In this paper, we compare the robustness in application of the Gaussian assumption of security return distributions to the robustness of the general stable assumption. Using actual stock return data to simulate the “real world, ” a stock market is constructed in which stock returns conform to a Gaussian distribution as well as to a stable Pareto-Levy distribution. Using these two sets of stock returns, efficient frontiers are generated under both assumptions of parametric environments. It is shown that the Gaussian assumption, and its incumbent statistical techniques, is preferable to the general stable assumption.

George M. Frankfurter, Joanne M. Hill, A Normative Approach to Pension Fund Management, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 4, Proceedings of 16th Annual Conference of the Western Finance Association, June 18-20, 1981, Jackson Hole, Wyoming (Nov., 1981), pp. 533-555

Where rates of return are perfectly correlated, risk reduction through diversification cannot be achieved. Where rates of return are less than perfectly correlated, however, then, to the extent that these interrelationships can be known, modern portfolio theory provides a framework in which risk reduction through diversification can be achieved. Markowitz was the first to give rigorous content to the concept of portfolio diversification [14], and to introduce a formulation for treating portfolio selection as a mathematical optimization problem. In order to facilitate application of his own covariance approach, Markowitz first suggested [15, pp. 96–101], and Sharpe later developed a market model formulation according to which it is assumed that the rates of return on various securities “are related only through common relationships with some basic underlying factor” [18, p. 281]. More than 25 years have passed since Markowitz introduced his original formulation, and the literature dealing with the portfolio selection problem that he identified has grown considerably since then. Unfortunately, many problems remain which prevent full and effective implementation of this framework for investment analysis.

In this study, alternative real and simulated market indexes are examined as proxies for the “common factor” required by the Sharpe portfolio selection model [13]. The ex post performance of efficient and well-diversified portfolios generated by the model based on the different indexes is compared. The results indicate no significant difference in performance between real and simulated indexes, although the degree of diversification is much lower for portfolios based on indexes which relate well to the universe of securities. It is also shown that portfolios which are selected according to the Sharpe model (regardless of the index) outperform strategies which call for investing in the market portfolio.

John C. G. Boot, George M. Frankfurter, The Dynamics of Corporate Debt Management, Decision Rules, and Some Empirical Evidence, The Journal of Financial and Quantitative Analysis, Vol. 7, No. 4 (Sep., 1972), pp. 1957-1965