بررسي نحوه‌ي توزيع آماري نسبت هاي مالي در شركت هاي پذيرفته شده در بورس اوراق بهادار تهران

Investigating Statistical Distribution of Financial Ratios of Accepted Companies in Tehranʹs Stock Exchange

Introduction The use of financial ratios in a variety of performance evaluation and decision-making contexts is an increasingly important area of accounting research and practice. While many of the ratio applications employ methodology that relies on either univariate or multivariate normality assumptions and parametric tests procedures, surprisingly little is known about the distributional properties of financial ratios. In other words, such analyses assume that financial ratios or some transform of them, are normally distributed and satisfy certain stationarity assumptions. Recent empirical research casts doubt on these assumptions, even when the data are transformed and a significant number of outliers are eliminated in an effort to induce normality. In addition, financial ratio distributions could provide us with very important information about the behavior of firms, and they would be worth studying in that context, quite apart from their significance for statistical analysis. Given the limited knowledge concerning the distributional properties of financial ratios and the widespread use of ratios in a variety of decision contexts, more research is clearly needed. Research questions and hypothesis This study investigates the distributional characteristics of financial ratios and usefulness of deleting outliers and transforming data in normalizing financial ratios. Possessing due information on this area would prove effective in selecting the appropriate statistical instrument. Evidence on the distribution of financial statement numbers would also turn out to be a stimulus to subsequent research that promotes better understanding of the properties of financial statement data. A main area of statistical difficulty in the analysis of financial ratios is that of selecting appropriate techniques with regard to ratio distributions. When financial ratios are used, we assume that the data distribution is normal and use parametric tests. However, there seems not to be sufficient information and this calls for more research studies to be done on this area. Financial ratios can take any of the number of the distributional forms such as the gamma, Chi-square and normal. But normal distribution, among the others, is more appealing to researchers because many statistical tests invoke normality in the tested distribution. For this reason many researchers focus on normality in their analysis of the distribution of financial ratios. Because of this, the main question of this study is that, whether financial ratios follow normal distribution or not and the investigation of the effects of outliers and data transformation on the distributional characteristics of financial ratios. Based on these questions three main hypotheses and twelve minor ones were designed and investigated in the present study. Our sample included 145 companies which selected among the seven big industries of Tehranʹs Stock Exchange. Methods The present study makes use of kolmogorov- Smironov and Shapiro-Wilk tests for testing the hypothesis for the sample in the period between 1380-1384. We use Chebyshevʹs inequality for identifyingʹ and deleting the outliers and log normal, cube root and square root methods for data transformation. The initial data analysis involved investigating the histograms of each ratio and various statistics such as the mean, the median, the range, the standard deviation, the upper and lower ten percentiles, and the skewness and kurtosis coefficients. This analysis was performed on the complete and reduced data sets (that is, after deleting outliers) and after transforming data. Our sample included 145 companies which selected among the seven big industries of Tehranʹs Stock Exchange. Our sample is restricted to only those companies with the same year end. Results The result of this paper shows that assumption of normality for financial accounting ratios werenʹt reasonable and acceptable. Even after deleting the outliers and transforming data, no normal distribution of financial ratios was observed. Nevertheless, deleting the outliers and data transformation had a great impact on the reduction of skewness and kurtosis coefficient of financial ratios and made the financial distribution nearer to normal distribution. Discussion and Conclusion The aim of this paper is to provide empirical evidence on the statistical distributions of financial ratios. Evidence on this area is important because it guides the choice of statistical tools. Empirical evidence for the distribution of financial ratios seems to indicate non-normality caused by varying degree of skewness and the existence of extreme outliers. But even after deleting the outliers and transforming data, no normal distribution of financial ratios was observed. In other words ratios are not distributed normally in raw, truncated or transformed forms, but deleting outliers and transformation improve goodness- of- fit to the normal distribution. There are a number of reasons why distributions of financial ratios cannot be normal. The first is that it is in fact a distribution of the quotient of two variables, which have their own distribution, does not lead to normal distribution. The second reason is that there will, most of the time, be outside pressure on firm management to keep at least some of the ratios within certain acceptable limits. The third reason is that a number of ratios do not have a range of possible scores of (-00, +00) but possess a lower bound of zero, which may lead to skewness. One approach to deal with lack of normality is to explore the exact distribution of the ratios used in particular models and to use specially shaped statistical tests and tools which are convenient to the emerging distributions. Another alternative would be to develop methods that are based on distribution- free statistical theories