Partial moments and indexation investment strategies

Index-linked investment strategies are developing rapidly. However, few studies distinguish between the returns of an indexation portfolio above and below a benchmark index. In this paper, we first use upper partial moments (UPMs) and lower partial moments (LPMs) to measure upside and downside deviations, respectively, against a benchmark index. Next, we use a balance parameter to connect the UPMs with the LPMs and thereby unify an enhanced index model and index tracking model. We prove that both UPMs and LPMs are convex functions of portfolio position and offer a nonparametric estimation method to construct computing models. We conduct simulations to show the UPMs and LPMs trade-off characteristics of our two models. Using six global key indexes, we show that our enhanced index model outperforms the Omega model in terms of cumulative returns. In addition, because the weights of the constituents are stable, the performance of our index tracking model is similar to that of the conventional mean absolute deviation model.