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# On the Stable Paretian Behavior of Stock-Market Prices

Der-Ann Hsu, Robert B. Miller and Dean W. Wichern
Journal of the American Statistical Association
Vol. 69, No. 345 (Mar., 1974), pp. 108-113
DOI: 10.2307/2285507
Stable URL: http://www.jstor.org/stable/2285507
Page Count: 6
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## Abstract

In this article we present some empirical evidence which indicates that attempts to represent the probability distribution of the rates of return on common stocks by a member of the stable Paretian family of distributions, with $1 < \alpha < 2$, may be misleading and in fact may not produce an adequate fit to observed rates of return. We offer an alternative probability model for describing rates of return based on the hypothesized phenomenon of a changing variance. We test the "goodness of fit" of our model vis-a-vis a stable Paretian model for several series of rates of return. Finally we propose an extension of the stability test of Fama and Roll [6].

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