Myopic Robust Index Tracking with Bregman Divergence

Quantitative Finance 2021, https://doi.org/10.1080/14697688.2021.1950918

26 Pages Posted: 27 Aug 2021

See all articles by Spiridon Penev

Spiridon Penev

University of New South Wales (UNSW) - School of Mathematics

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics

Wei Wu

University of New South Wales (UNSW) - School of Mathematics and Statistics

Date Written: June 20, 2021

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 a 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.

Suggested Citation

Penev, Spiridon and Shevchenko, Pavel V. and Wu, Wei, Myopic Robust Index Tracking with Bregman Divergence (June 20, 2021). Quantitative Finance 2021, https://doi.org/10.1080/14697688.2021.1950918, Available at SSRN: https://ssrn.com/abstract=3894113

Spiridon Penev (Contact Author)

University of New South Wales (UNSW) - School of Mathematics ( email )

Department of Statistics
Sydney, New South Wales
2053 Australia

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics ( email )

Australia

HOME PAGE: http://www.mq.edu.au/research/centre-for-risk-analytics/pavel-shevchenko

Wei Wu

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

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