optimization problems, and show how these formulations can be cast into linear programming and quadratic programming problems using the properties of quadratic and extended linear forms. Beyond these standard formulations, we consider advanced optimization problems combining both ℓ1 and ℓ2 risk measures. We pay particular attention to active share constraints, which play a central role in fixed-income portfolio management. 

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