Distributional Properties and Transformation of Financial Ratios

Pages: 20 (7479 words) Published: October 12, 2010
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




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.
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Financial Ratios Essay
  • Financial ratios Essay
  • financial ratio Essay
  • Course: Financial Ratios and Ratio Essay
  • Financial Ratio Essay
  • Essay about financial ratios
  • Financial Ratios Essay

Become a StudyMode Member

Sign Up - It's Free