index tracking with control on the number of assets

Abstract

Index tracking is a passive investment strategy, which aims at generating portfolios to reproduce a specific market index’s performance. This article proposes a model for a index tracking problem with control on the number of assets in the portfolio, which corresponds to a restriction in transaction costs. The model is applied to Ibovespa (sample: 67 stocks) from January/2009 to July/2012. Portfolios were formed without limiting the amount of stocks and limiting this amount to 40, 30 and 20 stocks, with rebalancing periods of 20, 40 and 60 trading days. The results were satisfactory especially for the 60 days rebalancing period, in which transaction costs become lower due to the longer rebalancing period. We also verified that changes in Cplex parameters didn’t influence the results especially in relation to the computational times. Therefore, we also conclude about the need of using heuristic approaches to form portfolios with smaller amounts of assets.