The index tracking problem with a limit on portfolio size

Abstract

For a passive fund manager tracking a benchmark, it is not uncommon to select some, and not all the assets in the index to his portfolio. In this thesis, we consider the problem of minimizing the tracking error under the mean--variance formulation which gives us a quadratic objective function. Our model includes a cardinality constraint, that puts a limit on the portfolio size. Our problem is a mixed integer nonlinear problem with a convex, quadratic objective function. For this NP-Hard problem, we apply continuous as well as Lagrangian relaxations. We illustrate a subgradient algorithm, modified to our problem. We also present two construction and three improvement heuristics to this problem. Our approaches are compared to the results of an exact and an interrupted solver and computational time is of interest. Our data sets range from 50-400 (500), with real constituent weights from S&P Dow Jones Indices for the largest set of index.