# Comparison of Ratings: Methods and Algorithms

The rating process has some problems, such as

• A relatively small number of updated communicative ratings.

• Difficulties of comparison of estimation between different rating agencies.

• Absence of any integrative effect from available competitive estimations of independent agencies.

• A demand for extended usage on independent rating estimations primarily owing to modeling techniques.

We aim to achieve a comparison capability of independent estimations of different ratings. In this way the elaboration and development of the approaches and methods are especially urgent because of synergy opportunities connected with the limitations mentioned above. For these aims the Joint Rating Environment (JRE) was introduced, and included a selection of basic rating scales, the building of a mapping system of external and internal ratings to a base scale, and the common usage of all rating estimations for every class of issuer or financial instrument.

We used statistical approaches to calculate the distance between different ratings for the same entities. Also we selected a basic scale, in which we proposed to measure the difference between ratings, and proposed to use mapping between rating scales, while our aim is to find functional approximations of such maps.

Econometric approaches were studied in the paper (Ayvazyan et al. 2011). In this method, firstly, the econometric order choice models for every CRA were determined. Then the correspondence between latent variables for the model for the basic CRA and every other CRA model in polynomial form was estimated. These gave an opportunity to determine the mapping of every CRA scale to the basic scale at last.

The main points of distance algorithm for the rating scales’ comparison include not only the methodology of agency-scales mapping, principles and criteria for

Fig. 1 The system of scale mappings

comparison of rating scales, but also the choice of an optimization algorithm, the construction of a comparison scheme and a table, the principles of result auditing during that time and so on (Hainsworth et al. 2012).

In this paper Moody’s rating scale is used as a basic scale, but the results must be practically invariant to the choice. The system of mapping, which was presented in Fig. 1, was established. In this figure the first group of mapping deals with the correspondence between the rating and numerical scales, which is reasonable because of the rating’s orderliness. The mappings to the basic scale

Fi (a,/ : NSi! BS

for every rating scale Ri were parameterized, and our aim is to find the vectors aj for each scale i = 1,…, N, where N—the number of the scales.

We have considered some parameterization of mappings Fj(aj) = aii * fi(Ri) + ai2, using functions fi(Ri) from some classes and a vector of parameters of the map aj = (an, ai2). At this step we have formulated the task of the parametric optimization problem. We used a square measurement between rating images in this research:

min V (F-1 (Rnjt, an) – F,-2 , a,-2))

{ai, i = 1,…N} Q

Above we mean that

Q—the set of combinations of points over time

q = {quarter t, bank j, the rating of the basic agency Riijt, the rating of the other agency Ri2jt g;

Fi1 and Fi2—the maps for j1 and i2 scales as defined above.

During the research we compare linear, power and logarithmic function classes fi, which were used for the evaluation of map dependences.

An additional analysis of the default statistics for Moody’s and S&P gives us an opportunity to use a priority logarithmic approximation, which we use in this paper for empirical analysis. It must also be mentioned that for the previous problem we

 Rating scale ait ai2 Moody’s (Russian scale) 0.254 2.202 Standard and poor’s 0.916 0.146 Standard and poor’s (Russian scale) 0.265 2.113 Fitch ratings 0.749 0.594 Fitch ratings (Russian scale) 0.213 2.162 AK&M 0.269 2.491 Expert RA 0.373 2.329 RusRating 0.674 1.016 National rating agency 0.163 2.474 Number of estimations 3,432 Pseudo-R2 0.902

 Italic texts were connected with statistical summaries of the tables.

could have used econometric program packages such as eViews or STATA because of the use of the quadratic criteria (the experiments with other criteria showed the robustness of the comparison results).

We provided this analysis for both Russian and international data. For the Russian data we had a sample for a time span of 20 quarters (from 1Q 2006 till 4Q 2010), as well as the data for periods until 2012 in other examples. We have collected data from three international agencies (Moody’s, S&P and Fitch) on both international and national scales, as well as from four Russian agencies (AK&M, NRA, RusRating and Expert RA). This sample has included 7,000+ pairs of ratings for 370 Russian banks with any rating during this time span.

The result of the optimization task decision is presented in Table 1.

The results derived from this can be presented both in scheme (Fig. 2) and table interpretations. At this point we have constructed a scale correspondence, which may be used in practice for regulatory and risk management purposes.

It should be mentioned that the correspondence between international agencies on traditional scales are not identical, and we can compare the difference between these agencies with the Russian banks.

It also should be noted that the results included in the scheme are stable. We have compared the results not only with a different base scale, but also with two different methods such as distance and econometric methods. The results obtained give us the opportunity to acquire comparable estimations of entities for both regulation and risk management aims.

For the international banks’ models an accurate forecast was generated in nearly 40 % of cases. The forecasting power may be estimated by mistakes on the part of the models, which in the case of no more than two grades gave a probability of 1-2 %. These results were comparable with previous models, but extended to three international rating agencies simultaneously.

The signs for all the models were almost equal, and could be easily explained from a financial point of view. Coefficient sign analysis allowed us to make the following conclusions:

• The size of the bank is positive for a rating level increase, also as capital ratio and asset profitability as the retained earnings to total assets ratio.

• Such ratios as debt to asset and loan loss provision to total assets have a negative influence on the rating grade.

• Macro variables are also important for understanding the behavior of bank ratings, and are presented with a negative sign for the corruption index and inflation.