Accounting identities and the distribution of ratios

Abstract

This study describes the influence of accounting identities on the statistical distribution of financial ratios. It is supported by evidence on cross-section distributions of raw numbers and ratios extracted from accounting reports of UK industrial firms for the period 1983–1987. First, this study recalls that where raw numbers are lognormally distributed, then ratios are expected to be positively skewed. Accordingly, the fact requiring an explanation is why some ratios are symmetrical or even negatively skewed, not why the distribution of ratios is positively skewed. This study then shows that apparently symmetrical ratios occur because accounting identities act as external boundaries, constraining the long tail of their otherwise skewed distribution to become much smaller. Ratios that are symmetrical or negatively skewed simply reflect the existence of these boundaries. They revert to positive skewness after being inverted, thus making it difficult to accept the hypothesis that the skewness of ratios stems from non-proportionality. Since bounded ratios may induce misleading results when used for calculating confidence intervals orPvalues, a procedure is suggested to avoid constraints where necessary.