Essays on index tracking and portfolio optimization

This dissertation focus on portfolio optimization models designed for index tracking investment strategy. The final content is composed by three articles. The first article is entitled “Index Tracking with Controlled Number of Assets Using a Hybrid Heuristic Combining Genetic Algorithm and Non-linear Programming”, which has been accepted for publication in the Annals of Operations Research. The second article is “Index Tracking and Enhanced Indexing using Cointegration and Correlation with Endogenous Portfolio Selection”, and it has been accepted for publication in The Quarterly Review of Economics and Finance. Lastly, the third article is “Investigating the Use of Statistical Process Control Charts for Index Tracking Portfolios”, and it has already been submitted and is currently under review. In the first paper, we discuss the index tracking strategy using mathematical programming. First, we use a non-linear programming formulation for the index tracking problem, considering a limited number of assets. Since the problem is difficult to be solved in reasonable time by commercial mathematical packages, we apply a hybrid solution approach, combining mathematical programming and genetic algorithm. We show the efficiency of the proposed approach comparing the results with optimal solutions, with previous developed methods, and from real-world market indexes. The computational experiments focus on Ibovespa (the most important Brazilian market index), but we also present results for consolidated markets such as S&P 100 (USA), FTSE 100 (UK) and DAX (Germany). The proposed framework shows its ability to obtain very good results (gaps from the optimal solution smaller than 5% in 8 minutes of CPU time) even for a highly volatile index from a developing country. In the second paper, the attention is turned to the analysis of two alternative methods to solve the index tracking optimization problem. This article investigates the out-of-sample performance of cointegration and correlation methods for index tracking (IT) and enhanced indexing (EIT) strategies applied to Brazilian and U.S. market data. Our goal is to compare both methods as we strongly explore cointegration in relation to previous studies: we make the portfolio selection endogenous to the problem for this approach. The tests are performed using data from 2004 to 2014 with samples of 57 assets for Brazilian data and 96 assets for U.S. data; portfolios are built using combinations of at most 10 of these assets. Despite the extensive tests carried out, the overall result shows similar performance for both methods. For IT in the Brazilian market, there was a trade-off between better tracking error and higher turnover for cointegration (with the opposite for correlation), this pattern was not clear in the U.S. market. The outcome for the EIT also does not clearly favor cointegration or correlation. Finally, the third article is dedicated to the discussion regarding the use of statistical process control charts to regulate index tracking portfolios. In this article, our goal is to introduce a statistical process control charts approach (SPC) to monitor the rebalancing process of index tracking (IT) portfolios. SPC methods derive from statistics and engineering as tools to control production process. We use exponentially weighted moving average (EWMA) control charts to monitor IT portfolios based on two combined charts: portfolios’ tracking error performance and portfolios’ volatility. As a result, we endogenously control the rebalancing process of the portfolios based on their performance and on their risk conditions over time. Computational tests are performed to evaluate the developed approach in comparison with the traditional fixed period strategy, using data from Brazilian and U.S. market from 2005 to 2014. Cointegration and correlation methods are applied to form the portfolios. The results show that SPC approach can be a viable alternative to portfolio rebalancing.