Development of financial distress measures

Introduction. There are four stages in the development of financial distress measures in current practice:

• univariate analysis;
• multivariate analysis;
• probit and logit analysis; and
• advanced analytical

Univariate analysis assumes ‗that a single variable can be used for predictive purposes‘ [1] and identifies factors related to financial distress. It does not provide a measure of the relevant risk and univariate model as proposed by William Beaver provided a ‗moderate level of predictive accuracy‘ [2].

In the next stage of financial distress measurement, multivariate analysis (also known as multiple discriminant analysis or MDA) attempted to ‗overcome the potentially conflicting indications that may result from using single variables‘ [1].

During the 1980s and 1990s, the trend has been to use probit (PR) and logit (LR) methods, which require less restrictive assumptions [3].

More recently, probit and logit analysis has been compared to a more advanced analytical tools, neural networks. Researches had found that the approaches perform similarly and should be used in combination.

Belarusian Practice and Global Tendencies. The importance of financial ratios for company analysis has been known for more than a century. A review of the literature indicates that among the first researchers applying financial ratios for bankruptcy prediction were Ramser (1931), Fitzpatrick (1932) and Winakor and Smith (1935). Fitzpatrick, for example, used a univariate analysis of 13 ratios to indicate a failure. The Fitzpatrick model did not, however, show a significant relationship with failure. Later on, many studies have evaluated financial ratios as the most effective factors on bankruptcy.

The ratio analysis approach has been defined by the Belarusian bankruptcy legislation as one of the most important ways of assessing the insolvency of national enterprises.

From an economic point of view, one of the problems in the regulation of issues related to bankruptcy is to assess the solvency of the debtor, which is a legal basis for the commencement of bankruptcy proceedings, as well as to determine the ability or inability to restore the solvency of the debtor. Current Ratio and (or) Working Capital Ratio are the criteria for the recognition of a company as a solvent at the end of the reporting date.

Accordingly, in Belarus a company is recognized as insolvent when both Current Ratio (Current Assets/Current Liabilities) (К1) and Working Capital Ratio ((Equity-Long Term Liabilities)/Long Term Assets) (К2) are below the defined limit at the end of the reporting period (Decree No 1672 of 12 December 2011, 2011; Resolving Insolvency. Methodology, 2014).

Insolvency, acquiring sustainable, is a company‘s insolvency over the four quarters prior to the reporting date. Further, insolvency, having sustained is a company‘s insolvency over the four quarters prior to the reporting date with the Financial Liabilities to Total Assets Ratio ((Current Liabilities+Long Term Liabilities)/Total of Balance) (К3) no more than 0.85 independently of the type of economic activity.

Thus, the present Belarusian national methodology of bankruptcy estimation is based on solvency ratio analysis measured by three indicators (K1, K2 and K3), which algorithms are defined by the Regulations No 140/206 of 27 December 2011 approved by the Ministry of Finance of the Republic of Belarus and the Ministry of Economy of the Republic of Belarus (Regulations No 140/206 of 27 December 2011, 2011). In conformity with this approach, the National Committee of Statistics and Analysis calculates annual solvency ratios of the Belarusian enterprises based on the official statistical reports (National Statistical Committee of the Republic of Belarus, 2014).

In addition, we should add that the same concept for bankruptcy prediction is used in the Russian Federation as we have very close economic relations and the same economic conditions.

Although the ratio analysis is simple and fast algorithm for bankruptcy estimation, it has many limitations. Because of them Fisher‘s MDA method (1936) was applied by Altman his Z-score model in1968, the first bankruptcy classification model to apply the MDA technique.

In our national Belarusian practice we also have an example of MDA models. One of these models is Savitskaya‘s model that was estimated using an initial sample composed of 200 Belarusian enterprises. These enterprises were all agricultural enterprises from the period between 1995 and 1998 [4]:

Z = 0.111X1 + 13.239X2 +1.676X3 + 0.515X4 + 3.8X5, (1) 

where

X1 – Working Capital/Current Assets;

X2 – Working Capital/Noncurrent Assets; X3 – Sales/Average Current Assets;

X4 – Earnings before Interest and Taxes/Average Current Assets; X5 – Equity/Total Assets.

A survey of the literature shows that the majority of international failure prediction studies employ the MDA, which has many disadvantages, so its popularity declined considerably after the 80s. At the same time, new methods have emerged based on the logit and probit methods, which partially help to avoid using the above premises.

The logistic regression (or logit regression) analysis was put forth in the 1940s as an alternative to Fisher's classification method, linear discriminant analysis. Unlike the MDA, the logistic regression does not assume multivariate normality and provides several statistics that indicate the significance of each variable. It also handles relatively smaller sample sizes better than the discriminant analysis.

In the Belarusian national practice, we also have an example of the creation of logit regression model. The latest bankruptcy model by G.V. Savitskaya is a logit regression model, which was tested on data of 2,160 Belarusian agricultural enterprises of 2003 [4]: 

Z = 1 – 0.98X1 – 1.8X2 – 1.836X3 – 0.28X4, (2) 

where

X1 – Working Capital/Current Assets;

X2 – Working Capital/Average Current Assets; X3 – Equity/Total Assets;

X4 – Equity/Average Current Assets; Interpretation of the model:

Z ≤ 0 – stable financial situation;

Z ≥ 1 – unstable financial situation, the probability of bankruptcy is high. Values between 0 and 1 show the level or degree of financial stability.

Another commonly used approach is the probit analysis that is very similar to the logistic regression. The main difference between them is that the probit function assumes a cumulative standard normal distribution, whereas the logistic function assumes a binomial distribution. Both methods employ the maximum likelihood estimation and should produce very similar results, especially with large sample sizes.

There is no example of probit models developed in our Belarusian practice.

Beyond Univariate Analysis MDA, LR and PR. All above mentioned statistical methods have high accuracy of prediction and could easily interpret the results of the analysis. The MDA, LR and PR parametric models used in bankruptcy analysis are widely discussed among specialists. Countless academic investigations are devoted to applications, comparisons or reevaluations of the above mentioned models.

Statistical models for company default prediction are of practical importance but all of them have certain limitations:

1. The forecast accuracy depends on the selection of the most descriptive variables - financial ratios;
2. The reduction of statistical reliability prediction for distant

Therefore, there are other complex techniques for bankruptcy prediction based on nonparametric algorithms. Among other statistical methods applied to bankruptcy analysis are the gambler's ruin model (Wilcox, 1971) [5], option pricing theory (Black and Scholes, 1973) [6], recursive partitioning (Frydman et al., 1985) [7], neural networks (Tam and Kiang, 1992) [8] and rough sets (Dimitras et al., 1999) [9], to name a few. Mostly, the creation and development of these models was possible due to modern electronic technologies that have facilitated the use of Big Data and mathematical algorithms to predict future financial problems.

In recent years, the area of research has shifted towards non-structural and semi-parametric models since they are more flexible and better suited for practical purposes than purely structural ones. For example, corporate bond ratings published regularly by rating agencies such as Moody's or Standard & Poor‘s strictly correspond to company default probabilities estimated to a great extent statistically. Moody's RiskCalc model is basically a probit regression estimation of the cumulative default probability over a number of years using a linear combination of non-parametrically transformed predictors.

As we can see, there are many different approaches to the bankruptcy prediction models, each having own limitations. Because of this (and not only), neither the Altman models nor other balance sheet-based models are recommended for use with financial companies. This is because of the opacity of financial companies' balance sheets and their frequent use of off-balance sheet items. There are market-based formulas used to predict the default of financial firms, but they have limited predictive value because they rely on market data (fluctuations of share and options prices to imply fluctuations in asset values) to predict a market event (default, i.e., the decline in asset values below the value of a firm's liabilities).

We also should take into consideration that forecasting models rely on the assumption that the relationship between the dependent variable (i.e. failure probability) and all independent variables is stable over time (Zavgren, 1983). Yet, there is evidence that this stability is highly questionable (Charitou et al., 2004) and that the true forecasts of a model may be unreliable if this assumption is incorrect (Mensah, 1984). Indeed, all models are sensitive to some parameters that describe macro-economic environments, and any change may influence their accuracy (Mensah, 1984; Platt et al., 1994). In practice, then, models need to be re-estimated frequently to counterbalance the effects of such phenomena (Grice and Ingram, 2001).

In their attempts to overcome or reduce model instability, some authors have suggested to take into account some macro-economic factors responsible for this phenomenon (Mensah, 1984; Platt et al., 1994; Grice and Dugan, 2003; Bilderbeek and Pompe, 2005). Mensah, for example, developed four models using samples from the 1972-1973, 1974-1975, 1976-1977, and 1978-1980 periods for different economic environment and found that the accuracy and structure of the models changed during these periods (Mensah, 1984). Bearing in mind this finding, we would expect impressive differences from Altman‘s model which was derived from a sample prepared and analysed up to 50 years ago.

They also showed that by using some economic indicators (inflation rate, interest rate, growth rate, etc.) to weight traditional explanatory variables, it became possible to stabilize obtained results. In most cases, this solution is applicable only a posteriori when the nature of the macro-economic changes, their consequences and effective instruments to combat them are known, but a priori nobody knows what should be done.

Other authors showed that it is necessary to take advantage of sampling variations caused by changes in the economic environment and that it is possible to improve model accuracy in the short term by using measures representing variation of ratios over time (coefficient of variation (CV), mean-square (standard) deviation). However, most of them did not study the stability of model accuracy in the long term (Dambolena and Khoury, 1980; Betts and Belhoul, 1987).

Another major concern is the time period from which to select the companies for the estimation sample. As shown by a number of specialists, Altman‘s 1968 model, which was based on a broad selection of companies over a 20-year period, does not retain its effectiveness over time and across different industries.

In addition, the MDA, LR and PR models are traditionally mono-period models relying on a snapshot of a company‘s financial profile taken at a particular point in time.

As business and economic conditions change over short periods of time, so the coefficients of any models should also be adjusted. We need to apply this approach to all bankruptcy prediction models. In order to form an accurate model, together with using of probability of bankruptcy is an essential statistic for valuation and other types of financial analysis, one must consider the current macroeconomic conditions, including growth rates, inflation, interest rates, and other macroeconomic information that forms real macroeconomic environment.

Moreover, the estimation sample should include companies from the same industry and comparable macroeconomic surroundings or environments. Such customization should be implemented into each bankruptcy model because any change in environmental conditions may greatly reduce a model‘s accuracy and resulted in poor prediction reliability. It has been demonstrated that variations in economic cycles (alternating periods of economic growth and downturn or recession) and, to a lesser extent, changes that companies may face in terms of inflation, interest or tax rates, monetary or credit policy, export-import policy and institutional environment, have an influence on financial ratio distributions and on the border between failed and non-failed companies (Mensah, 1984; Platt et al., 1994; Grice and Dugan, 2003; du Jardin, P., Severin, E., 2012).

Conclusions. Meanwhile, the situation in bankruptcy analysis has changed dramatically. Larger data sets with the median number of failing companies exceeding 1,000 have become available. 20 years ago the median was around 40 companies and statistically significant inferences could not often be reached. The spread of computer technologies and advances in statistical learning techniques have allowed the identification of more complex data structures. Basic methods are no longer adequate for analyzing expanded data sets. A demand for advanced methods of controlling and measuring default risks has rapidly increased, in anticipation of the New Basel Capital Accord adoption (Cízek, P., Härdle, W., Weron R., 2005).

In such conditions, we consider that:

1. It is impractical and unrealistic to attempt to create an absolutely stable bankruptcy model by including more and more macro-economic factors into the bankruptcy
2. It is necessary to create an automatic ‗mechanism‘ for aggiornamento of any bankruptcy model. Maybe, it would make sense to incorporate such an algorithm of customization into the national bankruptcy (insolvency) legislation. This should provide the directions for the national ranking growth of Resolving Insolvency methodology of Doing Business report of the World Bank and the International Monetary
3. Such customization should include not only new set of bankruptcy models‘ parameters but also certain new economic indicators taking into consideration economic environment and recessionary and downturn
4. Except for issues encountered when deciding how to form the prediction model, the ideal process would include a large sample size of both bankrupt and non-bankrupt companies chosen randomly from the overall population of
5. The ratio of bankrupt to non-bankrupt companies in the sample should reflect the ratio observed in the overall population. This would eliminate errors resulting from the prior probabilities adjustment we employed for functions (Jeffrey Lui, 2002).

References

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