Selecting a discrete portfolio

We study the problem of selecting an optimal portfolio out of a finite set of available assets. Assets are characterized by their expected returns and the covariance matrix, and investors are assumed to have a mean–variance utility, that is, their utility function is linear in the mean and variance of the portfolio they hold. When assets are negatively correlated, or even when a slightly more general condition is satisfied, we provide an algorithm for selecting an optimal portfolio. We illustrate the usefulness of this algorithm by some comparative statics result. When assets can be positively correlated, we deliver a negative result regarding the existence of useful algorithms for selecting an optimal portfolio.