Vitaly Serbin, Milan Borkovec and Michael Chigirinskiy
Volume 9, Number 2, Second Quarter 2011
The goal of this paper is to study and compare two popular techniques used by practitioners to reduce the sensitivity of optimal portfolios to uncertainty in expected return for a typical portfolio optimization problem. Specifically, we investigate whether including transaction costs into the optimization problems objective function addresses the robustness issue. We weight this approach against the robust optimization method described in Goldfarb and Iyengar (2003). The latter directly incorporates the distribution of estimation errors in the optimization problem and determines the optimal portfolio allocation by selecting the least favorable realization of the expected returns in the investors uncertainty region.
Our analysis focuses on the return maximization problem with constraints on total risk or tracking error and a transaction cost penalty in the objective function. We demonstrate that not only are the effects of incorporating a transaction cost penalty into the optimization problem similar to those of modeling uncertainty in expected returns, but that there are also some interesting differences. We offer some insights into the observed interplay between modeling transaction costs and modeling return uncertainty.