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, otherportfolio 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 toreproduce 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 optimizationalgorithm based on data of an estimation period. The assumption is that this portfoliodoes also have the highest tracking quality in the crucial investment period. Many approachesfor optimizing a tracking portfolio have already been published in literature. Usually, one ofthree measures (mean absolute deviation, mean square error, and tracking error variance) isused in order to measure the tracking quality.An interesting research question is how stablethese measures are. Do they produce tracking portfolios with the same tracking quality in theestimation period and the investment period? Are the tracking portfolios with a high trackingquality in the estimation period compared to the alternative tracking portfolios also those witha high relative tracking quality in the investment period? And finally, do the three traditionalmeasures produce tracking portfolios which are of high value from the investor’s point ofview?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 sizeswe analyze the absolute and the relative stability. Furthermore, we introduce a measure for theex post tracking quality from an investor’s point of view and compare the resulting trackingportfolios from the prior analyses using this measure.The results indicate a poor stability forevery of the thre