Distributional properties of the book to market ratio and their implications for empirical analysis

Abstract

Financial accounting standards, government regulatory requirements and the capital market assumptions on which received asset pricing theory is based are used to develop a linear-quadratic diffusion process under which the unconditional probability density of the book to market ratio of equity will be either Gaussian (that is, normal) or the Pearson Type IV. Empirical analysis based on book to market ratios drawn from the Compustat North America Standard & Poor’s Fundamentals Quarterly Database shows the Pearson Type IV probability density provides a superior fit to firm book to market ratio sample distributions when compared to the Gaussian density with around two-thirds of firm sample book to market ratio distributions failing standard Gaussian goodness of fit tests. Moreover, around one in eight of the firm book to market ratio sample distributions return parameter estimates for the Pearson Type IV which are compatible with a non-convergent (that is, undefined) variance and higher moments. It is also shown how the inverse hyperbolic sine transformation can be used to mitigate the adverse consequences of heteroscedasticity and non-convergent moments in empirical work involving the book to market ratio.