Title: Algorithms for l1-norm minimisation of index tracking error and their performance

Authors: Sergei P. Sidorov; Alexey R. Faizliev; Andrew A. Khomchenko

Addresses: Risk Institute, Saratov State University, Russian Federation, Russia ' Risk Institute, Saratov State University, Russian Federation, Russia ' Risk Institute, Saratov State University, Russian Federation, Russia

Abstract: The paper considers the index tracking problem with cardinality constraint and examines different methods for the numerical solution of the problem. Index tracking is a passive financial strategy that tries to replicate the performance of a given index or benchmark. The aim of investor is to find the weights of assets in her/his portfolio that minimise the tracking error, i.e., difference between the performance of the index and the portfolio. In this paper, we examine three different algorithms for index tracking error minimisation in l1-norm (greedy algorithm, algorithm for l1-norm minimisation with relaxation and differential evolution algorithm) and compare the empirical performance of the portfolios obtained by means of the algorithms.

Keywords: index tracking; portfolio optimisation; greedy algorithms; differential evolution algorithms.

DOI: 10.1504/IJMOR.2017.087743

International Journal of Mathematics in Operational Research, 2017 Vol.11 No.4, pp.497 - 519

Available online: 26 Oct 2017 *

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