A linear model for tracking error minimization

This article investigates four models for minimizing the tracking error between the returns of a portfolio and a benchmark. Due to linear performance fees of fund managers, we can argue that linear deviations give a more accurate description of the investors' risk attitude than squared deviations. All models have in common that absolute deviations are minimized instead of squared deviations as is the case for traditional optimization models. Linear programs are formulated to derive explicit solutions. The models are applied to a portfolio containing six national stock market indexes (USA, Japan, UK, Germany, France, Switzerland) and the tracking error with respect to the MSCI (Morgan Stanley Capital International Index) world stock market index is minimized. The results are compared to those of a quadratic tracking error optimization technique. The portfolio weights of the optimized portfolio and its risk/return properties are different across the models which implies that optimization models should be targeted to the specific investment objective. Finally, it is shown that linear tracking error optimization is equivalent to expected utility maximization and lower partial moment minimization. (C) 1999 Elsevier Science B.V. All rights reserved. JEL classification: C63; G11.