Algorithms for index tracking

The problem of selecting a portfolio of securities to track the performance of a given index is formulated in mathematical programming terms. Optimal weights for given sets of included securities are obtained using linear complementarity algorithms, and various methods of search among neighbouring sets of securities are considered. The problem of local optima is considered, and various methods, including simulated annealing, are suggested for overcoming this. The solution depends on estimation of the covariance matrix and expected returns for the constituent securities; tracking of the FT-SE 100-share index for the calendar year 1988 is solved using various estimation techniques.