Optimal Diversification: Is It Really Worthwhile?

Executive Summary. Recent research has demonstrated that the Markowitz efficient frontier is fuzzy and may consist of many statistically indistinguishable frontiers. Therefore, it opens the possibility that an efficient portfolio developed by mean-variance analysis may not be any more efficient than a naively diversified portfolio. Using an efficiency test developed by Gibbons, Ross, and Shanken (1989), we find evidence to support that an efficient portfolio is statistically more efficient than a corresponding naively diversified portfolio when the portfolio formation period is the same as the period used for testing the efficiency difference. However, no evidence is found to support that an efficient portfolio is statistically more efficient than a corresponding naively diversified portfolio when the portfolio formation period differs from the test period. Thus, in practical terms, efficient portfolios may not be superior to naively diversified portfolios in a statistical sense.