DISTRIBUTIONAL PROPERTIES AND TRANSFORMATION OF FINANCIAL RATIOS: THE IMPACT OF THE ACCOUNTING ENVIRONMENT Jussi Nikkinen and Petri Sahlstr¨ m o
This study investigates the distributional properties of ﬁnancial ratios and the usefulness of the Box and Cox (1964) power transformation in normalizing ﬁnancial ratios in different kinds of accounting environments. The results indicate that the Box-Cox power transformation can substantially improve the normality of ﬁnancial ratios. The transformation can completely remove the non-normality induced by skewness. However, some kurtosis remains after the transformation. The distributional properties and the usefulness of the transformation are not dependent on the accounting environment. Therefore, researchers can use same ﬁnancial ratios in different accounting environments. However, some caution is needed in the case of proﬁtability ratios that are substantially affected by the accounting practices and economic situation.
This paper examines distributional properties and the transformation of ﬁnancial ratios in different accounting environments. Many of the studies in accounting Advances in International Accounting Advances in International Accounting, Volume 17, 85–101 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0897-3660/doi:10.1016/S0897-3660(04)17005-0
¨ JUSSI NIKKINEN AND PETRI SAHLSTROM
rely on the assumption of normality of ﬁnancial ratios and this issue has therefore received a great deal of attention in accounting literature. Despite the required normality, ﬁnancial ratios are highly non-normal as reported for example, by Deakin (1976), Buijink and Jegers (1986), Ezzamel and Mark-Molinero (1990), and Kallunki (1998). Furthermore, these studies suggest that non-normality is an international phenomenon. Non-normality of ﬁnancial ratios may be caused by the lack of proportionality between the numerator and denominator of ﬁnancial ratios as Barnes (1982) shows. Non-normality of ﬁnancial ratios may also be caused by their deﬁnitions. Some ﬁnancial ratios such as quick ratio and current ratio are limited to be greater than zero and some ratios such as equity to total capital ratio have an upper limit of 100%. In addition, differences in accounting practices, in ﬁnancial characteristics of companies, in business culture and in economic situations across countries can be expected to affect the distributions of ﬁnancial ratios.1 The purpose of this study is to investigate the distributional properties of ﬁnancial ratios and the usefulness of the Box and Cox (1964) transformation in normalizing the distribution of ﬁnancial ratios in different accounting environments. For this purpose, the distributional properties of a set of commonly used accrual-based ﬁnancial ratios and market-based ﬁnancial ratios are analyzed in ten different countries. The countries are selected on the basis of the theoretical classiﬁcation system of ﬁnancial reporting practices by Nobes (1983, 1998). The accrual-based ﬁnancial ratios used in the study represent four key economic dimensions of a ﬁrm, i.e. proﬁtability, ﬁnancial leverage, liquidity and efﬁciency (see e.g. Foster, 1986). In addition to these ratios, a set of commonly used market-based ﬁnancial ratios is analyzed. The results of the study have important implications for researchers and ﬁnancial analysts since statistical tests and methodologies used in accounting studies and analyses often assume that ratios are normally distributed. Statistical tests such as the standard t- and F-tests, tests of equality of covariance matrices and the Box test for homogeneity of variance (Stevens, 1996) are affected by non-normality due to the skewness and kurtosis of the distributions (Barnes, 1987; Mardia, 1974). In addition, for example, the linear discriminant analysis is based on the assumption of multivariate normality (Eisenbeis, 1977). Furthermore, the statistical...
References: Ali, A., & Hwang, L. (2000). Country-speciﬁc factors related to ﬁnancial reporting and the value relevance of accounting data. Journal of Accounting Research, 38, 1–21. Amemiya, T. (1985). Advanced econometrics. Blackwell. Ball, R., Kothari, S. P., & Robin, A. (2000). The effect of international institutional factors on properties of accounting earnings. Journal of Accounting and Economics, 29, 1–51. Barnes, P. (1982). Methodological implications of non-normally distributed ﬁnancial ratios. Journal of Business Finance and Accounting, 9, 51–62. Barnes, P. (1987). The analysis and use of ﬁnancial ratios: A review article. Journal of Business Finance & Accounting, 14, 449–462. Bartov, E., Goldberg, S. R., & Kim, M.-S. (2001). The valuation-relevance of earnings and cash ﬂows: An international perspective. Journal of International Financial Management and Accounting, 12, 103–132. Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society (Series B), 26, 211, 252. Buijink, W., & Jegers, M. (1986). Cross-sectional distributional properties of ﬁnancial ratios in Belgian manufacturing industries: Aggregation effects and persistence over time. Journal of Business Finance & Accounting, 13, 337–363. Cheng, A., Liu, C. S., & Schaefer, T. (1996). Earnings permanence and the incremental information content of cash ﬂows from operations. Journal of Accounting Research, 34, 173–181. David, R., & Brierley, J. (1985). Major legal systems in the world today. London, UK: Stevens & Sons. Deakin, E. B. (1976). Distributions of ﬁnancial accounting ratios: Some empirical evidence. Accounting Review, 1, 90–96. Dechow, O. (1994). Accounting earnings and cash ﬂows as measures of ﬁrm performance: The role of accounting accruals. Journal of Accounting and Economics, 18, 3–42. Doupnik, T. S., & Salter, S. B. (1993). An empirical test of a judgmental international classiﬁcation of ﬁnancial reporting practices. Journal of International Business Studies, 24, 41–60. Eisenbeis, R. A. (1977). Pitfalls in the application of discriminant analysis in business, ﬁnance, and economics. Journal of Finance, 32, 875–900. Ezzamel, M., & Mar-Molinero, C. (1990). The distributional properties of ﬁnancial ratios in U.K. manufacturing companies. Journal of Business Finance and Accounting, 17, 1–29. Foster, G. (1986). Financial statement analysis. Englewood Cliffs, NJ: Prentice-Hall. Guenther, D. A., & Young, D. (2000). The association between ﬁnancial accounting measures and real economic activity: A multinational study. Journal of Accounting and Economics, 29, 53–72. Hung, M. (2001). Accounting standards and value relevance of ﬁnancial statements: An international analysis. Journal of Accounting and Economics, 30, 401–420. Judge, G. G., Lee, T.-C., & Hill, R. C. (1985). Introduction to the theory and practice of econometrics. Wiley.
Distributional Properties and Transformation of Financial Ratios
Kallunki, J.-P. (1998). The impact of transformations on the distributional properties of ﬁnancial ratios: Finnish evidence. Advances in International Accounting, 11, 155–168. Leuz, C., Dhananjay, N., & Wysocki, P. D. (2003). Earnings management and investor protection: An international comparison. Journal of Financial Economics (forthcoming). Mardia, K. V. (1974). Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies. Sankya, 36, 115–128. Nobes, C. W. (1983). A judgmental international classiﬁcation of ﬁnancial reporting practices. Journal of Business Finance and Accounting, 10, 1–19. Nobes, C. W. (1998). Towards a general model of the reasons for international differences in ﬁnancial reporting. Abacus, 34, 162–187. Nobes, C. W., & Parker, R. (2000). Comparative international accounting (6th ed.). London: Pearson Education Limited. Rees, W. (1998). A valuation based test of accounting differences in Europe. Working Paper. University of Glasgow. Rummel, R. J. (1970). Applied factor analysis. Evanston: Northwestern University Press. Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality. Biometrika, 52, 591–611. Snedecor, G. W., & Cochran, W. G. (1989). Statistical methods. Iowa State University Press. Spitzer, J. J. (1982). A primer on Box-Cox estimation. Review of Economics and Statistics, 64, 307–313. Stevens, J. (1996). Applied multivariate statistics for the social sciences. NJ: Lawrence Erlbaum. Watson, C. J. (1990). Multivariate distributional properties, outliers, and transformation of ﬁnancial ratios. Accounting Review, 65, 682–695. Weetman, P., & Gray, S. J. (1991). A comparative international analysis of the impact of accounting principles on proﬁts: The USA vs. the U.K., Sweden and the Netherlands. Accounting and Business Research, 21, 363–379. Wilk, M. B., Shapiro, S. S., & Chen, H. J. (1968). A comparative study of various tests for normality. Journal of the American Statistical Association, 63, 1343–1372.
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