  We derive new results related to the portfolio choice problem for power and
logarithmic utilities. Assuming that the portfolio returns follow an
approximate log-normal distribution, the closed-form expressions of the optimal
portfolio weights are obtained for both utility functions. Moreover, we prove
that both optimal portfolios belong to the set of mean-variance feasible
portfolios and establish necessary and sufficient conditions such that they are
mean-variance efficient. Furthermore, an application to the stock market is
presented and the behavior of the optimal portfolio is discussed for different
values of the relative risk aversion coefficient. It turns out that the
assumption of log-normality does not seem to be a strong restriction.
