Geometric Mean Approximations of Individual Security and Portfolio Performance**

William E. Young and Robert H. Trent

Journal of Financial and Quantitative Analysis, 1969, vol. 4, issue 2, 179-199

Abstract: 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.

Date: 1969
References: Add references at CitEc
Citations: View citations in EconPapers (20)

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:jfinqa:v:4:y:1969:i:02:p:179-199_01

Access Statistics for this article

More articles in Journal of Financial and Quantitative Analysis from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().