The University of Southampton
University of Southampton Institutional Repository

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


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.

PDF takeda13.pdf - Version of Record
Restricted to Repository staff only
Download (1MB)

More information

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


Local EPrints ID: 350499
ISSN: 1619-697X
PURE UUID: 591f13fb-0a9d-4f87-ab6f-21d90fe2976c

Catalogue record

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

Export record



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

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.