The Distribution of Financial Ratios—A Note

Three competitive distributions are offered by the literature to explain the non-normality and skewness of the cross-sectional distribution of financial ratios: the mixture of normal distributions, the lognormal distribution, and the gamma distribution. Using a new technique, this paper shows that the lognormal distribution and the gamma distribution are not supported by the empirical evidence. Although these two distributions indeed capture skewness, they do not portray the correct shape of the distributions. The non-normal stable Paretian distribution seems to be good candidate to describe the distribution of financial ratios.

ANOTHER LOOK AT EVIDENCE ON THE DISTRIBUTION OF CERTAIN SPECULATIVE PRICES

Benoit Mandelbrot suggests that prices of certain commodities follow stable Paretian distribution laws. Our results indicate that ARCH-type models fit some Mandelbrot time series fairly well. In other cases, tests for nonlinear dependence and chaos reject the ARCH specification. However, the patterns of dependence exhibited by these data are generally not consistent with the hypothesis that they are generated by a chaotic dynamic process.