Index tracking with constrained portfolios

Passive portfolio management strategies, such as index tracking, are popular in the industry, but so far little research has been done on the cardinality of such a portfolio, i.e. on how many different assets ought to be included in it. One reason for this is the computational complexity of the associated optimization problems. Traditional optimization techniques cannot deal appropriately with the discontinuities and the many local optima emerging from the introduction of explicit cardinality constraints. More recent approaches, such as heuristic methods, on the other hand, can overcome these hurdles. This paper demonstrates how one of these methods, differential evolution, can be used to solve the constrained index‐tracking problem. We analyse the financial implication of cardinality constraints for a tracking portfolio using an empirical study of the Down Jones Industrial Average. We find that the index can be tracked satisfactorily with a subset of its components and, more important, that the deviation between computed actual tracking error and the theoretically achievable tracking error out of sample is negligibly affected by the portfolio's cardinality. Copyright © 2007 John Wiley & Sons, Ltd.