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Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios

Takeda, Akiko, Niranjan, Mahesan, Gotoh, Jun-ya and Kawahara, Yoshinobu (2013) Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios Computational Management Science, 10, (1), pp. 21-49. (doi:10.1007/s10287-012-0158-y).

Record type: Article

Abstract



Index tracking is a passive investment strategy in which a fund (e.g., an ETF: exchange traded fund) manager purchases a set of assets to mimic a market index. The tracking error, i.e., the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable transaction cost and, accordingly, decreases the return of the constructed portfolio. On the other hand, a portfolio with a small cardinality may result in poor out-of-sample performance. Of interest is, thus, constructing a portfolio with good out-of-sample performance, while keeping the number of assets invested in small (i.e., sparse). In this paper, we develop a tracking portfolio model that addresses the above conflicting requirements by using a combination of L0- and L2-norms. The L2-norm regularizes the overdetermined system to impose smoothness (and hence has better out-of-sample performance), and it shrinks the solution to an equally-weighted dense portfolio. On the other hand, the L0-norm imposes a cardinality constraint that achieves sparsity (and hence a lower transaction cost). We propose a heuristic method for estimating portfolio weights, which combines a greedy search with an analytical formula embedded in it. We demonstrate that the resulting sparse portfolio has good tracking and generalization performance on historic data of weekly and monthly returns on the Nikkei 225 index and its constituent companies.

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e-pub ahead of print date: 1 February 2013
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 350499
URI: http://eprints.soton.ac.uk/id/eprint/350499
ISSN: 1619-697X
PURE UUID: 591f13fb-0a9d-4f87-ab6f-21d90fe2976c

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Date deposited: 27 Mar 2013 12:29
Last modified: 18 Jul 2017 04:34

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Contributors

Author: Akiko Takeda
Author: Jun-ya Gotoh
Author: Yoshinobu Kawahara

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