The curvature of the tracking frontier: A new criterion for the partial index tracking problem

Abstract

Index tracking aims to select portfolios that imitate the behavior of a stock index. A tracking strategy is referred to as partial when the tracking portfolio is solely formed by a subset of stocks, so enabling a substantial cost reduction in comparison with full tracking. Three criteria are usually employed in the literature when building the tracking portfolio: tracking error variance, excess return and tracking portfolio variance. This paper considers a new parameter for use with the above: frontier curvature. This criterion is not defined for a particular portfolio, but for all the portfolios that define the tracking frontier. The main implication is that a manager can satisfy different investment profiles with the same subset of stocks. The manager will therefore reduce transaction costs as all the portfolios on the frontier contain the same stocks.