Myopic robust index tracking with Bregman divergence

S. Penev*, P. V. Shevchenko, W. Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 an expectation of a function of the difference between the returns of the index and of the portfolio. We also assume that there is model 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 (true) distribution of the components of the index. In this scenario, we derive the optimal robust index tracking portfolio 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 portfolio with the optimal non-robust portfolio. We show that, especially during market downturns, the robust portfolio can be very advantageous.

Original languageEnglish
Pages (from-to)289-302
Number of pages14
JournalQuantitative Finance
Volume22
Issue number2
Early online date23 Jul 2021
DOIs
Publication statusPublished - 1 Feb 2022

Keywords

  • Bregman divergence
  • Index tracking
  • Kullback–Leibler divergence
  • Robust index tracking

Fingerprint

Dive into the research topics of 'Myopic robust index tracking with Bregman divergence'. Together they form a unique fingerprint.

Cite this