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.
The second part of the paper is dedicated to empirical applications using the ICE BofA Corporate Bond indices (Global, EUR, and USD). We first illustrate the differences between ℓ1- norm and ℓ2-norm optimization and their impact on tracking error volatility. We then apply the Barra multi-factor risk model and decompose portfolio risk into common factor and specific risk contributions. The third application addresses active portfolio management, where we decompose expected excess returns into carry, rolldown, and repricing components. The fourth application considers the classical problem of portfolio decarbonization. The fifth application examines the sensitivity of portfolio construction to alternative clustering and bucketing methodologies. The sixth and final application illustrates the practical challenges of constructing investable portfolios and demonstrates that the difference between model and investable portfolios is a primary issue in fixed-income optimization.
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