تاثیر توزیع آماری نسبت‌های مالی بر مقادیر مدل آلتمن با استفاده از شبیه‌سازی مونت‌کارلو

هدف: در این پژوهش با استفاده از تکنیک شبیه‌سازی مونت‌کارلو به بررسی این موضوع می‌پردازیم که شکل توزیع آماری نسبت‌های مالی مورداستفاده در مدل آلتمن تا چه اندازه‌ای مقدار احتمال ورشکستگی را تحت تاثیر قرار می‌دهد. روش: در این پژوهش از داده‌های 104 شرکت پذیرفته‌شده در بورس اوراق بهادار در بازده زمانی سال‌های 1395 الی 1398 استفاده‌شده است. جهت انجام محاسبات اولیه، پردازش داده‌ها از طریق نرم‌افزار excel صورت گرفته و در ادامه تحلیل‌های آماری از طریق نرم‌افزارهای matlab و minitab انجام شد. یافته‎ها: یافته‌های حاصل از انجام پژوهش به کمک تکنیک شبیه‌سازی مونت‌کارلو نشان داد که از بین نسبت‌های مالی مورداستفاده در مدل آلتمن، در خصوص نسبت‌های x1 تا x4 نرمال بودن یا نرمال نبودن توزیع نسبت‌ها تاثیری در تغییر مقدار احتمال ورشکستگی ندارد. همچنین، نتایج نشان داد که در خصوص نسبت x5 تغییر توزیع آماری می‌تواند مقدار احتمال ورشکستگی را تغییر دهد که این مطلب به معنی موثر بودن این نسبت در افزایش یا کاهش مقدار احتمال ورشکستگی است. نتیجه‎گیری: نتایج حاصل از یافته‌های این پژوهش بیان‌کننده این مطلب است که اگرچه در مدل آلتمن از نسبت‌های مالی مختلف به‌عنوان متغیرهای پیش‌گو استفاده می‌شود اما بررسی شکل توزیع این نسبت‌ها نشان داد که آگاهی از شکل توزیع آماری متغیرهای x1، x2، x3 و x4 تاثیری در آگاهی از توزیع مقادیر متغیر z-score ندارد و تنها تغییر شکل توزیع آماری متغیر x5 می‌تواند برای پیش‌بینی تغییرات شکل توزیع متغیر z-score کافی باشد.

the effect of statistical distribution of financial ratios on altman model values using monte carlo simulation

objective: in most bankruptcy prediction models, financial ratios are input data, and finally, the output of these models is an index that will be the criterion for assessing bankruptcy risk. on the other hand, according to the results of some studies, the statistical distribution of financial ratios is often not normal, and attempts are made to normalize them by removing outliers and logarithmic transformation. according to the above, the question that arises is what effect the form of distribution of financial ratios can have on the measurement of indices such as the bankruptcy index and its statistical distribution. since the measurement of the bankruptcy risk index is a function of various financial ratios, the form of the statistical distribution of these financial ratios can affect the measurement and statistical distribution of the bankruptcy risk index. in this research, in order to investigate whether the shape of the statistical distribution of financial ratios can affect the probability of bankruptcy or not, by using the altman bankruptcy model and using the monte carlo simulation technique, the effect of the shape of the statistical distribution of some financial ratios on the risk of bankruptcy was investigated. methods: in order to investigate the effect of statistical distribution of financial ratios on the distribution shape and altman zscore values, monte carlo simulation technique based on inverse transform sampling method has been used. in this research, the data of 104 companies listed on the stock exchange in the period of 2017 to 2020 has been used. for initial calculations, data processing was performed through excel software and then statistical analysis was performed through matlab and minitab softwares. results: findings from the study using the monte carlo simulation technique showed that among the financial ratios used in the altman model, regarding the x1 to x4 ratios, the normal or abnormal distribution of the ratios has no effect on changing the probability of bankruptcy. also, the results showed that regarding the x5 ratio, changing the statistical distribution can change the value of bankruptcy probability, which means that this ratio is effective in increasing or decreasing the probability of bankruptcy. conclusion: in this research, using historical data and monte carlo simulation technique, the influence of statistical distributions of financial ratios on the values and shape of zscore distribution was investigated. since the zscore variable itself is a function of the predictor variables x1, x2, x3, x4, and x5, and since these predictor variables may not have the same distributions, investigating the effect of changing the distribution of the predictor values on the values and shape of the distribution of the zscore variable in the usual ways statistics can be a difficult and complex task. in order to get rid of these problems and as an alternative way, the monte carlo simulation technique was used in order to determine the values and shape of the distribution of the zscore variable by the variables of financial ratios. using the monte carlo simulation technique, a series of values were simulated for each variable assuming its independence from other variables. the result of this simulation showed that changing the distribution of x1, x2, x3 and x4 values had no effect on changing the prediction of bankruptcy probability. in other words, the type of statistical distribution of these variables did not play a role in explaining the probability of bankruptcy. this result can indicate that changing the values of these variables in a possible domain through simulation with a skewed distribution, which causes the values of the variables to decrease in a high volume of simulated cases, will not be able to change the probability of bankruptcy. on the other hand, regarding the variable x5, the change in the shape of the statistical distribution could change the probability of bankruptcy. thus, the conclusion that can be drawn is that according to altman’s model, among the variables whose statistical distribution was examined, only the change in the x5 variable, i.e. the ratio of sales to total assets, was able to change the probability of bankruptcy, and this shows the high impact of this variable in has bankruptcy of the business unit. as the results showed, changing the distribution of x5 variable from gamma (which is a chula distribution) to normal distribution caused the values of this variable to increase for some simulated cases and at the same time decrease the probability of bankruptcy. thus, it is inferred that increasing the ratio of sales to total assets can be an important factor in reducing the probability of bankruptcy. these results can be important for users in the sense that in altman’s model, knowing the distribution of the ratio of sales to total assets, one can predict the distribution of zscore values. the sensitivity analysis performed on altman’s model indicators using simulation shows that, in general, a business unit can focus on increasing sales in order to reduce the probability of bankruptcy.