On the index tracking and the statistical arbitrage choosing the stocks by means of cointegration: the role of stock picking

Abstract

In this paper, we propose a new methology for Index Tracking (IT) by means of cointegration which provides some significant improvements on that field. As the quality of the tracking portfolio (TP) depends highly on the stock selection procedure, we propose picking the stocks using a model selection technique based on optimizing the cointegration level of the TP and the benchmark index instead of selecting, as in previous papers the assets by ad hoc decisions. To illustrate an empirical application of these techniques we use daily closing prices in the Dow Jones Industrial Average (DJIA) index over two different periods; one period which goes from 1 January 1990 to 31 December 2001 previously used by other authors, and the bear and a turmoil period, which goes from January 2007 to May 2012, inside the current financial crisis. Using only five assets we are able to successfully track the DJIA index and our results improve the IT technique based on cointegration that chooses stocks with maximum capitalization level. We also have compared our results with a more traditional procedure based on correlation and again our results reveal superiority. The empirical illustration not only has been focused on the TP itself, but has also been extended to tracking the index with an added profitability of 5, 10, 15 or 20% and to long-short strategies, producing profitable results.