The credi porfolio managemen by he economeric models: A heoreical analysis Abdelkader Derbali To cie his version: Abdelkader Derbali. The credi porfolio managemen by he economeric models: A heoreical analysis. 2018. <hal-01696010> HAL Id: hal-01696010 hps://hal.archives-ouveres.fr/hal-01696010 Submied on 30 Jan 2018 HAL is a muli-disciplinary open access archive for he deposi and disseminaion of scienific research documens, wheher hey are published or no. The documens may come from eaching and research insiuions in France or abroad, or from public or privae research ceners. L archive ouvere pluridisciplinaire HAL, es desinée au dépô e à la diffusion de documens scienifiques de niveau recherche, publiés ou non, émanan des éablissemens d enseignemen e de recherche français ou érangers, des laboraoires publics ou privés.
The credi porfolio managemen by he economeric models: A heoreical analysis Abdelkader & Derbali 1 Absrac: This main idea of his paper is o examine heoreically he curren model of credi porfolio managemen. We employ he credi porfolio view o examine he defaul probabiliy measuremen. The developmen of his ype of model is based on a heoreical basis developed by several researchers. The evoluion of heir defaul frequencies and he size of he loan porfolio are expressed as funcions of macroeconomic and microeconomic condiions as well as unobservable credi risk facors, which explained by oher facors. We developed hree secions o explain he differen characerisics of his model. The purpose of his model is o assess he defaul probabiliy of credi porfolio. Keywords: Risk managemen; Credi risk; Defaul probabiliy; Credi Porfolio View. JEL Classificaion: G13; G21; G28 1. Inroducion The problem of evaluaion of he failure probabiliy of any borrower was he cener of he bankers as soon as hey began o lend some money. The quaniaive modeling of he credi risk for a debor is raher recen in fac. Besides, he modeling of he credi risk associaed wih insrumens of a porfolio of credi such as, he loans, he pledges, he guaranees and he byproducs (who consiue a recen concep). A cerain number of models were developed, including a he same ime he applicaions of propery developed for he inernal cusom by he financial insiuions, and he applicaions inended for he sale or for he disribuion (Hickman and Koyluoglu, 1999). The big financial insiuions recognize his necessiy, bu here is a variey of approaches and rival mehods. There are hree ypes of models of credi porfolio in he course of use a presen (Crouhy e al., 2000): The srucural models: here are wo models of managemen of credi porfolio who are supplied in he lieraure: Moody's KMV model (Porfolio Model) and CrediMerics model by JPMorgan. The Macro-facors model (Economeric model): The Credi Porfolio View model inroduces in 1998 by Mckinsey. The acuarial models CSFP (Credi Suisse Firs Boson): his model (CrediRisk+) is developed in 1997. The main idea for his paper is o answer he quesion follows: How he defaul probabiliy is defined by he credi porfolio models? 1 Assisan Professor, Higher Insiue of Managemen of Sousse, Sousse Universiy, Tunisia 1
Then, he organizaion of his paper is as follows. In secion 2, we define he economeric models and we define he main characerisics of he model Credi Porfolio View. We provide he forecas of he defaul rae in secion 3. The secion 4 is considered o presen he condiional marices of ransiion. We conclude in secion 5. 2. The Economeric Models (CREDIT PORTFOLIO VIEW OF MACKINSEY) Credi Porfolio View is a model wih muliple facors which is used o feign he common condiional disribuion of he defaul probabiliy and migraion for various groups of esimaion and in differen indusries (Crouhy e al., 2000). This model was developed by Wilson (1997) wihin McKinsey. The approach developed by his auhor bases iself on he hypohesis ha he probabiliy of defec and migraion are conneced o macroeconomic facors such as he level of he long-erm ineres rae, he growh rae of he GDP, he global unemploymen rae, he exchange raes, he public spending, he savings. Credi Porfolio View is based on he occasional observaion which supposes ha he defaul probabiliy, as well as he probabiliy of migraion, is conneced o economic cycles. When he economy is in siuaion of recession, hen he cycles of credi are also lesser. If i is he opposie case (he economy is in siuaion of expansion) hen he cycles of credi become sronger. In oher words he cycles of credi follow he endency of economic cycles. Because he sae of he economy is widely driven by macroeconomic facors, Credi Porfolio View proposes a mehodology o connec hese macroeconomic facors o he probabiliy of defaul and migraion. Provided ha he daa are available, his mehodology can be applied in every counry, in he differen secors and in he diverse classes of borrowers of he obligors who reac differenly wihin he economic cycle. The way ha a model Credi Porfolio View works is as follows (Smihson, 2003): 2
Simulae he sae of he economy. Adjus he rae of defaul o he sae of he simulaion of he economy. Aribue a probabiliy of defaul for every debor on he basis of he simulaions of he sae of he economy. The value of he individual ransacions aribued o he debors according o he probabiliy of defec is deermined on he basis of he simulaions of he sae of he economy. Calculae he loss of he porfolio by adding he resuls for all he ransacions. Repea all he sages quoed above cerain number of imes o map finally he disribuion of he losses. In he model Credi Porfolio View of McKinsey, he hisoric raes of defaul for he various indusries are described according o he macroeconomic variables specified by he user of he model: ( Probabilliy of defaul f GDP, Unemploymen Rae,, Exchange Rae In he approach McKinsey, he raes of defec are commanded by a sensibiliy in a sand of he facors of he sysemaic risk, or he specific facors o he company. The able below summarizes he main characerisics of he model of McKinsey (Smihson, 2003): Table 1 The main characerisics of he model Credi Porfolio View Uni of Segmenaion owards analysis indusries and on counries. The daa Empirical esimaion of he raes by defaul of defaul according o he macroeconomic variables. (For example: he GDP, he unemploymen rae) The Obained from he correlaions srucure of banding he chosen correlaion macroeconomic variables and he The engine of he risk esimaed facors of sensibiliy. The adjusmen of he ARMA model (Auoregressive Moving Average model) wih he evoluion of he macroeconomic 3
The disribuion of he raes of defec The horizon facors. The shocks undergone by he sysem deermine he sandard deviaion of he average of he raes of defec concerning he level of he segmen. Logisic (Normal disribuion). The mauriy of he marginal defaul rae year by year. Source: Smihson (2003) 3. The forecas of he defaul rae In he Credi Porfolio View model, he probabiliies of defaul are modeled as being a Logi funcion. In his modeling he independen variable is a specific speculaive index in every counry and which depends on macroeconomic variables. The Logi funcion allows ha he values of probabiliy of defaul are included beween 0 and 1 (Crouhy e al., 2000; Hamisulane, 2008). P j, 1 1 e Y j, Y β β X β X β X ε And ε ~ N(0, σ ) 2 j, εj, j, j,0 j,1 j,1, j,2 j,2, j, m j, m, j, Where, indicae he condiional probabiliy of defaul for period for he debors of he indusry j and represen an indicaion semming from a model in m facors.,,..., are coefficiens o be esimaed by he mehod he Ordinary Las Squares (OLS).,,, are values of economic variables in he dae of he indusry or he counry j. represen a erm of error which is normally disribued and independen of. The model of McKinsey so land us land us noe, as i is a model of macrofacors who are represened by variable macroeconomic who follow a Auoregressive model of order 2 (AR2): X γ γ X γ X ω And j, i, j, i,0 j, i,1 j, i, 1 j, i,2 j, i, 1 j, ω ~ N(0, σ ) 2 j, ωj, Where:, and are a coefficiens o be esimaed and is a erm of error which is normally disribued and independen of. In his frame, our objecive is o resolve he sysem below: P j, 1 1 e Y j, 4
Y β β X β X β X ε j, j,0 j,1 j,1, j,2 j,2, j, m j, m, j, X γ γ X γ X ω j, i, j, i,0 j, i,1 j, i, 1 j, i,2 j, i, 1 j, Where is he vecor of he innovaions such as: ε E ~ N (0, ) And ω ε ω, ε ε, ω ω Where, and Represen he marices of correlaion. In case he parameers are esimaed, hen i is possible o feign he probabiliy of defaul by basing iself on hisorical daa. Credi Porfolio View uses ired marices of ransiion of economic cycles. 4. The condiional marices of ransiion By basing iself on he marices of ransiion in he economic cycles which are proposed by he Credi Porfolio View, we can deermine he siuaion of he economy (Crouhy e al., 2000). Noing in his respec ha, he marices of ransiion in he Credi Porfolio View are differen o hose of he marices of migraion in he CrediMerics (Hamisulane, 2008). Credi Porfolio View proposes a ool based on he following raio: Where, secor j and on observed daa. P j, φsdp represen he probabiliy of defaul feigned for dae and for he represen he hisoric defaul probabiliy which is based If P j, 1 hen he economy is in period of recession and if φsdp hen he economy is in period of expansion. P j, φsdp 1 Credi Porfolio View suggess employing his raio o adjus he probabiliy of migraion. So, he marix of ransiion muli-period is given by he following formula:, T Pj M M( ) φsdp 1 Where, M(.) can ake wo differen values. So, M(.) = M L if and M(.) = M H if P j., 1 φsdp Where, M L indicaes he marix of ransiion in he case of a period of recession and M H indicaes he marix of ransiion in he case of a period of expansion. 5
We can simulae a lo of ime he marix of ransiion o deermine he probabiliy of defaul for any esimaion and for any period. The mehodology of Mone Carlo Simulaion can be used o deermine he disribuion of he defaul probabiliy for any period. The forces and he weaknesses relaive o he Credi Porfolio View model are presened in Table 2. Table 2 The forces and he weaknesses relaive o he Credi Porfolio View model The forces The weaknesses Credi In he Credi porfolio View Porfolio View model, connecs he we use macroeconomic probabiliy of daa which canno be defaul and he available for a counry marices of or a business secor. ransiion wih This model economic indicaors. In oher deermines only he probabiliy of defaul words, he of a counry or a probabiliy of business secor and no defaul is sronger an issuer. in period of recession han in period expansion. 5. Conclusion of Source: Hamisulane (2008) In his paper, we presen a heoreical approach s concerning he model of managemen of credi porfolio by he Credi Porfolio View model. The Credi Porfolio View model proposes a mehodology which links macroeconomics facors o defaul and migraion probabiliies. The calibraion of his model necessiaes reliable defaul daa for each counry, and possibly for each indusry secor wihin each counry. The probabiliy of failure depends in hese models of macroeconomic facors such as unemploymen, he rae of increase GDP, he ineres rae long-erm. References Ali, A. and Daly, K. (2010). Macroeconomic deerminans of credi risk: Recen evidence from a cross counry sudy. Inernaional Review of Financial Analysis, (19):165 171. Allen, L. and Saunders, S. (3003). A survey of cyclical effecs in credi risk measuremen models. BIS Working Paper, No. 126, New York Universiy. Bensoussan, A., Crouhy, M. and Galai, D. (1995). Sochasic equiy volailiy relaed o he leverage effec II: Valuaion of European 6
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