Dynamic index tracking via stochastic programming

Index tracking (IT) is an investment strategy aimed at replicating the performance of a given financial index, taken as benchmark, over a given time horizon. This paper deals with the IT problem by proposing a stochastic programming model where the tracking error is measured by the Conditional Value at Risk (CVaR) measure. The multistage formulation overcomes the myopic view of the static models considering a longer time horizon and provides a more flexible paradigm where the initial strategy can be revised to account for changed market conditions. The proposed formulation presents a bi-objective function, where the two conflicting criteria wealth maximization and risk minimization, are jointly accounted for by properly choosing the weight to attribute to the two terms. The model is encapsulated within a rolling horizon scheme and solved iteratively exploiting each time the more update information in the generation of the scenario tree. The preliminary computational experiments carried out by considering as benchmark the Italian index FSTE-MIB seem to be promising and show that, on an out-of-sample analysis, the tracking portfolios follow the benchmark very closely, overcoming it on the long run.