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).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1007/s10287-012-0158-y
ISSNs: 1619-697X (print)
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Organisations: Southampton Wireless Group
ePrint ID: 350499
Date :
Date Event
1 February 2013e-pub ahead of print
Date Deposited: 27 Mar 2013 12:29
Last Modified: 17 Apr 2017 15:48
Further Information:Google Scholar

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