About Ratings & Segments on IRB Approach
João Pires da Cruz1

Introduction
The Basel Committee on Banking Supervision, on the process of definition of the New Capital Accord, establishes a stepwise framework for regulatory capital allocation for credit risk, starting on what is designated as Standard Approach, in which banks must allocate capital according to regulatory rules, and finishing on what is designated as the Advanced IRB Approach, in which banks must allocate capital based on their own risk evaluation and on the committee guidelines for that evaluation. The committee defines several guidelines for the IRB Approach depending on the type of credit exposure but, technically, we can group the several lines of attach into two ways of deal with the credit portfolio, the rating approach, for the major exposures like banks, sovereigns and corporate; and the segmentation approach for retail and small business exposures. The most accepted credit risk frameworks are rating based models since, historically, the aim of the models was the bond market, the market of debt securities issued by stable corporations, banks and states. In this market, the assumption that a debt security is less risky than other debt security become the essence of the market, since debt issuers need to disclose information to lower the price of the debt security, affected by a risk premium over the interest rate. And the disclosed information includes rating agencies evaluations of financial figures, operational processes, company market risks, costumer risks, etc…. A bond issuer to be ratted at a high grade must be completely ‘undressed’ and accompanied by a rating agency and, with a very good probability, the rating agency evaluation is valid for the time horizon of the risk model and the rating criteria are well known by all intervenient – market, issuer and agency. In these conditions one can say ‘this bond is better than that’. But a bank portfolio is not made only of big exposures. And since the most accepted models are rating based, many banks are building scoring applications for smaller customers in order that the same risk models can also be applied, leaving behind the committee suggestion for segmentation. In this document, we focus on the scoring vs. segmentation problem and why segmentation is clearly the best approach to Basel II problem.

What is rating?
When someone rates something, gives that something an ordinal place. That something becomes ‘better’ or ‘worse’ than another of the same kind. This states the obvious, but when we are talking about credit risk, this means that the probability of the one borrower defaults is less than other borrower with a lower grade. If we are talking about big corporations (banks included) and states, it is more or less intuitive what kind of factors will be important for that probability of default in a time horizon of one year. The political stability of country of residence of the
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Partner at KPI Solutions, SA; can be reached at joao.cruz@kpisolutions.pt 1/5

corporation, the economic growth, the financial structure of the corporation, the loyalty of the customers, the employee quality, etc…The kind of factors that a rating agency can relate to a probability of default is, for our purpose, indifferent. Let us keep in mind that there are factors associated with an exposure that can lead that exposure to be less risky than others. Now, let us make a visit to a normal bank counter somewhere in a mid size European country. Obviously, the bank manager responsible by the counter will not act like a rating agency. He will not send dozens of auditors to someone home or to a small company office to evaluate all risks that the possible debtor is subjected. He can ask for some financial figures of the possible debtor and, based on his reasoning, he will make his own mental rating. Many times, his mental rating, due to the same reason why the bank has a counter on that place with that manager – the knowledge of the environment – is a much better risk assessment than some other mechanical risk assessment, because on the manager mind several factors are being weighted at the same time – the personal relation to the debtor, his knowledge of the business quality of the company, the good relation with the community and many other subjective factors, that are better insurances to the bank that other quantifiable factors. Nevertheless, the bank needs to have a risk evaluation, independent of the commercial managers’ mental rating. For that purpose, banks usually extend their rating approach to all segments of the credit portfolio, both ‘big’ costumers and ‘small’ costumers, making use of scoring systems that override the commercial manager mental rating. But, doing so, aren’t we merging different concepts just to take an incorrect shortcut? For analyzing this question let us take a look to the differences between rating and scoring.

Scoring/ Rating
Since it’s impossible to have a structured evaluation of all financial and risk factors for all costumers on the time horizon of a risk evaluation, banks are going on a scoring strategy. The main difference between a rating, as in credit rating, and a scoring, as in credit scoring, is that rating is the result of a full company evaluation, of all possible/required company information and a scoring is based on a predictive model based on the existent information. The difference seems semantic but in fact it is not. We can have many, several or few information; a scoring will always come out, but not a real rating. Rating we already know what it is. Several auditors evaluate financial and risk figures of the company under evaluation, look at its straights and weakness’ and classify it according with their earlier experience. Scoring is a mechanical task, despite the fact that it can be human supervised, used for fast classification based on massive information. More, when we are talking about private costumers, many countries have legal limitations regarding what costumer characteristics may be used in credit scoring (ex.: Race, gender or age). In fact, the score is given by the total conjunction of the characteristics according to the occurrence of defaults but there is no proper explanation on what generated the default. This means that the scoring model can be adjusted with the occurrence of new defaults but will give always a ‘blind’ probability in the sense of an intensity function. And with ‘blind’ probabilities we will not have a default prevision, just a default pattern based on the today’s knowledge. Rating, on the other hand, is a default prevision since all risks, market and financial figures counts. There is company risk assessment by the assessment of the risks of the company. And, using scoring, where are the qualitative, valid and important, assessments of the local counter manager that know the small costumer, his history, his commitment, his reputation?

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Micro-credit experiences have taught us a big lesson in the past few years, some ‘life collaterals’ are much more important than real estate ones. We should notice that these factors are not a reason why a bank should dismiss a risk evaluation. In fact risk evaluation must take place even if the bank has the best counter managers in the market. But the risk evaluation should be understandable and complementary to the manager assessment, not override it. A mechanical scoring process overrides the manager assessment and, as we have seen earlier, does not give an understandable evaluation of the risk. In conclusion, rating is a good tool for capital allocation for credit risks, but scoring it’s not. Mostly because ratings are driven by the risks that affect the company and with scorings we are hiding those risks, but also because we are killing the biggest asset on a commercial bank, the managers feeling. So we have seen that ratings are useful tools for evaluating capital allocations and scorings are not. But what should banks do with the small credit portfolio? The answer is on the New Capital Accord and on the Merton-Vasicek Model - segmentation.

Basel II risk evaluation rules
The Basel Committee on Banking Supervision, in his Third Consultative Paper, gives two major guidelines for risk evaluation, one for ‘big’ costumers, like banks, sovereign and corporations, and one for retail and small business costumers. The ‘big’ costumer line is clearly a ‘rating line’. Because costumers with the specified level of sales (50 million euros) have relatively stable risk factors and heavy funding needs, which mean that, both the costumer and lending banks, have the need for periodic risk factors assessments. And, for the lending bank, the expected profitability justifies that assessment, since the volume of the exposure grants the complete payment of the evaluation costs. Additionally, companies with this level of sales are usually quoted on equity markets, which lead to periodic disclosure of information and to have its activity accompanied by hundreds of current and potential investors. Similarly, states with democratic regimes and free market policies are continuously controlled by external and internal entities that make financial information public. Due to these factors, the ‘big’ costumer line is adequately a ‘rating’ line, because even if a bank decides to rate this costumers in a different framework, it’s only choosing to evaluate the more or less stable, and well known, risk factors in a different way. And the expected profitability of the transactions can cover the costs of the successive rating revisions through the life of the exposure. The Committee establishes clearly that for bank, corporate and sovereign exposures, the ‘rating line’ should be used. For smaller costumers, the Committee gives the banks the option of going through the ‘rating line’ or changing to the ‘segmentation line’. The Committee states that for retail and small business costumer, segmentation, rather than rating, can be used. This means that the exposures can be organized in buckets with the same probability of default and loss given default in way that there are no underlying grading, i.e., a segment is not necessarily ‘better’ or ‘worse’, just different. But if we can intuitively see that grading costumers apparently leads to a better risk management, the segmentation option is not so intuitive. To make this clear, we will check on the Merton-Vasicek One Factor Model that can make us understand the advantages of segmentation in relation with a grading based risk evaluation.

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The Merton-Vasicek One Factor Model
The Merton-Vasicek One Factor Credit Risk Model is the conceptual model behind the Basel II formulation. Mainly due to Gordy’s2 work on proving that a One Factor model applied to a portfolio with homogeneous exposures in size and with defaults driven by one external factor is a bucket-like capital allocation framework. In the early consultative papers, the Committee faced the problem that most market accepted models are portfolio models, in which diversification plays a major role, and commercial practice is bucket based, like the old capital allocation rules. Since Gordy’s work, the One Factor Model becomes the ‘standard model’ for explaining credit risk. The model is very simple if we think about a corporation, but the assumptions are valid for all kind of debtors. One key assumption of the model is that the debtor defaults if the value of his assets (or the net between the assets and liabilities) go bellow a point where he can not fulfill his financial commitments. The other is that the value of his assets is driven by an abstract external index in the form

Vn = ρ ⋅ Y + 1 − ρ ⋅ ε n where Y is the external index, Vn is the value of the assets of the debtor, εn is an idiosyncratic factor and ρ is the dependence between the index and the value of the assets of the debtor, typically expressed as a linear correlation. If we consider that exists a level bellow which the debtor defaults, and consider that Y and εn standard normal distributions, we have the expression for the capital requirement for α realizations of the index Y ,

 Φ −1 (PD ) + ρ ⋅ Φ −1 (α )   C (α ) = LGD ⋅ Φ   1− ρ   where LGD and PD are the loss given default and probability of default risk factors according with the Basel II framework and Φ is the gaussian function3. Simple substitutions and we will recognize the calibration formulas stated all over the Third Consultative Paper. The main point here is that correlation factor ρ is the residual spot of an abstract index that started all formulation. If we are dealing with full risk assessment rather than fulfilling the Basel II requirements (which gives ρ as a PD function), the factor PD is easily evaluated from the historical events giving us the last task of evaluating ρ. PD gives a direct mapping to a rating but, as we have seen earlier, evaluating a PD based of very unstable factors for time horizon of the risk evaluation is spurious. That’s what most of the banks are making with scoring systems, making PD’s for costumer that almost certainly will be trembling score up, score down during the time horizon of the analysis. They are grouping their costumers for what is volatile, and not for what is stable. Finding a score will most certainly give origin to a PD, but the correlation factor will be spread all over the scoring engine vectors. Since the committee put a value on the correlation factor, scoring became an option but, as we have seen earlier, risk evaluation is the great victim.

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Gordy, Michael B. ‘A risk-factor model foundation for ratings based capital rules’ - 2002 The demonstration is quite straightforward, and is documented in several papers. 4/5

Obviously, this is not inconsequent for the risk assessment of the bank portfolios, since given up correlation means to give up of local specificities of the portfolio. That’s why many national central banks are now correcting this by means of provisions. We can put our portfolio credit risk driven only by PD, but we are not managing risk, just fulfilling requirements, and that will have consequences on provisions.

Reasonable IRB Approach
The IRB approach is, first of all, a segmentation problem. First of all, we must separate the exposures that the accord and, additionally, the bank defines as exposures that costumers are subjected to a rating, i.e., someone can tell that the probability of default for that costumer is x because y. The remaining exposures should be organized in segments, related to an activity or where we can find some index that we can say ‘those costumers will default if…’. For those not familiar with risk evaluation methods will find this absurd. Are we evaluating risk without knowing what makes costumers default? Yes, but we can. By Basel II rules, we can. Obviously, we are not in fact managing risk, but we are evaluating it for regulatory purposes. That’s why segmentation, rather than scoring, is the proper method for evaluating credit risk for exposures where proper rating is not possible. On KPI Solutions we are developing credit risk models for some time now. And we develop scoring models, also. One conclusion we already achieved – scoring is good for credit approvals originated in places we don’t trust, but evaluating risk is an exercise where the knowledge of cause and effect is essential.

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