An algorithm for portfolio optimization with transaction costs

An algorithm for portfolio optimization with transaction costs

0.00 Avg rating0 Votes
Article ID: iaor2008808
Country: United States
Volume: 51
Issue: 11
Start Page Number: 1676
End Page Number: 1688
Publication Date: Nov 2005
Journal: Management Science
Authors: ,
Keywords: programming: convex
Abstract:

We consider the problem of maximizing an expected utility function of n assets, such as the mean-variance or power-utility function. Associated with a change in an asset's holdings from its current or target value is a transaction cost. This cost must be accounted for in practical problems. A straightforward way of doing so results in a 3n-dimensional optimization problem with 3n additional constraints. This higher dimensional problem is computationally expensive to solve. We present a method for solving the 3n-dimensional problem by solving a sequence of n-dimensional optimization problems, which accounts for the transaction costs implicitly rather than explicitly. The method is based on deriving the optimality conditions for the higher-dimensional problem solely in terms of lower-dimensional quantities. The new method is compared to the barrier method implemented in Cplex in a series of numerical experiments. With small but positive transaction costs, the barrier method and the new method solve problems in roughly the same amount of execution time. As the size of the transaction cost increases, the new method outperforms the barrier method by a larger and larger factor.

Reviews

Required fields are marked *. Your email address will not be published.