Optimal trading of a security when there are taxes and transaction costs

We study the problem of investing in securities in order to maximize the after-tax rate of return. We consider a single stock modeled as geometric Brownian motion along with the objective of maximizing the long-run growth rate of after-tax wealth. We show that it is optimal not only to cut short the losses, but also the profits, even though there is no distinction between short and long term tax rates. This surprising result may be due to the possibility of using the tax system to reduce after-tax volatility.