Corporate Bond Portfolio Optimization with Transaction Costs

Although much research has been devoted to portfolio optimization, starting with the seminal work of Markowitz (1952), relatively little has been focused on corporate bond portfolio optimization, particularly when there are multiple bonds in which to invest. In this paper, we propose a methodology addressing the problem of corporate bond portfolio optimization in a multi-period environment with transaction costs. We model interest rates using a classic CIR process and we model the defaultable bonds using a reduced form model. In this model, risk neutral default intensities evolve according to a CIR process with the Brownian motion terms correlated across the bonds. The bonds are then valued using the basic affine model of Duffie and Singleton (2003). Bond price paths are created using this affine model along with a translation from risk neutral probabilities to physical default probabilities to determine whether or not default has occurred in a period. Our portfolio optimization methodology melds simple binomial tree optimization with a technique from control theory called receding horizon control (RHC) which is used for solving large, computationally difficult problems. This methodology can accommodate a wide variety of bond dynamics beyond those mentioned above as well as a wide variety of performance objectives. Essentially, this methodology breaks down the portfolio optimization problem into a sequence of problems solved over time which allows one to incorporate changes in the system dynamics and to overcome issues of computational complexity. Through Monte Carlo simulation we demonstrate results showing our methodology can significantly outperform the bond portfolio methodology of holding a constant proportion of the portfolio in each bond. Note that this research is ongoing and thus this paper does not contain the complete analysis that will be done by the summer of 2006.