An analysis of a mean-variance enhanced index tracking problem with weights constraints

Wanderlei Lima De Paulo,Marta Ines Velazco Fontova,Renato Canil De Souza

doi:10.21511/imfi.15(4).2018.15

Wanderlei Lima De Paulo, Marta Ines Velazco Fontova + Show 1 more

Open Access

https://doi.org/10.21511/imfi.15(4).2018.15

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Abstract

In this paper, the authors deal with a mean-variance enhanced index tracking (EIT) problem with weights constraints. Using a shrinkage approach, they show that constructing the constrained EIT portfolio is equivalent to constructing the unconstrained EIT portfolio. This equivalence allows to study the effect of weights constraints on the covariance matrix and on the EIT portfolio. In general, the effects of weights constraints on the EIT portfolio are different from those observed in the case of global minimum variance portfolio. Finally, the authors present a numerical asset allocation example, where the S&amp;amp;P 500 index is used as the market index to be tracked using a portfolio composed of ten stocks, in which the constrained EIT portfolio shows a satisfactory performance when compared to the unconstrained case.

Highlights

An index tracking problem aims at establishing an optimal allocation so that the return of the portfolio replicates the return of a market index, without purchasing all of the assets that compose the market index
The effects of weights constraints on the enhanced index tracking (EIT) portfolio are different from those observed in the case of global minimum variance portfolio
The authors present a numerical asset allocation example, where the S&P 500 index is used as the market index to be tracked using a portfolio composed of ten stocks, in which the constrained EIT portfolio shows a satisfactory performance when compared to the unconstrained case

Summary

INTRODUCTION

An index tracking problem aims at establishing an optimal allocation so that the return of the portfolio replicates the return of a market index (passive management strategy), without purchasing all of the assets that compose the market index. In this paper, we deal with a mean-variance EIT problem with weights constraints. In this case, it is not possible to obtain an analytic solution, but the problem can be solved using a quadratic programming algorithm. Considering the same framework, we have shown that constructing a constrained mean-variance EIT portfolio is equivalent to constructing an unconstrained EIT portfolio (as studied in Paulo et al, 2016). This equivalence allows us to study the effect of weights constraints on the covariance matrix and on the EIT portfolio.

PROBLEM FORMULATION minimize

ASSET ALLOCATION