Optimal portfolio selection and dynamic benchmark tracking Alexei A. Gaivoronski * , Sergiy Krylov, Nico van der Wijst Department of Industrial Economy and Technology Management, Norwegian University of Science and Technology, Alfred Getz vei 1, N-7491, Trondheim, Norway Available online 16 March 2004 Abstract This paper analyzes different approaches to portfolio selection when the requirement to portfolio performance is formulated relative to a given benchmark. For example, it may be desirable to track a market index as closely as possible. We develop several portfolio selection algorithms based on different perceptions of risk and different risk/ target measures, ranging from the traditional variance to the more modern value-at-risk. In a dynamic setting we address the issue of optimal portfolio rebalancing. We develop an algorithm for determining whether or not to re- balance a given portfolio, based on transaction costs and new information about market conditions. Our approaches are tested on a set of stock data from the Oslo stock exchange. Ó 2004 Published by Elsevier B.V. Keywords: Index tracking; Portfolio replication; Benchmark following; Portfolio selection; Risk measures; Transaction costs 1. Introduction Index investing has assumed large proportions since the first index funds were introduced in the mid-1970s. Corporate pension plans in the USA, for example, are now reported to invest over a quarter of their domestic equity holdings in index funds and these funds are similarly popular among private investors. Index investing is a passive strategy in the sense that no activities, like stock picking or timing, are undertaken to earn a higher return than the market as a whole. However, this does not mean that nothing needs to be done, particularly not if the chosen portfolio tracks an index rather than replicates it on a smaller scale. It is with these tracking portfolios that this paper is concerned. The objective of such a portfolio may simply be to track an index as closely as possible with a limited number of stocks. Alternatively, the benchmark for a portfolio may be the target return for the ‘‘guaranteed’’ investment products of funds and insurance companies. Another example of a benchmark is the performance of comparable competitors, which may be used to evaluate fund managers’ performance. Ideally, the decisions involved in setting up and maintaining a tracking portfolio would be embed- ded in a decision support system that presents the choices and trade-offs in a clearly structured way. Important elements in such a system would be: * Corresponding author. Fax: +47-73-593603. E-mail addresses: alexei.gaivoronski@iot.ntnu.no (A.A. Gai- voronski), sergiy.krylov@iot.ntnu.no (S. Krylov), wijst@ iot.ntnu.no (N. van der Wijst). 0377-2217/$ - see front matter Ó 2004 Published by Elsevier B.V. doi:10.1016/j.ejor.2003.12.001 European Journal of Operational Research 163 (2005) 115–131 www.elsevier.com/locate/dsw