MINIMAL COST INDEX TRACKING UNDER NONLINEAR TRANSACTION COSTS AND MINIMAL TRANSACTION UNIT CONSTRAINTS

Abstract

Index tracking is a very common and popular approach in portfolio management. When there is neither (nonconvex) transaction costs nor minimal transaction unit constraints, the problem can be formulated as a convex least square problem, so that it can be solved by standard methods. However, when the transaction cost is nonconvex and not negligible, or if there is a minimal unit constraint on the amount of transaction, the problem becomes a nonconvex minimization problem with discrete variables. In this paper, we will propose a branch and bound algorithm for solving this class of problems and show that it can solve an index tracking problem of practical size in a reasonable amount of computation time.