A multiobjective model for passive portfolio management: an application on the S&P 100 index

Abstract

Index tracking seeks to minimize the unsystematic risk component by imitating the movements of a reference index. Partial index tracking only considers a subset of the stocks in the index, enabling a substantial cost reduction in comparison with full tracking. Nevertheless, when heterogeneous investment profiles are to be satisfied, traditional index tracking techniques may need different stocks to build the different portfolios. The aim of this paper is to propose a methodology that enables a fund's manager to satisfy different clients’ investment profiles but using in all cases the same subset of stocks, and considering not only one particular criterion but a compromise between several criteria. For this purpose we use a mathematical programming model that considers the tracking error variance, the excess return and the variance of the portfolio plus the curvature of the tracking frontier. The curvature is not defined for a particular portfolio, but for all the portfolios in the tracking frontier. This way funds’ managers can offer their clients a wide range of risk-return combinations just picking the appropriate portfolio in the frontier, all of these portfolios sharing the same shares but with different weights. An example of our proposal is applied on the S&P 100.

Keyword : index tracking, frontier curvature, tracking error variance, excess return, port-folio variance, mean-variance model, portfolio selection