Limitation of Ratio

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  • Topic: Financial ratio, Skewness, Normality test
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DISTRIBUTIONAL PROPERTIES AND TRANSFORMATION OF FINANCIAL RATIOS: THE IMPACT OF THE ACCOUNTING ENVIRONMENT Jussi Nikkinen and Petri Sahlstr¨ m o
ABSTRACT
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.

INTRODUCTION
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

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¨ 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...
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