Implementation of the Stress Test Methods in the Retail Portfolio

Transcription

1 Joural of Applied Fiace & Bakig, vol. 2, o. 6, 2012, ISSN: (prit versio), (olie) Sciepress Ltd, 2012 Implemetatio of the Stress Test Methods i the Retail Portfolio Pawel Siarka 1 Abstract Article refers to the issue of credit risk maagemet i commercial baks. Particular attetio is paid to the problem of stress testig. I additio, methods are preseted that allow predictio of the losses of the portfolio i the cotext of extreme evets relatig to the crises of fiacial markets. The author preseted the results of research based o the extreme values theory, the coditioal loss distributio fuctio ad the profitability aalysis of the loa portfolio. The achieved outcomes has bee show i the cotext of the provisios of the New Basel Capital Accord ad the subsequet cosultatio documets published by the Basel Committee o Bakig Supervisio. It was show that losses caused by the rare but still plausible evets could sigificatly exceed the miimum capital requiremets estimated i accordace with IRB method. JEL classificatio umbers: C13, C16, D81, G21, G32, G33 Keywords: Credit risk, Probability of default, Stress test, Profitability 1 Itroductio The begiig of the fiacial crisis is covetioally dated 15 September O that day the Lehma Brother wet bakrupt, which started the paic i fiacial markets. Dramatic fall i share prices o world markets was accompaied by a declie i liquidity i the iterbak market [1]. The deterioratig ecoomic situatio left o doubt that the slow dow of ecoomic growth is comig. These ad may other factors cotributed to the complex situatio i which may baks stood o the verge of bakruptcy. The iitial 1 Istitute of Fiacial Services, Wroclaw School of Bakig, Polad pawel.siarka@i4fs.pl Article Ifo: Received : August 16, Revised : September 29, Published olie : December 20, 2012

2 16 Pawel Siarka liquidity problems of Faie Mae or Freddie Mac proved to be oly the begiig of a tide of serious fiacial difficulties of compaies, amog which should be metioed istitutios like AIG, Merrill Luch, Goldma Sachs, Morga Staley, Citygroup, ad Royal Bak of Scotlad. The begiig of the crisis coicided with the chages made i global bakig system by the Basel Committee. Adopted i 2006 the New Basel Capital Accord [2] was desiged to itroduce ew stadards i the area of credit risk maagemet. The basis for this approach was that baks hold capital at the level protectig them from isolvecy. I fact, it was assumed that bak isolvecy ca occur o more frequetly tha oce every oe thousad years. The crucial step for the baks was the possibility to estimate the miimum capital requiremets based o statistical models. Accordig to the Basel Committee, the ew approach was to esure greater stability of the bakig system. Implemetatio of the priciples of credit risk maagemet i lie with the New Capital Accord was supposed to take several years. However it was assumed that the so-called. advaced methods will be used oly by largest baks, which will be able to cope with the process of implemetig a comprehesive risk maagemet system. I this framework, risk assessmet process provides a idividual borrower approach ad also the etire portfolio aalysis. Furthermore, the processes of assessmet of the forecast quality (back testig) ad the stress testig, were cosidered to be complemetary, but very importat. Particularly the last oe is importat from the perspective of the evets which begu i Accordig to the stress test aalysis the baks are required to aalyze the impact of extremely adverse evets o its fiacial coditio. What's more, baks are obliged to take ito accout the results of these forecasts i the process of estimatig ad allocatig the value of capital. The term of stress testig icludes a series of techiques which aim to assess the impact that rare, but still probable evets may have o fiacial istitutio. The results, which are a cosequece of chages of oe or more market factors are tested here. I particular, a stress test refers to the assessmet of the dagers of uexpected fiacial crises. I 2008, it tured out, that some baks are ot properly prepared to overcome the difficulties caused by the fiacial crisis. The Basel Committee has foud that may of them did ot perform stress testig, ad if this procedure was performed, the results were ot a itegral part of a comprehesive risk maagemet system. Therefore, the Basel Committee i the cosultatio documet published i 2009 [3] decided to iclude detailed rules for stress testig. It was emphasized that the stress test methods should be complemetary to the classical models used i the estimatio of credit risk. Thus, their results should be used durig the costructio of risk forecasts. I additio, baks were required to have liquidity cotigecy plas i case of difficulties i obtaiig fudig from exteral sources. It was emphasized that all iteral procedures relatig to the bak's credit risk maagemet process should be adopted by the board of the bak i writig. I particular, it should iclude descriptios of the statistical models, assumptios ad parameter estimatio techiques. The key issue that the Basel Committee was referred to, is the tight itegratio of the stress test aalysis i the framework of the risk maagemet process. Hece, special emphasis was placed for further use of the results i the process of decisio makig. Also, the Committee's opiio was expressed that the prerequisite for a effective risk maagemet system is a costat search for the factors affectig the risk. Amog the basic macroecoomic idicators that require costat moitorig are: iflatio, gross domestic product, iterest rates ad uemploymet rates. Attetio was also draw to the

3 Implemetatio of the Stress Test Methods i the Retail Portfolio 17 miimum frequecy of stress test aalysis. Retail baks should coduct stress-testig procedures at least oce a year. Withi the scietific work o stress testig, there are may papers addressed to corporate bakig. Peura ad Jokivuolle [4] performed a simulatio where they try to estimate the value of bak capital protectig it from isolvecy. For this purpose they took ito accout the ratig migratios reflectig the risk of the borrowers. Also, Virolaie [5] dealt with corporate loas. The subject of his research was the relatioship betwee the probability of isolvecy of borrowers ad macroecoomic factors. I his work the author has focused o data from the Fiish baks. Amog the factors affectig the chage i the level of the isolvecy of borrowers he distiguished GDP, iterest rates ad a debt ratio of eterprises. Also the same author i cooperatio with Sorge i a later work [6] preseted methods which the were used based o the data from the Fiish market collected i the years The example icluded the Fiish fiacial market crisis, which occurred i the mid-ieties. Pai [7] also dealt with the issue of the impact of macroecoomic factors o accoutig items reflectig the level of credit risk i the bak. The author studied the relatioship betwee the calculated risk provisios ad macroecoomic factors. The coclusios of the study were similar to those draw by Virolaiea. It tured out that the chages i GDP ad iterest rates may sigificatly affect the level of credit risk. Also, Rosch ad Scheule [8] dealt with the aalysis of stress test. The authors preseted a iovative approach based o the simulatio of variability of model parameters. For this purpose, they used oe factor model, where the value of probability of default was depedet o exteral variables. The authors preseted results of studies coducted o the basis of data obtaied from the ABA (America Bakers Associatio). Sigificat cotributio to the developmet of stress testig methods made Logi [9]. I his work he used the cocept of estimatig value at risk o the backgroud of extreme value theory. I this way the author addressed the issue of estimatig the value of losses at the level of probabilities, which observatio is usually ot possible due to the small sample size. This approach was the developed by researchers such as Martis ad Yao [10], Ami ad Kat [11], ad McNeil ad Frey [12]. Aother type of research o issues of stress test is a comprehesive aalysis of the etire bakig system of idividual coutry. Amog the iterestig publicatios, we should metio the study by Boss, Kre, Puhr ad Summer [13]. They preseted the SRM model (Systemic Risk Moitor), which is used to aalyze the credit risk of the Austria bakig sector. Thaks to implemetatio of this solutio, it is possible to regularly moitor fiacial coditio of the etire bakig sector. Also the research for the etire bakig system were coducted by Jurca ad Zema [14]. They aalyzed the impact of the ecoomic dowtur o the coditio of the bakig sector i Slovakia. The results of the research showed, that ufavourable cosequeces of a sigificat ecoomic slowdow ca be amortized through appropriate actios i the area of moetary policy. The purpose of this paper is to preset the issue of the stress testig i retail baks. For this purpose the author refers to a umber of approaches that ca be applied i the process of assessmet of credit risk i the cotext of highly adverse evets. I additio, the author preseted his cocept o the reports, which may be applicable i the credit risk maagemet systems. Moreover, the relatioship betwee potetial losses arisig from rare but still plausible evets, ad the level of losses resultig from IRB approach recommeded by the Basel Committee was examied. Thus, the hypothesis was verified which assumed that a comprehesive stress test aalysis system requires the descriptive

4 18 Pawel Siarka approaches usig the kowledge of experts especially whe adverse scearios eed to be created. I this article, after the itroductio oe preseted the methods that ca be used i the process of stress testig. The author described a approach based o the historical scearios, as well as the extreme values theory. The article eds with coclusios draw i order to idicate the directios of advace of the statistical methods used i the stress testig. 2 Stress Testig - Possible Approaches Oe of the possible approach to aalysis of stress test is to examie the impact of crisis evets observed i the past, o the curret fiacial coditio of the bak. This approach is iteded to provide replyig to the followig questio: what would happe today if there was a crisis o a scale that has already take place? The Basel Committee recommeds that this type of stress tests [15] should metio the problem of the liquidity collapse i 1987 or Black Wedesday i 1992, whe the UK govermet was forced to withdraw sterlig from the ERM (Europea Exchage Rate Mechaism). Amog other major evets that sigificatly affected the fiacial coditio of the baks, it is worth to iclude the crisis occurred i the bod market takig place i the first quarter of Usig historical scearios i the stress test aalysis, it is worth to cosider a umber of other evets of a crisis icludig: 1973 oil crisis, 1979 Soviet itervetio i Afghaista, 1989 the Nikkei idex correctio, 1990 Germa reuificatio, 1992 global ecoomic slowdow, 1994 crisis i Mexico, 1997 Asia crisis 1997 collapse of Hokkaido 1998 crisis i Russia, 1998 sale of the Japaese ye, 1998 collapse of LTCM, 1999 crisis i Brazil, 2000 crisis i Argetia, 2001 attack o the WTC 2001 slowdow of the idex dot-com, 2001 collapse of Ero, 2003 the war i Iraq, 2004 the declie i shares o the Italia stock exchage, 2004 terrorist attack i Madrid, 2008 the collapse of Lehma Brothers, 2008, the collapse of Bear Stears, 2010 the crisis i Greece, 2011 earthquake i Japa. Crises observed i recet years, carry a lot of relevat iformatio about the severity of the risks faced by fiacial istitutios. Durig the disturbaces occurrig o the fiacial markets, there are see ot oly sigificat chages i the prices of fiacial istrumets, but also a dramatic decrease i liquidity. Very egative effect is also a rapid

5 Implemetatio of the Stress Test Methods i the Retail Portfolio 19 trasformatio of oe kid of risk to aother. A example of shiftig of credit risk ito liquidity risk could be observed i This pheomeo has its source i the dyamic growth of credit risk, which ultimately results i problems with the fulfillmet of obligatios. Thus, eve whe the bak holds equity capable to protect it from credit risk, the spike i credit risk may cause the problems with some paymets, which could lead to bakruptcy. Implemetatio of the sceario method ca rely o of past evets, as well as hypothetical scearios. I this approach, we ca distiguish the sesitivity aalysis, i which oly oe factor is beig chaged. Other risk factors remai costat. The extesio of this method is to simulate potetial crises through a simultaeous chage of may factors depictig hypothetical fiacial market perturbatios. Hypothetical scearios are particularly relevat for the efficiecy of risk maagemet systems. This allows the use of expertise ad braistorm methods, which greatly expads the scope of the aalyzed scearios. The historical evets approach has several limitatios. I this method, we focus o a fiite set of evets, which may lead to a uderestimatio of losses. Actually it is wrog to assume that history has revealed all the worst scearios that may take place o the fiacial markets. Slightly differet approach to stress test forecasts preset methods that model the credit risk i the cotext of extreme evets [16], which probability of occurrece is very low. There are two basic methods. The first oe cosists i aalyzig the distributio of the maximum loss of the loa portfolio, while the secod uses the coditioal distributio fuctio of losses, assumig that the loss exceeded the give threshold limit. Both approaches allow to estimate the expected value of losses i highly ufavorable coditios for the bak. I the extreme value theory, we model the miimum or maximum loss determied for idepedet radom variables X,..., 1, X 2 X with the same distributio fuctio F [9]. Withi credit risk aalysis, oly the maximum values are cosidered. Hece the followig statistics is aalyzed : M max( X, X 2,..., X 1 The distributio of this statistic ca be preseted i the followig form: P ( M x) P( X1 x,..., X x) ( F( x)) ) Let us deote the probability of occurrece of the maximum loss below a certai threshold limit, as a result of experimets, by. It is kow that the value of this probability depeds o the umber of observatios. I further aalysis the probability of occurrece of the loss of the idividual observatios below the threshold limit will be deoted by p ad the relatioship betwee these probabilities ca be preseted as: p max p p max I the extreme value theory, we use the scale parameter a ad b. I this way, we

6 20 Pawel Siarka ormalize the variable M. The the distributio of the aalysed variable is as follows: M b lim P a x G( x) Oe of the most importat coclusios of the EVT theory of (Extreme Value Theory) is a theorem about of G fuctio, which ca be oe of the three possible forms: Type I 0 x 0 a ( x) a 0 a exp{( x) } x 0 Type II Type III a exp{ ( x) } x 0 a ( x) a 0 1 x b ( x) exp{ exp( x)} a The above distributio fuctios of the maximum loss deped directly o the iitial distributio fuctio of loss of the portfolio. First preseted form is called the Frechet distributio fuctio. It is characteristic for the observatios commig from the fat-tailed distributio fuctios such as Studet's t distributio. Aother is the Weibull distributio fuctio, which is obtaied whe extreme values come from the distributio without tail (eg. whe the values below a certai threshold limit are ot possible to achieve). The last type correspods to the Gumbel distributio, which is characteristic for the observatios from the thi-tailed distributios such as ormal distributio fuctio. It is worth otig that the distributio fuctio of extreme value where G( x) H(( x b)/ a), ca be represeted i geeral form [17]: ( x) exp H x ;,, 1 x Where, R, 0. If 0, we obtai Frechet distributio fuctio, whereas if 0, we obtai the Weibull distributio. For 0 we obtai Gumbel distributio fuctio. The Basel Committee i the New Basel Capital Accord recommeded a oe factor model [18] as the primary modelig tool for portfolio losses i the horizo of oe year. The cumulative distributio fuctio ca be preseted as follows: 1/ P [ L x] N N ( x) N ( PD)

7 Implemetatio of the Stress Test Methods i the Retail Portfolio 21 Where L is the loss of the portfolio defied as the percetage of loas that will default withi the horizo of 12 moths. PD is the probability of default of idividual loas i the portfolio, ρ is the borrowers asset correlatio. Furthermore N() deotes the cumulative 1 distributio fuctio of the stadardized ormal variable, ad N () is its iverse fuctio. Assumig that the loss of the loa portfolio at the horizo of 12 moths is modeled usig a oe factor approach, the cumulative distributio fuctio of the maximum loss ca be preseted i the followig form: ( x b ) G( x) exp exp. a Key elemets to estimate the distributio of maximum loss are umerical sequeces ad b. Their values ca be determied usig the followig formulas [19]: 1 a if x :1 F( x) ad a b 1 (1 F( x dx 1 F( a ) )) a where F is the cumulative distributio fuctio of portfolio losses, is the umber of radom variables which were used to estimate the maximum loss. The parameter ca be iterpreted as a forecast horizo, withi which we aalyze the distributio of the extreme losses. The basic loss distributio fuctio cocers oe-year period, hece is the umber of years durig which the extreme loss is cosidered. Figure 1 presets a example illustratig the use of extreme value theory i the process of stress testig. The report was draw up based o car loas data acquired from a fiacial istitutio operatig i Polad. I the aalyzed portfolio, the probability of default was 4.8%, while the borrowers asset correlatio was estimated at 2.79% [20]. The upper graph i Figure 1 shows the desity fuctio of portfolio losses resultig from oe factor model [18] ad also its cumulative distributio fuctio. The graph below shows two distributio fuctios of the maximum loss calculated for variat horizos.

8 22 Pawel Siarka Figure 1: The results of the stress test aalysis accordig to Extreme Value Theory. Source: author's work. With black color were marked the results of simulatio 1, which as described i the table i Figure 1, was carried out for five year horizo. Gray color represets the distributio of the maximum loss which the bak ca be expected over the ext oe hudred years. I the first case, the expected value of loss was 6.9%, ad by extedig forecast horizo to 100 years, the loss icreased to 10.4%. Stadard deviatios were estimated respectively at 1.58% ad 1.39%, which shows that the higher forecast horizo we assume the stadard deviatio of the maximum loss is smaller. Both results idicate that the expected values of losses uder adverse coditios, do ot exceed VaR999 (table o figure 1). However, the estimated volatility of the maximum loss leaves o doubt that the observatios of the maximum losses over VaR999 are highly probable (especially i the case whe forecast horizo is 100 years). I this case, the probability of exceedig VaR999 was 17.1%. Aother approach which allows to aalyse the results of extreme evets is the coditioal distributio fuctio model. I this framework, the losses are examied that occur above a certai critical threshold v. The value of this threshold is usually take at the level resultig from the estimatio of VaR (Value at Risk). Hece, this approach eables the assessmet of the scale of losses whe it exceeds established i the New Basel Capital Accord threshold - VaR999. I this approach, the distributio of losses L, provided that the loss exceeds the threshold value v [16] presets the followig fuctio : ( l) P( L v l L v) F v O the basis of the cumulative distributio fuctio F of the loss of the loa portfolio, it is therefore possible to preset the coditioal cumulative distributio fuctio, i the followig form:

9 Implemetatio of the Stress Test Methods i the Retail Portfolio 23 F v ( l) F( v l) F( v) 1 F( v) It should be emphasized that the cumulative distributio fuctio is crucially depedet o the threshold value v. As we icrease its value, we cosider the more extreme cases i the aalysis of the stress test. Figure 2 presets report cotaiig the results of the stress test aalysis usig the coditioal cumulative distributio fuctio of portfolio losses. Just as it took place i the previous example, the expected value of loss was equal to 4.8%, while the borrowers asset correlatio was 2.79%. Also o the basis of oe factor model, VaR999 ad VaR99 were estimated at the level of 9.8% ad 12.2% respectively. O this basis, oe ca assume that the loss of the portfolio should ot exceed 9.8% more ofte tha oce every 100 years, while 12.2% threshold may be exceeded ot more ofte tha oce every 1000 years. Figure 2: The results of the stress test aalysis - the coditioal distributio fuctio approach. Source: author's work. Figure 2 shows the report presetig the results of two simulatios addressig a critical value (threshold limit). These parameters idicate a threshold level of risk above which the coditioal cumulative distributio fuctio of portfolio losses is aalyzed. The first simulatio refers to the case whe the loss is calculated whe it exceeds the VaR99. O the basis of a coditioal distributio fuctio it was calculated that whe the loss exceeds 9.8%, the we ca expect with probability 95%, that it will ot be higher tha 14.6%. The secod simulatio examies the coditioal cumulative distributio fuctio of losses i case whe loss goes beyod the level equal to VaR999. I this case, the

10 24 Pawel Siarka probability of higher losses tha 16.8%, is oly 5%. Critical thresholds icluded i the aalyzed scearios ca be iterpreted as realizatios of potetial crises of varyig severity. Higher threshold value implies more extreme fiacial market shock. It is worth otig that the results obtaied i both simulatios exceed the value of VaR999 that is the basis for the miimum capital requiremets i lie with the New Capital Accord. Therefore, havig regard to the stress test aalysis, the bak should cosider the possibility of icurrig additioal losses. A alterative approach to the problem of stress testig reveal methods which use portfolio profitability aalysis. Uder this cocept, the loa portfolio is treated as a debt istrumet. So its iteral rate of retur it possible to determie. The profitability of the loa portfolio estimated i this way, allows to specify ot oly the future profits or losses, but also allows to determie the risk appetite which for the bak is the maximum acceptable level of credit risk. By icludig the costs of fudig i profitability aalysis, we are able to estimate the effective margi, which the bak ears o the loa portfolio. I order to determie the margi, cash flows related to the loa portfolio have to be divided ito two groups [21]. Oe of them is associated with portfolio represeted i the balace sheet as a asset, while the secod refers to its fudig (liabilities). Estimatio of iteral rate of retur for a particular loa portfolio is carried out based o of all real cash flows [21]. The value of IRR (Iteral Rate of Retur) [16] of loa with istallmets ca be determied by fidig the roots of the polyomial of -th degree, which requires umerical algorithms. Mothly IRR ca be calculated usig the followig equatio: F1 F2 F X (1 IRR) (1 IRR) (1 IRR) where X - value of cash flows at the time of loa gratig, 0 - umber of istallmets, F - et value of cash flows at time t, t Cash flow at time zero is determied by the equatio: X 0 Y c o where: c-sum of the et commissios ad isurace premiums, Y - The iitial value of the loa, o - operatig costs, Cash flows i subsequet periods are risk-adjusted omial values of the schedule istallmets : X X The variable F t t kor, t X kor, t is a adjustmet of istallmet X t arisig from upaid part of the pricipal as a result of credit risk, as well as the lack of due iterest. The value of is calculated based o the followig equatio: X kor, t

11 Implemetatio of the Stress Test Methods i the Retail Portfolio 25 1 l Y 1 t k j X kor, t j k 1 (1 iom) for t k 0 where: l - fial loss (credit risk measured as the ratio of irrecoverable capital ad the iitial value of loa), k - the average time whe the isolvecy appears, i - omial iterest rate of loa, om X - istallmet i period t (t = 1,..., ). t Aalogous estimates of the iteral rate of retur of cash flows related to fudig must be carried out usig the followig equatio: 1 IRRP ( 1 w) iref wikw 1 ( iref ir (1 p)) 1 res where: w - percetage of equity i total fudig, i - cost of equity, kw i - iterest rate of deposits, ref res - the obligatory reserve ratio, i r - iterest rate of obligatory reserves (0.9 of rediscout rate), p - the rate of fuds trasferred to the EU Guaratee Fud (estimated o the basis of iterest o obligatory reserve). Based o the portfolio profitability approach, the value of the effective margi is calculated as the differece betwee the iteral rate of retur of loa portfolio ad the fudig liabilities. Thus, the effective margi is give by EM IRR A IRR P where: EM - portfolio effective margi, IRR A - Iteral rate of retur of the loa portfolio, IRR - Iteral rate of retur of fudig liabilities. P Effective margi of the portfolio allows the assessmet of its profitability i compariso to other istrumets that are i the bak balace sheet. Moreover, it is hady tool i the process of stress testig. Profitability model takes ito accout such variables as average life expectacy of loas, the effect of early repaymets causig reductio of the loa life, loa iterest rate, credit risk, the cost of equity ad may other factors. Hece the preseted model ca be used i the simulatio of highly ufavorable evets. Scearios ca be created both with respect to historical, as well as hypothetical chages i these factors. Aother solutio is to estimate the multivariate distributio fuctio of risk factors, ad the use its shape to specify extreme values characterizig usually the

12 26 Pawel Siarka fiacial crises. Figure 3 presets the results of profitability aalysis of the car loas portfolio as well as values of used parameters. The simulatio was performed for a loa portfolio worth 30 ml EUR. The average omial legth of loas life expressed i moths, was adopted at 60 moths. Furthermore, it was assumed that due to the effect of early repaymet, the effective average loa schedule will be reduced by 20%. Nomial iterest rate of loas was 13.1% per year. I the area related to the commissio, it was assumed that the average bak commissio is 3%, of which oe percet is paid to the fiacial itermediary who sells the loas. I additio, the fiacial itermediary is etitled to add their ow commissio by icreasig the gross value of loa up to 4%, which is a egative flow for bak at the momet whe the loa is grated. I the bak portfolio all loas are isured i case of death of the borrower ad the fee is 2% of its value. Part of this fee (0,8% of the gross value of loa) is trasferred to the the isurace compay as its remueratio. Due to the fact that bakig activities are associated with may fixed costs, i the profitability aalysis were assumed wage costs, depreciatio costs ad other costs amoutig to 3%, 4% ad 4% respectively. Aother sigificat cost to the bak is credit risk. Based o the bak experiece, it was assumed that 6% of the iitial loas value will ot be recovered. Furthermore, it was assumed that credit risk appears o average at aroud 20 th istallmet. I order to determie the costs of fudig, it was assumed that the equity is the source of 10% of the total fiacig. Due to the specific structure of equity i the cosidered bak, the cost of equity was set to zero. The most sigificat elemet of costs is the average iterest rate of deposits, which was assumed at 5.5%. The additioal cost for a bak is the obligatory reserve which has to be deposited at the cetral bak (2% of all deposits). Figure 3: The results of the profitability aalysis of the loa portfolio. Source: author's work

13 Implemetatio of the Stress Test Methods i the Retail Portfolio 27 O the basis of made assumptios, the bak cost of fudig was estimated at the level of 5.05%, while the effective iterest rate of the loa portfolio was 7.28%. The differece betwee these values is the effective margi, which i this case is 2.23%. This result should be iterpreted as the average aual retur of the assets obtaied by bak durig the etire life of the portfolio. A positive value idicates that the bak will geerate profit, which i total will be equal to EUR. I order to perform stress test aalysis, it is ecessary to chage the parameters affectig the profitability of the loa portfolio, which simulates a potetial fiacial crisis. Table 1 shows the obtaied results based o the chagig of credit risk uderstood as a fial loss. Table 1: The results of the stress test aalysis profitability approach. Fial Loss 6% 7% 8% 9.85% Cost of fudig 5.1% 5.1% 5.1% 5.1% Effecitve iterest rate 7.3% 6.7% 6.1% 5.1% Effecitve margi 2.2% 1.7% 1.1% 0.0% Balace of cash-flows Source: author's work. The simulatio ivolved icrease i the credit risk from the expected level of 6% to levels amoutig to 7%, 8% ad 9.85%. As it was expected, the value of the effective margi decreases with icreasig risk. Similarly, the total amout of et cash flows geerated by the loa portfolio is beig reduced. For the bak particularly importat is the value of risk threshold at which the bak stops geeratig positive sum of cash flows. The icrease i risk above this value meas icurrig losses ad the cosequet reductio of bak capital. I the aalyzed example due to the icrease of fial loss by 3.83 percetage poits, the metioed limit was reached. Thus, by examiig the sesitivity of the portfolio profitability, the bak's positive fiacial result threshold was estimated at 9.85% of fial loss. Obtaied risk threshold seems to be much higher tha expected level ad cosequetly quite safe. However i the cotext of ufavorable but still plausible evets, this value ca be quickly reached ad become a real threat. 3 Coclusios The preset paper addresses the issue of stress testig of bak loas portfolio. Curretly the problem of maitaiig a adequate level of liquidity, it is the most importat challege facig the global fiacial system i the opiio of the Basel Committee. The ability to determie the cosequeces of crises icreases the stability of the bakig system affectig the global ecoomy. The guidig objective of the Basel Committee is to create such stadards, the baks could cope with temporary perturbatios of the fiacial markets without the eed of support of public fuds. Stress testig methods preseted i the article are essetially a developmet of the methods used i other research areas. It should be emphasized that approaches focusig o the modelig of rare evets have also disadvatages. Most of them is based o the historical data that are used to estimate the parameters. Limited set of historical

14 28 Pawel Siarka observatio raises legitimate cocers about uderestimatio of potetial risks. We should ot assume that all possible egative scearios have already bee realized. Therefore, the spectrum of methods used i the process of stress testig should be exteded to approaches based o hypothetical scearios. Creatig a uique combiatio of macroecoomic variables o the basis of expertise, ca ehace our uderstadig of the scale of a future crises. Udoubtedly o the groud of stress testig, the profitability aalysis of loa portfolio is very importat from a practical poit of view. The distributio of portfolio losses does ot reflect the a complete picture of the ecoomic situatio of the bak. The kowledge about the losses is of course extremely importat, but ultimately is oly oe elemet of the puzzle. The bak maager stadig i frot of the problem of decisio makig should take ito accout both cost ad reveue aspects. Therefore, it is importat to develop the area of statistical models that allow assessmet of the fiacial coditio of baks i a more comprehesive maer. The results of the study idicate that the process of calculatig the credit risk limited oly to estimatig miimum capital requiremets is highly iadequate. By simulatio of crisis evets it was show that the excess of VaR999 barrier that protects the baks from isolvecy, it is quite likely. These results should ecourage the authorities of may baks to implemet the stress tests methods. Moreover, it is ecessary to cotiuously moitor risk i the cotext of adverse evets. Refereces [1] R. Barua, F. Battaglia, R. Jagaatha, J. Medis ad M. Oorato Basel III: What s New? Busiess ad techological challeges, 2010, [2] Basel Committee o Bakig Supervisio, Iteratioal covergece of capital measuremet ad capital stadards: A revised framework, comprehesive versio, [3] Basel Committee o Bakig Supervisio, Priciples for soud stress testig practices ad supervisio, Bak for Iteratioal Settlemets Cosultative Documet, [4] S. Peura, E. Jokivuolle, Simulatio based stress tests of baks regulatory capital adequacy, Joural of Bakig ad Fiace 28, 2004, pp [5] K. Virolaie, Macro Stress Testig with a Macroecoomic Credit Risk Model for Filad,, Bak of Filad, Discussio Paper, 2004, o. 18. [6] M. Sorge, K. Virolaie, A comparative aalysis of macro stress testig methodologies with applicatio to Filad, Joural of fiacial stability, 2, 2006, [7] D. Pai, The Provisioig Experiece of the Major UK Baks? a Small Pael Ivestigatio, Bak of Eglad Workig Paper, Jauary [8] D. Rosch ad H. Scheule, Stress-Testig Credit Risk Parameters: A applicatio to retail loa portfolios, Joural of Risk Model Validatio 1, Sprig 2007, pp FSI Award 2008 Wiig Paper 57 [9] F.M. Logi From value at risk to stress testig: The extreme value approach, Joural of Bakig & Fiace 24, [10] F. Martiz,F. Yao, Estimatio of Value-At-Risk Ad Expected Shortfall Based o Noliear Models of Retur Dyamics Ad Extreme Value Theory, Studies i

15 Implemetatio of the Stress Test Methods i the Retail Portfolio 29 Noliear Dyamics ad Ecoometrics, 10(2), 2006, [11] G. Ami, H. Kat, Hedge Fud Performace : Do the Moey Machies Really Add Value?, Joural of Fiacial ad Quatitative Aalysis, 38, 2003, [12] A.J. Mceil, R. Frey, Estimatio of Tail-related Risk Measures for Heteroscedastic Fiacial Time Series: A extreme value approach, Joural of Empirical Fiace, 7, 2000, [13] M. Boss, G. Kre, C. Puhr, M. Summer Systematic Risk Moitor: A Model for Systematic Risk Aalysis ad Stress Testig of Bakig Systems, Austria Natioal Bak, Fiacial Stability Report 11, [14] J. Zema, P. Jurca, Macro Stress Testig of the Slovak Bakig Sector, Workig Paper, [15] Basel Committee o Bakig Supervisio, Supervisory Framework for the Use of Backtestig i Cojuctio with the Iteral Models Approach to Market Risk Capital Requiremets, [16] K. Jajuga Risk maagemet, PWN Warszawa, [17] P. Embrechts, S. Resick, G. Samoroditsky, Extreme Value Theory as a Risk Maagemet Tool, North America Actuarial Joural, 3, Number 2, [18] R.C. Merto, O the Pricig of Corporate Debt: The Risk Structure of Iterest Rates, Joural of Fiace, 29, 1974, p [19] M. Czekala M, Positioal statistics i ecoometrical modelig process, Wroclaw Uiversity of Ecoomics, Wroclaw, [20] P. Siarka, Estimatio of asset correlatio of retail exposures based o car loas i Polad, Bak & Credit, 42(3), Natioal Bak of Polad, 2011, Warszawa. [21] P. Siarka, Applicatio of a loa profitability model i the process of stress testig, Bak & Credit, 42(2), Natioal Bak of Polad, 2012, Warszawa.