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On Geometric and Arithmetic Portfolio Performance Indexes

Published online by Cambridge University Press:  19 October 2009

Marvin Rothstein
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Extract

The literature of Index numbers contains much discussion of the relative merits of geometric and arithmetic averages of prices and quantities. The controversy on this subject dates from the middle of the nineteenth century and is fully described by Crowe [2], In recent times both types of averages have been applied to security price relatives to measure the performance of groups of securities over time. The purpose of this paper is to demonstrate the properties of these security indexes and to show the relationships between them and an index based upon a more general type of average called the power mean. The concluding section of this paper contains the proof of an interesting and important limit property which provides the conceptual link between geometric and arithmetic security indexes.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 7 , Issue 4 , September 1972 , pp. 1983 - 1992
Copyright
Copyright © School of Business Administration, University of Washington 1972

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References

[1]Cohen, Kalman J., and Fitch, Bruce P.. “The Average Investment Performance Index.” Management Science, Vol. 12, No. 6, 1966, B195–B215.CrossRefGoogle Scholar
[2]Crowe, Walter R.Index Numbers. London: McDonald & Evans, Ltd., 1965.Google Scholar
[3]Fisher, Lawrence. “Some New Stock-Market Indexes.” Journal of Business, Vol. 39, No. 1, Part 2, 1966, pp. 191–225.CrossRefGoogle Scholar
[4]Fisher, Lawrence, and Lorie, James A.. “Rates of Return on Investments in Common Stocks.” Journal of Business, Vol. 37, No. 1, 1964, pp. 1–21.CrossRefGoogle Scholar
[5]Hardy, G.H.; Littlewood, J.E.; and Polya, G.. Inequalities. London: Cambridge University Press, 1934.Google Scholar
[6]Hartford Courant. “New Performance Index Published by Gutman,” February 14, 1971, p. 13C.Google Scholar
[7]Latané, Henry A., and Tuttie, Donald L.. Security Analysis and Portfolio Management. New York: The Ronald Press Co., 1970.Google Scholar
[8]Southern Connecticut Business Journal. “Performance Record To Be Published,” February 9, 1971, p. 4.Google Scholar
[9]Taylor, Angus E.Advanced Calculus. New York: Ginn and Co., 1955.Google Scholar