Constructing models for credit ratings and default probabilities

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Introduction

Banking system is one of the main parts of the economy as banks are key players on many financial markets. Banks are the most frequent and large intermediaries in lending, creation of money supply and other financial transactions. Because of that, the stability of banks and of the whole banking system is very important for the stability of the economy.

Numerous crises have proven that defaults of several banks can produce dramatic effect on the global banking system and, afterwards, on the global economy. Furthermore, those crises have shown that existing measures of banks' financial stability are not very reliable and useful. This leads to the creation of many researches aimed at improving instruments for analysing banks stability.

Such instruments are mainly used for regulatory purposes. Government authorities use different measures to identify the riskiest banks and to prevent their bankruptcy or, at least, to minimize losses given default. For instance, Basel II and Basel III agreements rely on external and internal credit ratings. It is necessary for governments to analyse banks' financial stability in order to maintain stability of the country's economy and to decrease costs, associated with financial distress (f.e. costs for Deposit Insurance or for funding banks). Government not only needs to identify overall stability of banks, but rather it needs to understand which factors can influence stability and, as a result, monitor and control banks basing on these factors.

Besides government, measures of banks' financial stability are used by many other economic agents, including private investors (depositors) and management of a bank. Investors can estimate level of risk of their investment in various banks, relying on these measures, while bank's management can use those measures for internal purposes: they may serve as the basis for strategic decisions and internal risk management.

Current most popular and reliable instrument for measurement of banks' financial stability is the credit rating given by authorized agencies. Those agencies act as independent experts and assign ratings in symbolic form, where each grade (collection of symbols) represents different level of bank's financial stability. Ratings help to determine the position of the financial institution relative to its competitors and, consequently, understand which banks are likely to fail in the future.

There is also an important indirect effect of ratings. As banks understand the importance of them to many external users, they try to achieve higher rating grades by changing structure of its balance sheet and income statements. This, in turn, helps banks to become more stable and, thus, decreases overall problem of financial instability itself.

Another popular instrument used to measure bank's financial stability is the measure received from Probability of the Default (PD) model. The similarity between these two instruments is that both of them can be used to rank banks and understand “which one is better”. However, the main difference is that Probability of the Default model can give precise estimation of the probability of bank becoming insolvent, instead of assigning a subjective financial stability level. Because of that difference, this model is usually used by regulators, rather than investors.

Despite those measures are those that are most frequently used, there are still disadvantages of both. Main one is connected with over- and underfitting issues. Ratings given after Credit Crunch of 2007 are considered too conservative, as rating agencies value their reputation. In the same time, probabilities of the default are, on the contrary, too optimistic, due to low number of observed defaults (unbalanced sample). Furthermore, their disadvantages can be seen empirically: even with presence of models for estimation of them, there is a comparatively large amount of “unexpected” defaults.

It can be reasonably argued that this topic is actually very relevant today and that is why this paper was written. Those measures help to solve many economic problems and there is a high demand on increasing performance and forecasting power of models aimed at estimating them. Absence of reliable measurement instruments means that all users of credit ratings and PDs need to continuously collect information and monitor banks. It is costly and requires a lot of time in order to analyse past data and make precise predictions. This leads to many researches on this topic, which try to improve existing models or create new measures.

This aim of the paper is to increase the forecast power of the existing models, aimed at forecasting banks' financial stability. It will be useful for all users of such models, as they would be able to make reliable forecasts of banks' ratings and credit risks. Main purpose of this paper is to construct models for estimating two most popular measures of financial stability basing on publically available information, and, secondly, to try to combine those two measures in order to achieve higher accuracy of estimation and higher forecast power. Final model of this paper would be constructed on the base of Credit Rating (CR) model combined with transformed ratings received from Probability of the Default model. Afterwards, this model would be compared with separate models.

Before making a combination, there would be changes in original models, which also can lead to the increase in the forecast power. Firstly, CR model itself can be reconstructed and improved. For this purpose, several articles from Russian and foreign authors would be studied. Those articles include researches on types of CR models, significant explanatory variables and various approaches on determining dependent variable. Secondly, Probability of Default model would be analysed and its variables would be changed in an attempt to increase its forecast power. Moreover, we would try to achieve more balanced data for PD models.

Models would be estimated using data from Central Bank of Russia, which consists of RAS statements of all Russian licensed banks. There is data on all financial accounts of banks, so it would be possible to calculate different accounting ratios, which later can be used as explanatory variables for modelling banks financial strength. In addition, data on macroeconomic factors would be used. This data would be taken from Rosstat and World Bank databases.

Information on the dependent variables (credit ratings and default observations) would be taken from other open-sources, which would be discussed later. There would be data on ratings from top-3 foreign agencies (Moody's, S&P and Fitch) and largest Russian accredited agency - Expert RA. Mapping of scales would be performed to transform those ratings into the single scale.

This paper would be structured as follows. First section would contain literature review of articles connected with Credit Rating model and Probability of the Default model. Different models and explanatory variables would be discussed and most useful ones would be chosen. Moreover, attention would be paid to mapping of rating scales. In the next section the main hypothesis would be stated and data for testing it would be described. In addition, the problem with an unbalanced sample for Probability of the Default model would be fixed. Afterwards, two ordered logit models would be estimated separately with the use of Step-Wise procedure and PCA analysis and their predicted values would be compared with actual figures in order to measure the forecast power. Finally, the combined model would be estimated and its out-of-sample forecasting power would be measured in order to prove the initial hypothesis. Basing on these findings, conclusions would be made and further perspectives of the analysis would be highlighted.

1. Literature review

Firstly, literature concerning models and dependent variables for both, Credit Rating model and Probability of the Default model, should be reviewed. Then we need to focus on literature concerning explanatory variables for those models. Literature review is needed in order to use past experience of researches made on this topic, which will help to construct a reliable final model.

1.1 Choosing the model and the dependent variable for the CR model

For the purpose of predicting bank's ratings there exists three main types of models. First is a simple linear OLS, next are ordered logit/probit models and, finally, non-parametric models.

OLS is the simplest type of models, which is rarely used for estimation of ratings due to the discrete nature of credit ratings. Application of OLS gives inconsistent and biased estimates, which potentially leads to invalid econometric tests. Non-parametric models have better forecasting power, but they require complex and costly calculation and therefore would not be considered here.

Ordered logistic models are the ones who are in the middle between OLS and complex non-parametric models by their estimation accuracy. There are still drawbacks of these models, however, they would be used in this paper due to their balance between complexity and accuracy of estimates. The largest drawback is that the model works perfectly only on infinite samples (Hajek et al., 2010), therefore we have also focused on adjusting datasets and using as much observations as possible.

Logit/Probit are the models estimated by the maximum likelihood method. Ordered models differ from original logit/probit models in their assumptions about number of values that the dependent variable can take. Original binary models are constructed for variables that take only two values (0 or 1) and they would be useful for constructing PD models. Ratings can take more than two values (in this paper they would have 26 possible values), therefore ordered logistic models are needed to be used here.

Probit and logit models differ in their assumptions about the distribution of target variables. Probit assumes normal distribution of the target variable, while logit is based on the usage of the natural logarithm. Both models have certain drawbacks: logit models are very sensitive to multicollinearity of variables, whereas probit models are sensitive to the normality of the distribution (Totiamina, 2012). However, logistic modelling is inherently more reliable for stable periods of economic development (Kostrov et al., 2016). Basing on these facts, logistic models are chosen as the base ones for models in this paper. There were estimations performed on models of both types and it gave results in favour of logit model. To summarize, banks' credit ratings would be constructed using ordered logit model.

For the CR model, credit ratings given to banks by different agencies would be used as the dependent variable. Ratings would be taken from top-3 global rating agencies (Fitch, Moody's and S&P) and largest Russian agency, which was accredited by the Central Bank of Russia (Expert RA). Only those agencies were chosen as they are most popular ones and they are the only agencies who have large enough number of observations (ratings given to Russian banks), which is a condition for preforming successful mapping of ratings scales.

There is an important problem, which arises when comparing ratings given by different agencies. All of them assign ratings in symbolic form and each agency has its own opinion on which rating is “bad” or “good”. Moreover, foreign agencies can only assign ratings, which are lower than sovereign rating of the country, in which bank is located. At the same time, domestic agencies do not have an upper limit. Another reason for a mismatch in agency ratings is the divergence of expert opinions of consultants. In addition to this, many studies indicate that there are differences in the methodologies of rating agencies (Dyachkova et al., 2016). Because all of that, it is needed to normalize ratings from different agencies to the single scale and this scale should be numeric, in order to be able to use it in econometric models.

The process of mapping of rating scales is described in several articles, including articles by Sosyurko and Karminsky (2011) and Dyachkova and Karminsky (2016) and the report from CB of Russia (2016). Authors of these articles stated that first algorithmic approaches for mapping different scales used average PD for comparison of ratings. However, there are several problems with such approaches (Sosyurko et al., 2011):

· It is assumed that mixing of the corresponding distributions will not affect the resulting average PD value.

· Compared PDs are not necessarily uniform. They depend on the definition of a default, time horizon (through-the-cycle or point-in-time) and many other factors.

Another disadvantage of mapping scales using PDs was highlighted by Ayvazian et al. (2011). They stated that the feasibility of this approach is limited by the inadequacy of statistical data on defaults of Russian banks. There was also an attempt to apply this approach by Smirnov et al. (2010). That article was aimed to provide a mapping technique for Russian agencies (RusRating, Expert RA, AK&M and NRA), but the results showed that the probability of the default for different rating categories can be statistically indifferent from each other due to insufficient data. This again proves inapplicability of the approach based on PDs.

Later, there were some new approaches introduced, which were not based on PDs, but their main drawback is that they can only be applied to comparing two agencies, without referring to the single scale.

For mapping multiple scales to the single scale an article by Sosyurko and Karminsky (2011) would be used as the base one. It shows that the best comparison of multiple rating scales is made using linear-logarithmic transformations.

Firstly, we need to choose the base scale, to which all other scales would be mapped. Moody's has the largest amount of ratings given in Russia, so its scale would be used as the base. Then we can estimate the following equation:

M - Moody's international scale, as the base scale;

Ri - other agency's scale, which is needed to be mapped to the Moody's scale

Authors of this article used data on ratings of Russian banks from various agencies: international and domestic ones. With the help of the OLS, necessary coefficients were estimated. Found coefficients () were used to transform scales of needed agencies into the base scale.

As a result, following diagram was obtained. It shows the relationship of the symbolic ratings of various global and national agencies with the Moody's base scale in numeric format, where 1 is the highest reliability rating and 21 - the default rating.

Picture 1. Ratings mapping. Source: Sosyurko and Karminsky (2011)

Considering other possible approaches, the report made by Central Bank of Russia should also be studied. There are several techniques from foreign authorities reviewed, including approaches from Basel II, EU and USA. But for the purpose of mapping rating scales of Russian banks, foreign approaches are useless, because of the absence of needed data in Russia. There was also an approach from Ministry of Finance, which is suitable for Russia. It is based on mapping different scales into the base one using econometric modelling. Results are similar to what is discussed in Sosyurko et al. (2011), but there are also some additional stages described, which can be used in order to increase accuracy of mapping. However, those stages imply complex calculations and would not be covered in this paper.

Therefore, mapping of rating scales in this paper would be based mainly on the findings in the article by Sosyurko et al. (2011). Same modelling principles are applied to the newer data in order to receive mapping, which can be used for recent observations. After applying it, the following table 1 was received:

Table 1. Ratings mapping

	Fitch Ratings - Long-term international rating in foreign currency	Fitch Ratings - Long-term international rating in national currency	Fitch Ratings - National scale (Russia)	Moody's Investors Service - Long-term international rating in foreign currency	Moody's Investors Service - Long-term international rating in national currency	Moody's Interfax Rating Agency - National scale (Russia)	S & P Global ratings - Long-term international rating in foreign currency	S & P Global ratings - Long-term international rating in national currency	S & P Global ratings - Long-term rating, national scale (Russia)	Expert Rating Agency - National scale (Russia)
8					Baa1	Baa1	BBB+	BBB+
8,5	BBB+	BBB+	AAA(rus)				BBB	BBB	ruAAA
9				Aaa.ru	Baa2	Baa2
9,5	BBB	BBB					BBB-	BBB-
10	BBB-	BBB-	AA+(rus)		Baa3	Baa3			ruAA+	A++
10,5							BB+	BB+
11	BB+	BB+	AA(rus)	Aa1.ru	Ba1	Ba1	BB	BB	ruAA
11,5	BB	BB	AA-(rus)
12				Aa2.ru	Ba2	Ba2	BB-	BB-	ruAA-
12,5	BB-	BB-	A+(rus)						ruA+
12,5			A(rus)
13	B+	B+	A-(rus)	Aa3.ru	Ba3	Ba3	B+	B+
13,5			BBB+(rus)	A1.ru					ruA	A+
14	B	B	BBB(rus)	A2.ru	B1	B1	B	B	ruA-
14,5	B-	B-	BBB-(rus)				B-	B-	ruBBB+
15	CCC+	CCC+	BB+(rus)	A3.ru	B2	B2			ruBBB
15,5			BB(rus)	Baa1.ru			CCC+	CCC+	ruBBB-	A
15,5			BB-(rus)						ruBB+
16	CCC	CCC	B+(rus)	Baa2.ru	B3	B3			ruBB
16				Baa3.ru
16,5			B(rus)	Ba1.ru			CCC	CCC	ruBB-
17				Ba2.ru					ruB+
17			B-(rus)		Caa1	Caa1	CCC-	CCC-	ruB
17,5				Ba3.ru						B++
17,5				B1.ru					ruB-
18				B2.ru
18	CC	CC		B3.ru	Caa2	Caa2
18,5				Caa1.ru						B+
19	C	C	CCC(rus)	Caa2.ru	Caa3	Caa3
19,5				Caa3.ru						B
20				Ca.ru	Ca	Ca				C++
20,5										C
21	D	D	D(rus)	C.ru	C	C	D	D	ruD	E

In this table 8 is the highest possible rating in Russia equal to the maximum sovereign rating for the period of our interest, while 21 is the worst rating, which is assigned to insolvent banks.

There would be some further transformations of the dependent variable. In order to avoid the loss in consistency of the model, ratings were assumed to be unchanged until the moment of the new rating assignment. The final version of the dependent variable would be obtained by averaging all singe scale numeric grades of a bank in a particular quarter for all rating agencies. Due to non-integer rating groups (f.e. rating = 13,4), the numeric rating would be rounded to the closest integer or integer with a half (that is 13,5 for true average rating equal to 13,4) (Khromova et al., 2016). Therefore, in this paper 26 different groups of rating would be considered (in the scale 0-21, starting from 8 as a sovereign rating, with each step equal to 0,5 points). More precise explanation of transformations of the dependent variable for CR can be found in later sections.

1.2 Choosing the model and the dependent variable for the PD model

In this section the model for estimating banks' PDs and its dependent variable would be chosen and critically analysed. But before that, event of the default itself should be defined. There is no single definition of the default, instead articles on this topic state various triggers which usually lead to it. Article by Kostrov et al. (2016) states following indicators of default:

· Level of capital sufficiency of a bank is lower than 2%.

· Value of bank's resources drops lower than the minimum, set at the time of registration.

· Bank is unable to satisfy liabilities to creditors.

· Bank is funded by the Deposit Insurance Agency.

There are many researches which analyse models aimed at estimating bank's probability of default. Article by Totiamina (2011) summarizes information on this topic and describes main types of such models. They include models based on market indicators and fundamental factors, such as financial data, ratings given by rating agencies or macroeconomic data. All of these models have their own advantages and disadvantages.

PD models based on market indicators can only be applied to banks which have its shares listing on the stock exchange. Minority of Russian banks have such shares, so this type of models is not useful for research made in this paper. Then we should focus on models based on fundamental factors. Simplest one is based on macroeconomic data, but it does not allow to estimate PD of individual banks, so it is also useless in our case. Still, macroeconomic factors should be added in the model, but as additional ones. As this paper is aimed on combining PD model with credit rating model, we also cannot use PD models based on ratings given by rating agencies because of possible collinearity in the final combined model. Such models can be used in order to transform PD received from another model into the credit rating figure.

The only option left is to use models based on financial statements of a bank. Main advantage of models based on the financial statements is the availability of the necessary information, as banks must always disclose their financial statements. Still, there are some drawbacks, including the fact that financial statements can be analysed only after publishing, which creates serious time-lag.

This type of models can be divided into scoring models, linear models of discriminant analysis, and binary choice models. Models of discriminant analysis and scoring models do not imply a specific estimate of the probability of default, but allow classification of borrowers according to their default exposure (Totiamina, 2011). Therefore, for the aims of this paper we should use binary choice models (logit or probit). They are based on the maximum likelihood method, and the main idea is to identify factors (explanatory variables) which can affect the PD (dependent variable) in order to be able to predict the probability of a possible default, basing on values of financial data, which are open to the public.

Binary choice models are structured as follows: dependent variable can take 1 (in the event of default) and 0 (if bank is operating as usual), while explanatory variables are some internal figures from bank's financial statements and external figures, like macroeconomic factors and operational environment. Consequently, the resulted figure of PD is the estimated probability that the dependent variable will be equal to 1, given the observable explanatory variables.

Differences between two main types of binary choice models were discussed in the previous section. Basing on same arguments, we need to choose logit model for estimation of PDs. The differences between models for credit ratings and for default probabilities is that the first one uses ordered multinomial models with more than two possible outcomes, whereas PD model uses binary type models.

There also exist some more advanced models. Mainly they are based on non-parametric approaches.

However, such models require very complex and costly calculations, so they would not be covered in this paper.

1.3 Explanatory variables for both models

Models for estimating both, PDs and credit ratings, were chosen to be based on the internal financial and external macroeconomic data. Therefore, a single list of explanatory variables could be made for both of them. Afterwards, in the process of modelling, only significant variables would be left for each model.

As there are much more researches, aimed at analysing factors, which have influence on credit ratings of individual banks, rather than on default probabilities, we would firstly concentrate on explanatory variables from these researches. To start with, we need to analyse a couple of well-known methodologies for estimating banks' ratings. Two most popular of them are CAMELS and BFSR. First one is the simpler one, as it is based solely on financial data of a bank, which can be easily found in its financial statements. CAMELS methodology states that main factors, which should be estimated in order to compute ratings, are:

• Capital adequacy

• Assets (quality and size)

• Management Capability

• Earnings (profitability and efficiency)

• Liquidity

• Sensitivity

Due to its simplicity, this methodology has several serious drawbacks. Main one is an absence of factors connected to the operational and regulatory environment or the macroeconomic factors, while those factors were proven to be significant in the CR models.

Because of this, second most popular methodology was created and it is called BFSR. It is an extension of CAMELS, as it adds qualitative factors, such as information about environment in which bank operates, market position, competitors and etc. Full list of factors:

· Financial measures (from CAMELS methodology)

· Market position and relationships with other banks

o Market share

o Geographical diversification

o Stability and diversification of income

· Internal quality indicators

o Corporate governance

o Control mechanisms

o Transparency of financial statements

o Liquidity management, etc.

· Operational environment

· Regulatory environment

Second methodology includes factors based on the expert opinion and it can improve forecast power of the model. However, this paper is aimed to estimate ratings, given publically available information only, so factors which can be calculated from open-sources would be considered here. Still, we need to minimize CAMELS' drawbacks by adding macroeconomic data in the list of factors. Consequently, our model for credit ratings would consist out of two parts: the first one is the CAMELS part and the second one is macroeconomic part.

Next, it is necessary to understand which financial information to use in order to estimate factors defined by the methodology of our choice. To do this correctly, we need to understand how factors from the methodology influence bank's financial stability.

Firstly, each part of CAMELS methodology will be described. Each group of financial indicators included in the CAMELS methodology has a different impact on the credit stability of a bank:

· Capital adequacy is the most important factor, which is usually the main aim for regulators. It is so mainly because capital can act as a buffer for covering unexpected losses, which allows a bank to remain solvent. Its significance increases during times of global financial distress (crises), as low capital adequacy increases probability of default and, in turn, make the overall situation even worse. However, at the same time, too high capital leads to adverse consequences, one of which is the reduction of manoeuvrability and competitiveness. Therefore, capital adequacy should remain at an average level, to maintain the bank's reliability and, at the same time, without reducing its competitive qualities.

· Liquidity characterizes the bank's ability to pay on its short-term obligations. In other words, this factor shows to which extent bank's assets correspond to liabilities that it took. This indicator is also one of the key ones in determining the stability of a bank, since the lack of the ability to repay obligations greatly increases the probability of the default in case of adverse circumstances, like Bank Run.

· Earnings, which include profitability and efficiency of a bank, show how costs and revenues of a bank are correlated. These indicators show the effectiveness of a bank through comparing investments and returns that it made.

· Asset quality is also an extremely important indicator in determining the bank's financial stability. It consists out of most meaningful characteristics of banks assets: profitability, liquidity, volume and etc.

Each of these financial factors can be estimated by various accounting ratios from financial statements of banks. Table 2 in the next section summarizes ratios, which were included in CR models by authors of articles of our interest. Later some of those ratios would be eliminated, during the step-wise procedure, in order to decrease number of variables in our model and leave only significant and uncorrelated ones.

But before proceeding to the table of accounting ratios, we also need to decide which macroeconomic factors are important for estimation of bank's financial stability. Again, from the previous papers on this topic we can derive that most meaningful factors are:

· GDP, GDP per capita or GDP growth rate, which are the main indicators for measuring the level of development of the economy. Using past experience of estimating banks ratings, we can say that GDP per capita and GDP growth rates are the most significant indicators.

· Inflation is an another key factor that shows the stability of the economy in the country through the changes in the overall price level. There are several ways to measure inflation, but for the purpose of bank's rating estimation, Consumer Price Index (CPI) is usually used.

· Sovereign rating of the country has crucial importance as it creates the so called country ceiling. It means that international rating agencies cannot give a rating, which is higher than sovereign rating, even if a bank has perfectly matched balance sheet.

· Corruption is an another key concern. Like in any other sphere connected with regulation, there exists a variety of ways to escape from some restrictions. It should be noted that corruption indicators have an ambiguous sign in credit ratings models. In order to estimate corruption level, there exists a variety of indexes from authorised agencies.

· Finally, indicators of international relations, such as trade balance or exchange rates can be added. These indicators are needed to understand the level of international relationships between Russia and other countries around the world.

As we have noted in the beginning of this section, all information about most meaningful sides of a bank's stability can be used either in Credit Rating model or in the Probability of the Default model.

As we have discussed the importance of each factor, influencing banks financial stability, we can make a table 2, which consists out of indicators (mainly financial ratios) corresponding to each reasonable factor. In the table you would find names of groups of factors, factors (or indicators) themselves, reference to the article where this factor was mentioned, and, moreover, an expected sign of their coefficients in the model for ratings (for PDs these coefficients should be turned over).

Here it should be noted that most numerical rating scales are increasing with the rise of probability of default or other financial distress. It means that bank with rating “1” is more stable than bank with rating “5”. Consequently, “+” sign of indicator shows that higher values of it increase the probability of a distress of a bank, while “-”, in turn, means that higher values increase the financial stability.

Table 2. Explanatory variables

Factor's group and subgroup	Factor	Expected sign	Source paper
Earnings	Profitability	Return on assets	-	Sosyurko et al., 2010
		Return on equity	-	Peresetskiy et al., 2005
		Net interest margin	-	Guglielmo et al., 2012
		Net profit with reserves / Assets	-	Ayvazyan et al., 2011
		Interest income / Assets	-	Myakon'kikh et al., 2008
	Efficiency	Interest expenses / Interest income	+	Sosyurko et al., 2010
		Operational expenses / Operating income	+	Myakon'kikh et al., 2008
Liquidity	Current ratio	-	Karminskiy et al., 2011
	Deposits / Equity	+	Khromova et al., 2016
	Net assets / Deposits	-	Peresetskiy et al., 2004
	Liquid assets / Deposits	+	Peresetskiy et al., 2004
	Loans / Deposits	-	Ayvazyan et al., 2011
Capital adequacy	Tier I ratio	-	Sosyurko et al., 2010
	Equity / Assets	-	Guglielmo et al., 2012
Asset quality	Impaired loans / Loans	+	Karminskiy et al., 2014
	Loan loss reserves / Loans	+	Khromova et al., 2016
	Loan loss reserves / Assets	-	Karminskiy et al., 2007
	Impaired loans / Equity with loan loss reserves	+	Khromova et al., 2016
	Unreserved impaired loans / Equity	+	Lazaridez et al., 2016
	Loans net of reserves / Net interest income	+	Ayvazyan et al., 2011
Size	Ln (Assets)	-	Guglielmo et al., 2012
External factors	Macroeconomic factors	Infation	+	Emawtee, 2012
		GDP growth rate	-	Ayvazyan et al., 2011
	Operational enviroment	Sovereign rating	-	Karminskiy et al., 2011
		Corruption Perception Index	+	Khromova et al., 2016

To sum up, table of internal factors for both models will consist out of groups of factors, included in CAMELS methodology with two differences: management quality was omitted, due to its subjectivity, while size of a bank was added, as it was proven to be significant by numerous researches. Moreover, some external factors from BFSR methodology were added.

Some ratios in same groups would be heavily correlated, as they are used to explain very similar things and are often based on the same dataset. Due to this fact, first step of modelling in this paper would be focused on elimination of such variables through the Step-Wise procedure.

2. Stating hypotheses and collecting needed data

2.1 Main hypothesis

Previously, the importance of the topic of this paper was discussed and the literature on this topic was analysed. Now, the main hypothesis of this diploma paper can be stated. It looks as follows:

A combination of the Credit Rating model with the Probability of the Default model would give higher forecasting power than those models separately.

This hypothesis is potentially true due to the problem stated in the introduction: CR gives overestimated ratings (in numerical scale), while PD gives underestimated default probabilities. This, in turn, creates the potential for the increased forecast power of their combination. Now we can proceed to the collection of data, needed for estimation of our two models separately and estimation of the final combined model.

2.2 Data

In previous sections we have detected necessary dependent and explanatory variables for our models. Now it is time to select appropriate data, which can be used for modelling those variables.

Firstly, it is important to understand the time period for the whole dataset. Here we face following trade-off: it is better to use as much data as possible in order to achieve accuracy in determining long-term ratings and default probabilities, but if we will use too old data, it might give incorrect results for the current period. Old data is often useless, as rating agencies change their scales and meaning of their ratings over time, while banks themselves change structure of their balance sheets and begin to participate in new activities, which affect their stability (f.e. derivatives trading).

Last large change in banking sector was after Credit Crunch in 2007, when rating agencies raised the criteria for banks to receive high ratings and became more conservative in all their actions. Banks themselves started to suffer from stricter regulation and it was an abnormal number of defaults in those years due to systematic factors. Because of that, it is reasonable to study data, which was collected after 2007.

Models in this paper would be constructed on the base of data, collected from the beginning of 2008 till nowadays (first quarter of 2018). In total there are 41 quarterly periods. This allows us to achieve most reasonable balance between using large amounts of data and focusing on most recent observations.

Now we proceed to the collection of data needed for CR model. Dependent variable is a rating given by one of the top-three international agencies (Moody's, S&P and Fitch) or the largest Russian agency - Expert Rating Agency. Here it should be noted that most of them have several rating types and scales (national, international and etc.). This paper will take into account following ratings:

· Fitch Ratings - Long-term international rating in foreign currency

· Fitch Ratings - Long-term international rating in national currency

· Fitch Ratings - National scale (Russia)

· Moody's Investors Service - Long-term international rating in foreign currency

· Moody's Investors Service - Long-term international rating in national currency

· Moody's Interfax Rating Agency - National scale (Russia)

· S & P Global ratings - Long-term international rating in foreign currency

· S & P Global ratings - Long-term international rating in national currency

· S & P Global ratings - Long-term rating, national scale (Russia)

· Expert Rating Agency - National scale (Russia)

Data from other agencies can also be included, but there is a too small number of ratings given in period of our interest (less than 100 ratings during the whole period), while process of scales mapping needs large amount of data in order to be accurate. Therefore, other rating agencies were omitted.

Most of the data on ratings was taken from Reuters and CBonds. In first selection there were about 700 Russian banks, that had at least one rating from rating agencies of our interest in last 41 quarters. After downloading data, mapping of scales and switching of letter-scale into numerical were performed.

Thereafter, averaging process was made, as there might be several ratings for a bank from different agencies in one period, and it is incorrect to use only one of them. Firstly, banks which had range between ratings in one period equal to 5 or more points (where total scale is 21 point) were excluded (that made up less than 5% of the whole sample). Then average rating was found by giving equal weights to every rating given in one period.

However, there was another problem, that some banks had only a couple of ratings during the whole period of 41 quarters. Because of that, it was decided to extend existing ratings for periods with no rating, in order to receive correct and full panel data. This can be reasonably made as rating agencies do not need to reassign ratings every quarter and, if some rating is given in previous time period, we can assume that it is unchanged now, given that there are no newer ratings for this bank. So if some bank had, for example, rating equal to 10 in first time period and rating equal to 12 in tenth time period, we can assume that rating in time periods 2-9 is equal to 10, while rating in time periods 11-41 is equal to 12.

All these modifications of ratings data allowed us to achieve full panel for approximately 650 banks with rating (average one) in every time period (first quarter 2008 till first quarter 2018).

Now we switch to collecting data for the dependent variable of the Probability of the Default model. As the default is the discrete event, observable dependent variable can take only two values: 0 when there is no default and bank is still operating and 1 when default has actually occurred.

This data can be easily found in the open sources in the internet, like Banki.ru web-site. All information on banks that had a default in past 41 quarters was collected and modified in panel-type data. All in all, there were about 400 banks, defaulted in this period, while only 190 had at least one rating given by agencies of our interest. So we had left only those 190 banks, as for our final model (a combination of CR model and PD model) it is important that the set of banks should be the same.

There is a problem connected with Probability of the Default models arising due to comparatively low number of defaults occurred. For instance, if there are 41 periods and 100 banks, out of which 10% had defaulted, there might be only 10 defaults observed out of 4100 observations in total, as default occurs only in one period. This problem may negatively affect forecasting power of the model, as it underestimates Probability of the Default. Because of that, it was decided to extend default occurred for the previous two periods. So for the same example with 41 periods, 100 banks and 10% defaulted, defaults observed would be at least 30 out of 4200, which is far more reasonable figure. This will allow PD model to minimize underestimation of default probability and overestimation of banks financial stability.

Observations of defaults were also used for constructing Ratings model. There is a need in them, as rating agencies rarely assign worst-case rating (in our setting this is 21) after bank has defaulted. This can be explained by the fact that all ratings assigned need to be payed, but defaulted bank has no money for that. This causes following problem: banks, which had some positive rating in the past and have defaulted sometime after rating assignment, were extended to have same initial rating in all periods, even after default. This, of course, causes large bias in our models and it was decided to assign rating equal to 21, if we know that bank has defaulted in that (or previous) period. So if a bank had a rating equal to 10 in first period and was defaulted in tenth period, it will have 10 rating in 2-9 periods and 21 rating afterwards.

Now we need to find data for our explanatory variables. As it was mentioned earlier, we have same set of factors, and consequently of data, for constructing both, Probability of the Default and Ratings models. For calculating those factors, data from banks' financial statements (from CBR website, 101-102 forms) is used. This data includes:

Table 3.. Data for explanatory variables

#	Data
1	Impaired loans
2	% of capital held by investors
3	% of impaired loans
4	% of reserves for impaired loans
5	Reserves for impaired loans
6	Total assets
7	Loans
8	Net assets (w/o reserves)
9	Cash and equivalents
10	Deposits
11	Share capital
12	Net interest income
13	Interest income
14	Interest expences
15	Operational income
16	Operational expenses
17	Net profit/loss
18	Net interest margin
19	Infation
20	GDP growth rate
21	GDP per capita
22	Corruption Perception Index
23	Sovereign rating

Explanatory variables for both models can be calculated as following (right column represents accounts from financial statements numbered in previous table 3):

Table 4. Formulas for explanatory variables

Name in regression	Factor	Formula
X1	Return on assets	17/6
X2	Return on equity	17/11
X3	Net interest margin	18
X4	Net profit with reserves / Assets	17+5/8
X5	Interest income / Assets	13/6
X6	Interest expenses / Interest income	14/13
X7	Operational expenses / Operating income	16/15
X8	Current ratio	7+9/10
X9	Deposits / Equity	10/11
X10	Net assets / Deposits	8/10
X11	Liquid assets / Deposits	9/10
X12	Loans / Deposits	7/10
X13	Tier I ratio	11+17/8
X14	Equity / Assets	2
X15	Impaired loans / Loans	3
X16	Loan loss reserves / Loans	4
X17	Loan loss reserves / Assets	5/6
X18	Impaired loans / Equity with loan loss reserves	1/11+5
X19	Unreserved impaired loans / Equity	1-5/11
X20	Loans net of reserves / Net interest income	7-5/12
X21	Ln (Assets)	ln(6)
X22	Infation	19
X23	GDP growth rate	20
X24	GDP per capita	21
X25	Corruption Perception Index	22
X26	Sovereign rating	23

Data was aggregated from the site of Russian Central Bank and Mobile database. Those databases include accounts for more than 1200 banks, but still, not all banks from our previous sample (banks with ratings in at least one period) were found. After matching those two samples, a pre-final sample was made, which includes about 400 Russian banks. For those banks we have both, dependent variable (rating or default occurred) and explanatory variables (financial data).

Later, banks which have low amounts of financial data (less than 50% of needed data in periods prior to default) and which are nationalized were excluded. Nationalized banks (that have significant share of capital (50% or more), coming from the government) include: Sberbank, VTB, Gazprombank, Otkritye, Pochta Bank and several others. They were excluded due to the fact that CR model in this paper is aimed to estimate stand-alone ratings, were government actions are not included in rating calculation, while if government has a share of capital in a bank, it is certainly interested in increasing financial stability and affecting rating of that bank. After all modifications we have received the final sample which includes 338 banks.

Data in financial statements was mostly given in monthly form and reshaped into quarterly form by summarizing income statement figures and choosing last figure of the quarter for balance sheet figures. Moreover, data was in the wide-form, with banks on the y-axis and time periods on the x-axis, while we needed data in long-form with both, banks and periods, on the y-axis and explanatory variables on the x-axis (the panel data). In order to achieve such form, reshaping process using STATA and EViews was made.

All in all, final sample includes 41 time periods and 338 banks (13858 observations in total), each with ratings extended to all 41 periods, and data from financial statements on 26 factors.

3. Modelling

In order to achieve the goal of this diploma paper and to construct the final combined model, it is firstly needed to construct each model (Credit Rating model and Probability of the Default model) separately. This is needed to achieve the highest significance of each model, which, in turn, would increase the significance and the forecast power of the final model.

3.1 Modelling credit ratings separately

Modelling of credit ratings starts with considering the largest model with all available internal explanatory variables (without macroeconomic ones) and applying Step-Wise procedure to eliminate insignificant and strongly correlated ones.

Step-Wise procedure is applied in three steps:

1. Estimating the largest model - Model 1:

xtologit rat ROA ROE NIM NI_A IRev_A IEff Oeff CA_CL CL_E netA_CL liqA_CL Loan_Dep Tier1 E_A iLoan Res_L Res_A iLoan_ER uniLoan netLoan_II lnA

2. Excluding most insignificant and correlated explanatory variables (Loan_Dep, netA_CL, liqA_CL, IEff) and estimating the model with left variables - Model 2:

xtologit rat ROA ROE NIM NI_A IRev_A Oeff CA_CL CL_E Tier1 E_A iLoan Res_L Res_A iLoan_ER uniLoan netLoan_II lnA

3. Again, excluding insignificant and correlated explanatory variables (ROA, IRev_A, CA_CL, E_A, Res_L, netLoan_II, NI_A, uniLoan, iLoan_ER) to receive the final model (without quadratic variables and macroeconomic coefficients) - Model 3

Table 5. Step-Wise procedure for CR model

	Model 1	Model 2	Model 3
	Coefficient	P-value	Coefficient	P-value	Coefficient	P-value
ROA	1,3465720	0,2780000	1,3417480	0,2790000	0,0470869	**0,0300000
ROE	0,0631430	**0,0120000	0,0631940	**0,0120000
NIM	-3,1968360	***0,0010000	-3,2363490	***0,0000000	-2,9600880	***0,0000000
NI_A	-0,5173543	0,1800000	-0,5179676	0,1800000
IRev_A	0,2222617	0,7420000	0,2248188	0,7390000
IEff	-0,0155347	0,9120000
Oeff	-0,0009741	0,2790000	-0,0009754	0,2780000	-0,0010313	0,2520000
CA_CL	-0,0000015	0,7320000	-0,0000001	0,8870000
CL_E	0,0045355	**0,0150000	0,0045402	**0,0150000	0,0046799	***0,0090000
netA_CL	0,0000011	0,7480000
liqA_CL	0,0000197	0,9670000
Tier1	0,5561198	*0,1000000	0,5514977	*0,1000000	0,6034596	***0,0000000
E_A	-0,0463119	0,9220000	-0,0440612	0,9260000
iLoan	-1,1733830	***0,0050000	-1,1725080	***0,0050000	-1,3599280	***0,0000000
Res_L	0,0068886	0,9880000	0,0058772	0,9900000
Res_A	2,2917500	***0,0100000	2,2909680	***0,0100000	1,5807190	***0,0010000
iLoan_ER	-0,0267414	*0,0530000	-0,0266029	*0,0540000
uniLoan	-0,0223421	0,1130000	-0,0223366	0,1130000
netLoan_II	0,0000312	0,5670000	0,0000315	0,5630000
lnA	-0,0760145	**0,0490000	-0,0751861	**0,0480000	-0,0643806	*0,0660000
LogL	-15291,435	15291,496	-15486,215
AIC	31674,870	31668,990	31040,430
BIC	32013,850	31985,860	31291,430

* - significant at 10%, ** - significant at 5%, *** - significant at 1%.

Model 3, received after Step-Wise procedure, is as following:

xtologit rat ROA ROE NIM NI_A IRev_A Oeff CA_CL CL_E Tier1
E_A iLoan Res_L Res_A iLoan_ER uniLoan netLoan_II lnA

This model has mostly significant and uncorrelated coefficients (information about the significance of the coefficients of each model and about the correlation of variables is present in the annex 1), but there are still some insignificant ones (CL_E, Oeff). They cannot be omitted, as there should be explanatory variables for each group of meaningful factors in the CAMELS methodology (without management quality, which is a subjective factor by its nature). Insignificancy problem would be fixed by procedures applied in the next steps.

Model 3 has the lowest AIC and BIC (Akaike and Bayesian information criteria) among first three models. It is a clear indicator of its dominance over the Model 2 and Model 1, as those criteria are used to choose the best model, while penalizing for number of explanatory variables. Those criteria are relevant here due to a large number of variables in the initial model.

However, it is still needed to add macroeconomic coefficients for explaining systematic factors and quadratic terms for considering decreasing marginal effect of some variables. First set of macroeconomic explanatory variables would include infl, sovrat, gdp_c, gdp_g and corrup, while quadratic terms would be created for Oeff and lnA. Those variables would be included in the Model 4.

It should be noted that after adding Oeff2 (which is Oeff 2) to the original model, we have received higher significance of the new variable than it was of the Oeff itself. Therefore, it was decided to omit Oeff and leave only Oeff2. LnA2 is also significant, but together with the original LnA, therefore, both of them were leaved. Among coefficients of macroeconomic variables there were two strongly insignificant coefficients (gdp_g and corrup) and therefore they were excluded. Other were also insignificant on 10% level and strongly correlated between each other (table of correlations is in the annex 3).

In addition to the Model 4, we can apply Principal Component analysis for those new variables together with insignificant variables from the Model 3. It is needed mostly due to the high correlation between all macroeconomic variables and due to large number variables in total. Application of PCA leads to the estimation of the Model 5. Two new models and the model received from the Step-Wise procedure are summarized in the table 6 below.

Table 6. Models for estimation of CR

	Model 3	Model 4 (with macro & squared)	Model 5 (with PCA)
	Coefficient	P-value	Coefficient	P-value	Coefficient	P-value
ROE	0,047087	**0,030000	0,045034	**0,039000	0,045494	**0,037000
NIM	-2,960088	***0,000000	-2,624031	***0,002000	-2,674055	***0,002000
Oeff	-0,001031	0,252000
CL_E	0,004680	***0,009000	0,004524	**0,012000	0,004559	**0,011000
Tier1	0,603460	***0,000000	0,552941	***0,002000	0,567071	***0,001000
iLoan	-1,359928	***0,000000	-1,392402	***0,000000	-1,309400	***0,000000
Res_A	1,580719	***0,001000	0,987097	*0,057000	1,088232	**0,035000
lnA	-0,064381	*0,066000	1,167938	***0,000000	1,139238	***0,000000
Oeff2			0,000001	0,237000
lnA2			-0,040495	***0,000000	-0,039695	***0,000000
infl			-1,636311	0,203000
sovrat			0,080443	***0,009000
gdp_c			-0,000056	0,220000
pc1					0,034594	*0,081000
pc2					-0,024692	0,114000
LogL	-15486,215	-15469,678	-15472,326
AIC	31040,43	31015,36	31016,65
BIC	31291,43	31295,88	31282,41

* - significant at 10%, ** - significant at 5%, *** - significant at 1%.

From the results obtained, we can see that Model 4 actually performs better (according to AIC/BIC), but it should not be chosen, due to a high correlation of it variables. Therefore, Model 5 with PCA is chosen at this step. Most of the coefficients of the Model 5 are significant and uncorrelated, with the exception of Principal Component Variables, which are still better than pure macro coefficients and Oeff. Precise explanation of components of the PCs can be found in the annex 4.