Optimal portfolio selection for the small investor considering risk and transaction costs

A direct application of classical portfolio selection theory is problematic for the small investor because of transaction costs in the form of bank and broker fees. In particular, minimum fees force the investor to choose a comparatively rather small selection of assets. The existence of transaction costs leads to an optimization problem that juxtaposes those costs against the risk costs that arise with portfolios consisting of only a few assets. Despite the non-convex and, thus, complex optimization, an algorithmic solution turns out to be very fast and precise. An empirical study shows that, for smaller investment volumes, transaction costs dominate risk costs so that optimal portfolios contain only a very small number of assets. Based upon these results, the cost-effectiveness of direct investments is compared to alternative vehicles, particularly index certificates and exchange-traded funds, depending on the level of invested wealth.