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

Lookup NU author(s): Dr Xiaojing Song

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Abstract

Financial accounting standards, government regulatory requirements and the capitalmarket assumptions on which received asset pricing theory is based are used todevelop a linear-quadratic diffusion process under which the unconditional probabilitydensity 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 fromthe Compustat North America Standard & Poor’s Fundamentals Quarterly Databaseshows the Pearson Type IV probability density provides a superior fit to firm book tomarket ratio sample distributions when compared to the Gaussian density with aroundtwo-thirds of firm sample book to market ratio distributions failing standard Gaussiangoodness of fit tests. Moreover, around one in eight of the firm book to market ratiosample distributions return parameter estimates for the Pearson Type IV which arecompatible 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 mitigatethe adverse consequences of heteroscedasticity and non-convergent momentsin empirical work involving the book to market ratio.

Publication metadata

Author(s): Ma D, Melia A, Song X, Tippett M, Van der Burg J

Publication type: Article

Publication status: Published

Journal: The European Journal of Finance

Year: 2023

Volume: 29

Issue: 11

Pages: 1330-1353

Online publication date: 08/11/2022

Acceptance date: 05/09/2022

Date deposited: 09/10/2023

ISSN (print): 1351-847X

ISSN (electronic): 1466-4364

Publisher: Routledge

URL: https://doi.org/10.1080/1351847X.2022.2125818

ePrints DOI: 10.57711/rmz6-d209

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