Comparison and Development of Methods for Index Tracking

At the present time, there is a major trend in the financial markets of focusing on the common factors rather than the individual characteristics of assets. The reason for this growth in popularity is that the portfolios, which replicate the performance of the indices, simplify the investment process and, at the same time, act as building blocks that can be used to construct larger investment portfolios that meet the objectives of investors.

However, to invest into the selected index one needs to construct the portfolio, which approximates this index. This is called index tracking. Hence, the solution of the index tracking problem is a portfolio that approximates the index. This portfolio is called the tracking portfolio. It is easy to build a tracking portfolio on paper: simply buy the stocks in the same proportions as they appear in the index and hold this portfolio. However, there are some pitfalls in practice. The computation of an index value does not take into account transaction costs, the liquidity of the assets, or taxes. These factors can reduce the gains from indexing. To overcome these problems, various approaches have been developed.

The goal of this work is to make a comparison of the approaches to index tracking, highlighting their advantages and disadvantages, and identifying any problems with their application. On the basis of this comparison, a new method will be developed that improves on the existing ones.
We have developed a new approach fro financial index tracking based on Statistical Learning Theory.
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