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General Proof that Diversification Pays**

Published online by Cambridge University Press:  19 October 2009

Paul A. Samuelson
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Extract

“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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 2 , Issue 1 , March 1967 , pp. 1 - 13
Copyright
Copyright © School of Business Administration, University of Washington 1967

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References

1. Makower, H. and Marschak, J., “Assets, Prices, and Monetary Theory,” Economica N.S. (Vol. V, 1938), pp. 261–288Google Scholar. Markowitz, Harry M., “Portfolio Selection,” The Journal of Finance (Vol. VII, 1952), pp. 77–91Google Scholar and Portfolio Selection: Efficient Diversification of Investments (New York: John Wiley & Sons, 1959)Google Scholar; Tobin, James, “Liquidity Preference as Behavior Towards Risk,” Review of Economic Studies (Vol. XXV, 1958), pp. 65–86Google Scholar. The path-breaking article, Domar, E. D. and Musgrave, R. A., “Proportional Income Tax and Risktaking,” Quarterly Journal of Economics (Vol. LVII, 1944), pp. 389–422Google Scholar replaces variance by risk of loss (mean absolute loss) as dispersion parameters to be avoided. (This paper is reprinted in A.E.A. Selected Readings in Fiscal Policy and Taxation (Homewood, Ill.: Irwin, 1959)Google Scholar.

2. Samuelson, P. A., “A Fallacy in the Interpretation of Pareto's Law of Alleged Constancy of Income Distribution,” Essays in Honor of Marco Fanno, ed., Bagiotti, Tullio, (Padua, Cedam-Casa Editrice Dott. Antonio Milani, 1966), pp. 580–584Google Scholar.

3. Raiffa, Howard, unpublished Harvard Business School memos; Marcel K. Richter, “Cardinal Utility, Portfolio Selection and Taxation,” Review of Economic Studies (Vol. XXVII, 1959), pp. 152–166Google Scholar; Brown, E. C., “Mr. Kaldor on Taxation and Risk Bearing,” Review of Economic Studies (Vol. XXV, 1957), pp. 49–52Google Scholar; Hicks, J. R., “Liquidity,” Economic Journal (Vol. LXXII, 1962), pp. 787–802Google Scholar, depicts a rediscovery of some of the Markowitz theory. Also see Lintner, John, “Valuation of Risk Assets,” Review of Economics and Statistics (Vol. XLVII, 1965), pp. 13–37Google Scholar, and “Optimum Dividends and Uncertainty,” Quarterly Journal of Economics (Vol. LXXVIII, 1964), pp. 49–95Google Scholar and unpublished appendix.