DESCRIPTION OF MATHEMATICAL MODELS USED IN RATING ACTIVITIES
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1 July 2014, Frakfurt am Mai. DESCRIPTION OF MATHEMATICAL MODELS USED IN RATING ACTIVITIES This documet outlies priciples ad key assumptios uderlyig the ratig models ad methodologies of Ratig-Agetur Expert RA GmbH. Ratig methodologies used for assigig credit ad reliability ratigs are based o the ratig models. Ratig model for assigig credit ratig represets a regressio equatio where the explaied variable is usually the probability of default (delayed ad/or icomplete fulfillmet of obligatios) of the ratig object ad the explaatory variables are the quatitative ad qualitative (usually i the form of dummy variables) factors, iformatio for which may be received from the ratig object or other sources of iformatio available to the agecy. Commo priciples of buildig ratig models The purpose of preparig ratig model is idetificatio of factors largely ifluecig the probability of default (creditworthiess) of the ratig object as well as the form of this ifluece (positive/egative, liear/o-lier depedecy). Ratig model is the result of processig the database of source iformatio usig the methods of ecoometrics ad mathematic statistics. Buildig statistically sigificat regressio equatio requires fulfillig a umber of assumptios regardig the source data. Key assumptios regardig the source data are provided below: Market, to subjects of which the methodology is applied, ca be cosidered as relatively mature, therefore the data time series is available for at least 8 quarters. Total umber of objects of this type (or their aalogues) for which iformatio ca be gathered is ot less tha 20. Iformatio is available at least for 5 cases of defaults of the objects of this type (or their aalogues). Distributio of source data is close to ormal distributio (preferably), logistic distributio or Gompertz distributio (for checkig the hypothesis about ormal distributio the Perso criteria is used as mai method with 0,05 sigificace level is used o the basis of compariso of theoretical ad empirical frequecies). The collectio of iformatio about the objects similar to the ratig object is doe usig both free ad fee-based sources of iformatio. With icreased volume of available iformatio (i particular, from iformatio provided by the rated etities) improvemet of the ratig models shall be doe through icludig ew factors. 1
2 Whe formig the set of explaatory variables it is compulsory to take ito accout the experiece of preparig ratig models for similar markets. I particular, large weight i ratig models is usually give to idicators of capital adequacy, quality of assets, profitability ad liquidity. Therefore whe startig work o ew ratig model the set of quatifiable idicators (which ca be evaluated) is formed which ca approximate correspodig factors for this market metioed above. The modellig is usually based o the probit-regressio (model of biary choice: 1 etity has defaulted withi the period, 0 there was o default), evaluatio of its parameters is doe o the basis of most likelihood method. I some cases the logit-regressios are used (source data correspods to the logistic distributio) or gompit-regressio (source data correspods to the Gompertz distributio). Determiatio of ratig methodology Ratig methodology is a set of rules usig which the ratig object ca be assiged to oe of the ratig classes accordig to the array of data available for this ratig object. From mathematical poit of view by the methodology of ratig assessmet the superpositio of fuctios evaluatig particular characteristics of the rated object is assumed, coverted iitially to the probability of default ad the to particular ratig class o the basis of theoretical default matrix. R = Pd( g ( )) j Md i=1 p I the above formula: R ratig class, R Ratig scale Pd mootoe fuctio of trasformig the ratig score ito the probability of default g fuctio of evaluatig the parameter p, p parametric vector Md defied theoretical default matrix j fuctio of displayig the default probability set i form of a ratig class p represeted by three types of data: 1) Degeerate vector i the form of scalar oe-dimesioal value 2
3 2) Usual scalar vector 3) Vector of biary values (usually this is how the evaluatio of qualitative factors looks like o the basis of so called check-list ) g is preseted by the followig types of fuctios: 1) Liear fuctio 2) Noliear fuctio (power trasformatio, logarithms) 3) Piecewise-oliear fuctio g with bifurcatio o-liearity (piecewise liear with sharp chage of the respose) is used for support ad stress factors Theoretical default matrix defies correspodece of ratig classes to the rages of default probabilities. Usually the lower is the ratig class the wider is the rage of default probabilities which correspods to it. Dramatic icrease of the default probability rage usually occurs i the trasitio from B- class to CCC+ class (accordig to the iteratioal ratig scale of the agecy). Commo priciples of creatig ratig methodologies Usually the ratig methodology is based o ratig models which are statistically sigificat o the 0,1 sigificace level (further referred as alpha), however for exceptioal cases of immature markets the model with alpha up to 0,2 ca be used (i this case the ratig methodology iclude more coservative requiremets). Whe creatig the ratig methodology a whole rage of priciples shall be take ito accout which are ot icluded by the ratig model due to various reasos, icludig the specifics of source data (small umber of extremely large ad extremely small values). The most importat of these priciples are provided below: Priciple of sigificace. Eve if the impact o the creditworthiess of the correspodig factor withi the framework of the ratig model is statistically ot sigificat (with alpha less tha 0,1) the ratig methodology shall iclude aalysis of all accout of balace sheet ad profit&loss statemet o profits ad losses exceedig 5% of the assets (10% of the reveue) i order to idetify their ecoomic meaig. This is ecessary i particular for idetificatio of uusual ways of asset strippig or falsificatio of reports. Priciple of reasoable trust. All sigificat iformatio which ca be verified shall be verified. I this regard the ratig methodology shall cotai a rage of test for 3
4 verificatio of mistakes i provided data ad provide pealties for itetioal ad uitetioal mistakes. Priciple of groupig the factors. Due to the fact that icreasig the umber of explaatory variables (factors) might lead to decrease i the quality of ratig model (if above defied threshold depedig o the umber of observatios i the source data set this ca lead to iability to some methods of evaluatio, i particular the least squares method), idicators close by meaig (for example profitability of assets ad profitability of capital) ca be grouped before iclusio i the tested ratig model. Priciple of strog factors. Amog aalyzed idicators the factors which have sigificat ifluece o fiacial stability of the rated etity (support ad stress factors) shall be idetified. These factors shall be take ito accout separately ad have maximum weight i the methodology. Priciple of cumulatig the risks. Sigificace of egative factors icreases oliearly i case of their mutual ifluece o each other. This mutual ifluece ca be take ito accout whe formig stress factors i the ratig methodology. Priciple of supremacy of cotet over form. I the process of aalysis the priority shall be give to ecoomic ad ot accoutig cotet of the operatios, I relatio to that the ratig methodology ca take ito accout the expert correctios obtaied withi the framework of ratig model of evaluatig the explaatory variables with compulsory justificatio ad lik to the factors ot icluded i the ratig model. After takig ito accout the priciple metioed above the obtaied ratig methodology shall be calibrated by testig o the available sample of defaulted objects; form of the g shall be fixed, coefficiets shall be selected so that the value of the fuctio Pd( i=1 g ( p )) for all defaulted objects was approachig to 1 o the horizo of 6 moths prior to the default. The it should be checked that the obtaied coefficiets are ot givig false triggers for the majority of o-defaulted objects. Back-testig of the ratig methodologies Basic back-testig of the ratig methodologies is carried out with costructig the empirical default matrix ad comparig it with the theoretical. Serious deviatios of the actual default matrix from the theoretical ca idicate a reaso to review ratig methodology. Default matrix - sapshot of the trasitio matrix which represets a Markov trasitio matrix with discrete time: ( P ij ), where: 4
5 P ij probability of trasitio of the ratig objects from oe ratig class to aother (usually o the horizo of 15 moths). Trasitio matrix is costructed cotiuosly. For the default matric oly the probabilities of trasitio to the default class are take ito accout. I-depth back-testig icludes aalysis of whole trasitio matrix with the purpose of idetifyig abormally high probabilities of trasitios from oe ratig class to aother oe. Abormally high trasitio probabilities may idicate the ecessity of applyig more coservative approaches i board lie case, which may also require review of the ratig methodology. Frequecy of back-testig depeds o the specifics of the rated objects. The back-testig of all methodologies shall be doe at least oce i 2 years ad 2-3 times more frequetly for dyamically chagig markets (icludig immature) with accumulatig statistics of defaults. 5
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