The Stability of Traditional Measures of Index Tracking Quality

Today, the investment into indices has become a widely used strategy in portfolio management. While Index Funds and ETFs try to represent the performance of a single index, other portfolio strategies use indices as portfolio components to concentrate on the allocation task. Because an index cannot be purchased directly, it has to be rebuilt. This is called index tracking.

There exist different methods for index tracking. One of them is sampling and aims to reproduce the performance of an index by purchasing a smaller selection of its components. Therefore, the tracking portfolio with the highest tracking quality is searched using an optimization algorithm based on data of an estimation period. The assumption is that this portfolio does also have the highest tracking quality in the crucial investment period.

Many approaches for optimizing a tracking portfolio have already been published in literature. Usually, one of three measures (mean absolute deviation, mean square error, and tracking error variance) is used in order to measure the tracking quality.An interesting research question is how stable these measures are. Do they produce tracking portfolios with the same tracking quality in the estimation period and the investment period? Are the tracking portfolios with a high tracking quality in the estimation period compared to the alternative tracking portfolios also those with a high relative tracking quality in the investment period? And finally, do the three traditional measures produce tracking portfolios which are of high value from the investor’s point of view?

We perform an empirical study using the HDAX in order to answer these questions. Applying the three measures on different time periods and different tracking portfolio sizes we analyze the absolute and the relative stability. Furthermore, we introduce a measure for the ex post tracking quality from an investor’s point of view and compare the resulting tracking portfolios from the prior analyses using this measure. The results indicate a poor stability for every of the three traditional measures. Furthermore, the relation to the ex post tracking quality is weak. Thus, there is a need for further research in the area of sampling. It must be explored if there are alternative measures and/or alternative optimization algorithms to search for tracking portfolios which have the desired properties not only in the estimation period but also in the investment period.

For more details, seeĀ The Stability of Traditional Measures of Index Tracking Quality (