INVESTMENT DIVERSIFICATION UNDER UNCERTAINTY: AN EXAMINATION OF THE NUMBER OF SECURITIES IN A DIVERSIFIED PORTFOLIO*

THIS DISSERTATION is a study of the practical limits of common-stock diversification: in particular, an empirical study of the approximate number of securities needed for diversification. The paper examines the hypothesis that a point is reached where the addition of more securities to a common-stock portfolio shows little or no improvement in the portfolio's return, variability, and return over risk. Tests are applied, based on the criterion of return and variance of return, to assess the relative performance of mutual funds, Standard and Poor's 425 Industrials, and the cluster portfolios generated by the computer. An initial-sample universe of 140 securities generally representing the largest domestic corporations in sales, assets, or market value was selected for detailed analysis. The concept of meaningful diversification, based on the Markowitz formulation of return and variance of return, implies that the benefits from diversification are usually greatest when securities with substantially differing price movements-implying low correlation-are combined in a portfolio. In most of the literature on the subject, this is tantamount to saying that diversification among highly correlated securities is not meaningful in that little is gained in the returns-and-variance-of-returns sense because the variance of the portfolio tends to be linear with the return. However, it is shown that, due to scale factors, perfectly correlated securities can have materially differing price performance. To mitigate this result, an existing computer program with an objective function (object stability) was used in lieu of factor-analytic techniques to form clusters with relatively high "within"-group similarity and relatively low "between"-group similarity. The clusters (groups) formed the basic division of securities for further analysis. The procedure for generating each portfolio was to select one stock from each cluster. By varying the degree of similarity required within a group before combining securities it was possible to vary the number of clusters and, ultimately, the number of securities in a portfolio at will. The performance of the cluster and random portfolios was compared to the performance of Standard and Poor's 425 Industrials and thirty representative mutual funds on an ex-post (1960-63) and ex-ante (1964-65) basis. The results of the study showed that there are definite limitations concerning the ability of a large number of common stocks to reduce the variability of return or otherwise to give superior return-variance performance. Using analysis of variance and other statistical tests it was found that relatively few securities-less than twenty-can give about as good diversification as possible from investment in common stocks. Even fewer securities, between six and eleven, seemed to give noticeably good average investment performance when compared to all other types of common-stock funds. Further statistical tests showed that the relative performance, corrected for bias, of the average randomly selected fund purchased on a buy-and-hold basis was as good or better than the average mutual-fund performance of Standard and Poor's 425 Industrials.