A Monte Carlo Investigation of Characteristics of Optimal Geometric Mean Portfolios

We began this paper by posing four questions about the characteristics of optimal geometric mean portfolios. Tentative answers to these questions were obtained from an examination of the solutions to a relatively large number of geometric mean portfolio problems generated from a Monte Carlo simulation of ex-ante security return data. The results of this examination can be summarized as follows. First, the number of risky securities contained in an optimal geometric mean portfolio depends on one's expectations concerning future market conditions and on the conditions under which borrowing is permitted. If all capital must be invested, the investor who believes the market will fall should invest in just one security, he who believes the market will remain unchanged should diversify among two securities, while he who believes the market will rise should diversify among four to seven securities. In the event that some capital must be withheld from investment, the investor who believes the market will rise and who can borrow on reasonable terms will again diversify among four to seven securities, choosing the same securities in the same relative proportions as in the preceding situation. Should the investor be permitted neither to borrow nor to invest all his capital, his best portfolio consists of two to four securities, assuming he expects the market to rise.