Minimizing tracking error while restricting the number of assets

Thomas F. Coleman, Yuying Li and Jay Henniger

Journal of Risk

Abstract: ABSTRACT Tracking error minimization is commonly used by the traditional passive fund managers as well as alternative portfolio (for example, hedge fund) managers. We propose a graduated non-convexity method to minimize portfolio tracking error with the total number of assets no greater than a specified integer K. The solution of this tracking error minimization problem is a global minimizer of a minimization problem with a discontinuous counting function in a constraint. We attempt to track the globally minimal tracking error portfolio by approximating the discontinuous counting function with a sequence of continuously differentiable non-convex functions, a graduated non-convexity process. We discuss the advantages of this approach, present numerical results, and compare it with two methods from recent literature.

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