Mean–variance combining rules that outperform naïve diversification

Abstract

The mean–variance framework developed by Markowitz (1952). Portfolio selection, The Journal of Finance, 7(1), 77–91 is still the major model used nowadays in asset allocation and active portfolio management. However, the estimated mean–variance rules often fail to deliver superior performance compared with the simple naïve rule (the equally weighted portfolio) due to the problem of estimation errors. In this paper, I propose a portfolio construction method that is effective in dealing with estimation errors in the optimization process. Particularly, I specify the portfolio weights as an optimal combination of the equally weighted portfolio and a sample zero-investment portfolio. I show analytically that the proposed method alleviates the problem of estimation errors and dominates naïve diversification. I suggest two implementable versions of the combining method and show, empirically, their good performances relative to the naïve rule. The newly developed rules work well, particularly, for portfolios with a medium and high number of assets. Moreover, the outperformance persists generally even in the presence of transaction costs. Since the combinations are theory-based, my study may be interpreted as reaffirming the usefulness of the Markowitz portfolio theory in practice.