Modifying Sequential Monte Carlo Optimisation for Index Tracking to Allow for Transaction Costs

Leila Hamilton-Russell, Thomas Malan O’Callaghan, Dmitrii Savin and Erik Schlogl
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Leila Hamilton-Russell: The African Institute of Financial Markets and Risk Management (AIFMRM), University of Cape Town, Cape Town 7701, South Africa
Thomas Malan O’Callaghan: The African Institute of Financial Markets and Risk Management (AIFMRM), University of Cape Town, Cape Town 7701, South Africa
Dmitrii Savin: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

Risks, 2024, vol. 12, issue 10, 1-44

Abstract: Managing a portfolio whose value closely tracks an index by trading only in a subset of the index constituents involves an NP-hard optimisation problem. In the prior literature, it has been suggested that this problem be solved using sequential Monte Carlo (SMC, also known as particle filter) methods. However, this literature does not take transaction costs into account, although transaction costs are the primary motivation for attempting to replicate the index by trading in a subset, rather than the full set of index constituents. This paper modifies the SMC approach to index tracking to allow for proportional transaction costs and implements this extended method on empirical data for a variety stock indices. In addition to providing a more practically useful tracking strategy by allowing for transaction costs, we find that including a penalty for transaction costs in the optimisation objective can actually lead to better tracking performance.

Keywords: index tracking; sequential Monte Carlo; transaction costs; portfolio management (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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