Haim Levy and Moshe Levy
Even after more than six decades since the publication of the breakthrough article by Markowitz, the Mean–Variance framework is still the most commonly employed portfolio management tool. Yet, as portfolio managers know all too well, the optimal diversification and the induced performance are very sensitive to potential parameter estimation errors. This paper suggests two new and related portfolio optimization methods to deal with this problem: the Variance-Based Constraints (VBC), and the Global Variance-Based Constraints (GVBC) methods. By the VBC method the constraint imposed on the weight of a given stock is inversely proportional to its standard deviation: the higher a stock’s sample standard deviation, the higher the potential estimation error of its parameters, and therefore the tighter the constraint imposed on its weight. GVBC employs a similar idea, but instead of imposing a sharp boundary constraint on each stock, a quadratic “cost” is assigned to deviations from the naive 1/N weight, and a single global constraint is imposed on the total cost of all deviations. We find that these two new methods outperform existing methods. These results are obtained for two different data sets, and are also robust to the number of assets under consideration and to the number of return observations.