Myopic robust index tracking with Bregman divergence

TL;DR

This paper proposes a forward-looking, robust index tracking method using Bregman divergence to account for distributional uncertainty, demonstrating improved performance during market downturns.

Contribution

It introduces a novel robust index tracking approach based on Bregman divergence and derives a semi-analytical solution for the optimal strategy under distributional uncertainty.

Findings

Robust strategy outperforms non-robust during downturns

Semi-analytical solution derived for the robust tracking problem

Numerical results validate the effectiveness of the proposed method

Abstract

Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is an uncertainty in the distribution of the assets, hence a robust version of the optimization problem needs to be adopted. We use Bregman divergence in describing the deviation between the nominal and actual distribution of the components of the index. In this scenario, we derive the optimal robust index tracking strategy in a semi-analytical form as a solution of a system of nonlinear equations. Several numerical results are presented that allow us to compare the performance of this robust strategy with the optimal non-robust strategy. We show that, especially during market downturns, the robust strategy can be very advantageous.