Optimal benchmark tracking with small portfolios - Using the diversity measure to deal with constraints on number of stocks in a portfolio.

In this article the authors examine the problem of index tracking. Market capitalization-weighted indexes can be tracked by buying all the constituents at their actual weights, but the higher transaction and administration costs involved with this approach largely make this a non-practical solution. Minimizing a portfolio's tracking error with respect to the benchmark with a relatively small number of stocks is the central focus of the authors. They describe current portfolio optimization methods for the problem, and present a new mathematical optimization method that not only gives better results but also may be able to tackle other problems in portfolio optimization. The findings can easily be extended to solve portfolio construction problems that incorporate expected returns, variance of returns, transaction costs, and additional constraints.