Enhanced index tracking optimal portfolio selection

In this paper we present an analytical solution for an uni-period enhanced index tracking problem with limited number of assets held in the tracking portfolio. We consider an approach in which the tracking portfolio is composed of a given subset of assets, and the value function is written as the trade-off between the tracking error and excess return, balanced by an appropriate choice of a risk aversion parameter. This formulation allows an analytical comparison of the betas and value functions of the optimal portfolios with and without tracking. Our approach provides readily implementable formulae, being consequently easier for numerical implementation.