Building tracking portfolios based on a generalized information criterion

One important topic in financial studies is to build a tracking portfolio of stocks whose return mimics that of a chosen investment target. Statistically, this task can be accomplished by selecting an optimal constrained linear model. In this paper, we extend the Generalized Information Criterion (GIC) to constrained linear models with independently and identically distributed random errors and, more generally, with dependent errors that follow a stationary Gaussian process. The extended GIC procedure is proved to be asymptotically loss efficient and consistent under mild conditions. Simulation results show that the relative frequency of selecting the optimal constrained linear model by GIC is close to one for finite samples. We also apply GIC to build an optimal tracking portfolio for measuring the long-term impact of a corporate event on stock returns, and demonstrate empirically that it outperforms two competing methods.