Portföljoptimering med courtageavgifter

Sammanfattning: Ever since it was first introduced in an article in the Journal of Finance 1952, Harry Markowitz’ mean - variance model for portfolio selection has become one of the best known models in finance. The model was one of the first in the world to deal with portfolio optimization mathematically and have directly or indirectly inspired the rest of the world to develop new portfolio optimization methods. Although the model is one of the greatest contributions to modern portfolio theory, critics claim that it may have practical difficulties. Partly because the Markowitz model is based on various assumptions which do not necessarily coincide with the reality. The assumptions which are based on the financial markets and investor behavior contain the simplification that there are no transaction costs associated with financial trading. However, in reality, all financial products are subject to transaction costs such as brokerage fees and taxes. To determine whether this simplification leads to inaccurate results or not, we derive an extension of the mean-variance optimization model which includes brokerage fees occurred under the construction of an investment portfolio. We then compare our extension of the Markowitz model, including transaction costs, with the standard model. The results indicate that brokerage fees have a negligible effect on the standard model if the investor's budget is relatively large. Hence the assumption that no brokerage fees occur when trading financial securities seems to be an acceptable simplification if the budget is relatively high. Finally, we suggest that brokerage fees are negligible if the creation of the portfolio and hence the transactions only occurs once. However if an investor is active and rebalances his portfolio often, the brokerage fees could be of great importance.