Diversity and Sparsity: A New Perspective on Index Tracking

Yu Zheng, Timothy M. Hospedales, Yongxin Yang

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking portfolio must also be diverse in order to minimise risk-a requirement which has only been dealt with by ad-hoc methods before. We introduce the first index tracking method that explicitly optimises both diversity and sparsity in a single joint framework. Diversity is realised by a regulariser based on pairwise similarity of assets, and we demonstrate that learning similarity from data can outperform some existing heuristics. Finally, we show that the way we model diversity leads to an easy solution for sparsity, allowing both constraints to be optimised easily and efficiently. we run out-of-sample back-testing for a long interval of 15 years (2003-2018), and the results demonstrate the superiority of the proposed algorithm.
Original languageEnglish
Title of host publicationICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages5
ISBN (Electronic)978-1-5090-6631-5
ISBN (Print)978-1-5090-6632-2
Publication statusPublished - 14 May 2020
Event2020 IEEE International Conference on Acoustics, Speech, and Signal Processing - Barcelona, Spain
Duration: 4 May 20208 May 2020
Conference number: 45

Publication series

ISSN (Print)1520-6149
ISSN (Electronic)2379-190X


Conference2020 IEEE International Conference on Acoustics, Speech, and Signal Processing
Abbreviated titleICASSP 2020


  • Index tracking
  • portfolio optimisation


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