A Paradox in the Markowitz Mean-Variance Model with Transaction Costs

Abstract

This article is to show a paradox in the mean variance model for portfolio selection when the transaction costs are included. While a transaction cost decreases the mean of the rate of return of an investment, it also decreases its variance. Thus, for individuals with strong risk aversion, it is possible that the reduction in the variance would make the investment more attractive, even though the mean is lower. That is to say that, in the mean-variance framework, the transaction costs may increase the utility of some individuals. This is in conflict with a basic assumption that individuals are non-satiable.

Keywords: variance model, portfolio selection, risk aversion, transaction cost

JEL Classification: G10, G11