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Geometric Mean Approximations of Individual Security and Portfolio Performance**

Published online by Cambridge University Press:  19 October 2009

William E. Young  and
Robert H. Trent
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Extract

The objectives of this paper are to derive the relationship of the geometric mean of a distribution of positive values to the conventional first four moments — arithmetic mean, variance, absolute skewness, and absolute kurtosis — and to empirically evaluate certain approximations involving these four moments for estimating the geometric means of monthly and annual holding period returns for individual stocks and for portfolios. The geometric mean is shown to be positively related to the arithmetic mean and absolute skewness and negatively related to variance and absolute kurtosis. In the case of a normal distribution a very good approximation to the geometric mean is revealed to be a function of just the arithmetic mean and variance. Additionally, empirical evidence indicates that even though a number of the monthly and annual distributions deviate significantly from normality, the approximation involving only the mean and variance produces quite accurate estimates of the geometric means of these distributions.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 4 , Issue 2 , June 1969 , pp. 179 - 199
Copyright
Copyright © School of Business Administration, University of Washington 1969

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References

1.Arditti, D., “Risk and the Required Return on Equity”, The Journal of Finance, XXII (March, 1967), p. 19.Google Scholar
2.Bernoulli, D., “Exposition of a New Theory on the Measurement of Risk”, trans. Sommer, Louise, Econometrica, 22 (January, 1954).CrossRefGoogle Scholar
3.Cootner, P. H., “Stock Market Indexes — Fallacies and Illusions,” The Commercial and Financial Chronicle (September 29, 1966).Google Scholar
4.Fisher, L., “Some New Stock Market Indexes”, The Journal of Business, XXXIX (January, 1966), pp. 191–225.CrossRefGoogle Scholar
5.Fisher, L., and Lorie, J. H., “Rates of Return on Investments in Common Stocks”, The Journal of Business, XXXVIII (January, 1964), PP. 1–21.CrossRefGoogle Scholar
6.Latané, H. A., “Rational Decision Making in Portfolio Management,” Ph.D. Thesis, University of North Carolina, 1957, Chapel Hill, North Carolina.Google Scholar
7.Latané, “Criteria for Choice Among Risky Ventures”, The Journal of Political Economy, LXVII, No. 2 (April, 1959), pp. 144–155.CrossRefGoogle Scholar
8Latané, , “Investment Criteria: A Three Asset Portfolio Balance Model”, The Review of Economics and Statistics, XLV, No. 4 (November, 1963), pp. 427–430.CrossRefGoogle Scholar
9.Latané, , and Tuttle, D. L., “Criteria for Portfolio Building”, The Journal of Finance, XXII (September, 1967), p. 361.Google Scholar
10.Markowitz, H., “Portfolio Selection”, The Journal of Finance, VII (March, 1952), pp. 77–91.Google Scholar
11.Markowitz, H., Portfolio Selection: Efficient Diversification of Investments (New York: John Wiley and Sons, 1959).Google Scholar
12.Pearson, E. S., and Hartley, H. O., Biometrika Tables for Statisticians, Volume 1 (Cambridge: The University Press, 1954).Google Scholar
13.Renshaw, E. F., “Portfolio Balance Models in Perspective: Some Generalizations That Can Be Derived from the Two Asset Case”, Journal of Financial and Quantitative Analysis, II, No. 2 (June, 1967), pp. 138–139.Google Scholar
14.Savage, L. J., The Foundations of Statistics. (New York: John Wiley and Sons, 1954).Google Scholar
15.Sharpe, W. F., “Portfolio Analysis”, Journal of Financial and Quantitative Analysis, II, No. 2 (June, 1967), pp. 74–76.Google Scholar
16.Yule, G. U., and Kendall, M. G., An Introduction to the Theory of Statistics (New York: Hafner Publishing Company, 1950), p. 150.Google Scholar