On the optimal selection of portfolios under limited diversification - Sankaran, Jayaram K.; Patil, Ajay A. (Journal of Banking & Finance, 1999)
We address the problem of selecting portfolios which maximize the ratio of the average excess return to the standard deviation, among all those portfolios which comprise at most a pre-specified number, k, of securities. Under the assumptions of constant pairwise correlations and no short-selling, we argue that the simple ranking procedure of Elton, Gruber, and Padberg effectively solves the problem for all values of k, and that as a function of k, the optimal ratio increases at a decreasing rate. We also clarify why further generalization or extension of our results to other situations is improbable.