Knowledge that Transforms

This article will concern itself with the various techniques for selecting portfolios of securities. It should be made clear at the outset that a good portfolio is not just an amalgamation of a number of “good” stocks and bonds. Rather, it is an integrated whole, each security complementing the others. Thus, the investment manager must consider both the characteristics of the individual securities and the relationships between those securities. Until recently there was no comprehensive theoretical framework for the analysis of the latter aspect of the portfolio problem. Intuitive judgment and experience were the guidelines used by investment managers.

The Markowitz analysis of efficient portfolio selection, which can be interpreted as solving the quadratic-programming problem of minimizing the variance of a normal variate subject to each prescribed mean value, easily can be generalized (in the special case of independently distributed investments) to the concave-programming problem of minimizing the “dispersion” of a stable Pareto-Lévy variate subject to each prescribed mean value. Some further generalizations involving interdependent distributions will also be presented here.

“Don't put all your eggs in one basket, ” is a familiar adage. Economists, such as Marschak, Markowitz, and Tobin, who work only with mean income and its variance, can give specific content to this rule—namely, putting a fixed total of wealth equally into independently, identically distributed investments will leave the mean gain unchanged and will minimize the variance.

Papers and Proceedings of the Second Annual Meeting of the Western Finance Association, Berkeley, August 25-26, 1966, The Journal of Financial and Quantitative Analysis, Vol. 1, No. 4 (Dec., 1966), pp. 94-125

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John S. Y. Chiu, Errata: A Simulation Study of Effects of Multicollinearity and Autocorrelation on Estimates of Parameters, The Journal of Financial and Quantitative Analysis, Vol. 1, No. 4 (Dec., 1966), pp. 126-127

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