Selected Methods of optimized Sampling for Index Tracking – Evidence from German Stocks

Abstract

Abstract The aim of this study is to verify the tracking quality of four different optimization approaches used for approximate replication (sampling) of a stock index. These approaches include relative optimization, optimization according to Markowitz, the use of regression methods and linear optimization. To test the tracking qualities of these strategies, an empirical analysis of portfolios of 10 stocks included in the German stock index DAX is used to determine the in-sample and out-of-sample results. In addition, a portfolio composition based on market capitalization and an equally weighted portfolio are considered. The analysis shows that the in-sample results are quite similar for all index tracking methods used in this study. Considering the out-of-sample results, it can be stated that all four index tracking methods lead to a portfolio that initially shows a high degree of similarity to the benchmark. However, it is surprising that the equally weighted portfolio leads to the best overall results. Therefore, the analysis presented here gives the impression that the uncomplicated equal weighting is preferable to the more sophisticated index tracking methods considered in this study. JEL classification number: G11. Keywords: Index tracking, Sampling, Optimization, Tracking error, Residual risk.