The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which transaction costs are incurred to rebalance an investment portfolio. The Markowitz framework of mean-variance efficiency is used with costs modelled as a percentage of the value transacted. Each security in the portfolio is represented by a pair of continuous decision variables corresponding to the amounts bought and sold. In order to properly represent the variance of the resulting portfolio, it is necessary to rescale by the funds available after paying the transaction costs. We show that the resulting fractional quadratic programming problem can be solved as a quadratic programming problem of size comparable to the model without transaction costs. Computational results for two empirical datasets are presented.
Slightly revised Dec 6, 2002, to allow for the presence of homogeneous constraints.
Math Sciences, RPI, Troy NY 12180, USA. http://www.rpi.edu/~mitchj/papers/transcosts.html