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.

A widespread approach in the implementation of asset pricing models is based on the periodic recalibration of its parameters and initial conditions to eliminate any conflict between model-implied and market prices. Modern no-arbitrage market models facilitate this procedure since their solution can usually be written in terms of the entire initial yield curve. As a result, the model fits (by construction) the interest rate term structure. This procedure is, however, generally time inconsistent since the model at time t=0 completely specifies the set of possible term structures for any t extgreater0. In this paper, we analyze the pros and cons of this widespread approach in pricing and hedging, both theoretically and empirically. The theoretical section of the paper shows (a) under which conditions recalibration improves the hedging errors by limiting the propagation of an initial error, (b) that recalibration introduces time-inconsistent errors that violate the self-financing argument of the standard replication strategy. The empirical section of the paper quantifies the trade-off between (a) and (b) under several scenarios. First, we compare this trade-off for two economies with and without model specification error. Then, we discuss the trade-off when the underlying economy is not Markovian.