Factor based index tracking

Stock index tracking requires to build a portfolio of stocks (a replica) whose behavior is as close as possible to that of a given stock index. Typically, much fewer stocks should appear in the replica than in the index, and there should be no low frequency or integrated (persistent) components in the tracking error. The latter property is not satisfied by many commonly used methods for index tracking. These are based on the in-sample minimization of a loss function, but do not take into account the dynamic properties of the index components. Moreover, most existing methods do not take into account the known structure of the index weight system. In this paper we represent the index components with a dynamic factor model. In this model the price of each stock in the index is driven by a set of common and idiosyncratic factors. Factors can be either integrated or stationary. We develop a procedure that, in a first step, builds a replica that is driven by the same persistent factors as the index. This procedure is grounded in recent results which suggest the application of principal component analysis for factor estimation even for integrated processes. In a second step, it is also possible to refine the replica so that it minimizes a specific loss function, as in the traditional approach. In both steps the replica weights depend on the existing information on the index weights system. An extended set of Monte Carlo simulations and an application to the most widely used index in the European stock market, the EuroStoxx50 index, provide substantial support for our approach.