In today’s Portfolio Management many strategies are based on the investment into indices. This is a consequence of various empirical studies that show that the allocation over asset classes, countries etc. provides a greater performance contribution than the selection of single assets. For every portfolio containing indices as components the problem is that an index cannot be purchased directly. So it has to be rebuilt. This is called index tracking. The goal is to approximate the risk and return profile of an index.
There exist different approaches to track indices.
One widely used approach is sampling, where the index is reproduced by a so-called tracking portfolio with a smaller number of assets, mostly a subset of its components. When applying sampling one has to solve two sub problems: selecting the assets of the tracking portfolio and determining their fractions. The quality of tracking is measured by the tracking error, which expresses the deviation between the returns of the tracking portfolio and the returns of the index. The optimal tracking portfolio is the portfolio with the smallest tracking error among all possible tracking portfolios. This is usually calculated with past data, assuming that the tracking quality will remain in the future investment period. In the remainder of the paper, we show that the common approaches of sampling have weaknesses to generate tracking portfolios with a stable quality even in the estimation and investment period.
For more details, see A method for robust index tracking (springer.com)