Débats économiques et financiers N 1


 MargaretMargaret Anthony
 3 years ago
 Views:
Transcription
1 Débats économques et fnancers N 1 How dfferent s the regulatory captal from the economc captal: the case of busness loans portfolos held by the major bankng groups n France Mchel Detsch * et Henr Frasse ** [*] Autorté de Contrôle Prudentel Drecton des Etudes et Unversté de Strasbourg. Contact : (**) Autorté de Contrôle Prudentel Drecton des Etudes
2 SECRETARIAT GENERAL DE L AUTORITE DE CONTROLE PRUDENTIEL DIRECTION DES ÉTUDES How dfferent s the regulatory captal from the economc captal: the case of busness loans portfolos held by the major bankng groups n France Mchel Detsch and Henr Frasse February 2013 Les ponts de vue exprmés dans ces Débats Economques et Fnancers n engagent que leurs auteurs et n exprment pas nécessarement la poston de l Autorté de Contrôle Prudentel. Ce document est dsponble sur le ste de l Autorté de Contrôle Prudentel : The opnons expressed n the Economc and Fnancal Dscusson Notes do not necessarly reflect the vews of the Autorté de Contrôle Prudentel. Ths document s avalable on Drecton des Études  SGACP 1
3 How dfferent s the regulatory captal from the economc captal: the case of busness loans portfolos held by the major bankng groups n France Abstract: There s a growng concern about the dfferences between rsk weghted assets (RWAs) amounts across banks and across countres. Ths paper provdes new evdence on ths ssue by usng French Credt Regster data and frms ratngs hstores of more than French frms, ncludng a large proporton of Small and Medum szed frms, to compute captal requrements n busness loans portfolos of French bankng groups. Usng Credt Regster nformaton and ratngs provded by the Banque de France ratng system allows computng captal requrements by usng a sngle common credt rsk metrcs and actual emprcal rates of default at the bank s exposure level. Usng ths nformaton, captal ratos are computed for each bankng group operatng n the French busness loans market. The paper addresses the ssue of the ablty of Basel 2 Internal Ratng Based (IRB) formulas to hedge portfolo s credt rsk. Here, the analyss reles on an extenson of the asymptotc sngle rsk factor model (ASFR), whch was used for the calbraton of Basel II regulatory formulas. Therefore, a multfactor portfolo s credt rsk model s mplemented to compute economc captal requrements takng account of potental credt rsk concentraton n busness loans portfolos. The paper compares the requred captal ratos provded wth ths model wth the one requred by the regulaton. Our man fndngs are frstly that regulatory captal ratos do not underestmate credt rsk: Basel II regulatory captal requrements are larger than the economc captal requrements. Secondly, the sngle rsk factor regulatory model does not capture potental dversfcaton effects n busness loans portfolos. In the regulatory model, frms heterogenety s only captured by ther ratngs. The ntroducton n the portfolo credt rsk modelng of addtonal systematc rsk factors  whch are here sze and sector show that managng large portfolos composed of borrowers of dfferent sze or sector helps to produce dversfcaton effects. Such stuatons lead n most cases to a decrease of the captal level requred to cover future unexpected losses. Keywords: Credt Rsk, economc captal, regulatory captal, busness loans JEL Classfcatons : G21, G28, G32 De comben le captal réglementare s écarte tl du captal économque: le cas des prêts aux entreprses par les grands groupes franças Résumé : Il exste aujourd hu un débat sur la qualté des actfs des banques européennes et une éventuelle sousévaluaton du rsque de crédt dans l utlsaton des formules réglementares par les banques. Ce paper apporte des éléments de réponse à ce débat en mesurant les exgences en captal réglementares sur les portefeulles de crédts aux entreprses résdentes des sx premers groupes bancares opérant en France et en les comparant aux exgences en captal économque mesurées notamment en utlsant un modèle multfacteur de rsque de crédt de portefeulle. Ce modèle permet de tenr compte de l hétérogénété des entreprses emprunteuses en les dstnguant selon la talle ou le secteur. Il permet auss de détecter d éventuels effets de concentraton de portefeulle lés à l exstence de stuatons de défauts corrélés. Le paper explote les encours de crédt et l hstorque des ratngs de quelques entreprses, ncluant une fracton mportante de PME, dsponbles va la Centrale des Rsques et le système de cotaton des entreprses de la Banque de France pour la pérode Ces données permettent de calculer les exgences en captal en utlsant le même crtère objectf de défaut et le même système d évaluaton du rsque de crédt ndvduel des entreprses pour toutes les banques analysées. Le premer résultat est que les formules d exgences réglementares ne sousestment pas les le rsque de crédt de portefeulle. Les exgences réglementares calculées sont supéreures aux exgences économques dans une très large majorté de segments de portefeulle construts à partr des crtères de talle et de secteur. Le paper montre auss que le modèle réglementare surestme la sensblté des emprunteurs au cycle et sousestme le potentel de dversfcaton de portefeulle. Le potentel est ms en évdence dans ce paper dès lors que les facteurs de rsque addtonnels assocés à la dfférencaton des entreprses sont ntégrés dans l analyse. Au total, les exgences en captal économque sont trées à la basse par des effets de dversfcaton nduts par l hétérogénété des emprunteurs. Motsclés : Rsque de crédt, captal économque, captal réglementare, prêts aux entreprses Code JEL : G21, G28, G32 Drecton des Études  SGACP 2
4 Contents 1. INTRODUCTION THE DATA THE METHODOLOGY A SHORT VIEW OF THE MULTIFACTOR MODEL THE MULTIFACTOR MODEL AS BENCHMARK FOR CAPITAL REQUIREMENTS MEASUREMENT THE RESULTS: COMPARISONS OF REGULATORY AND ECONOMIC CAPITAL RATIOS TAKING ACCOUNT FOR BORROWERS HETEROGENEITY AND POTENTIAL CREDIT RISK CONCENTRATION: THE FIRM SIZE AS AN ADDITIONAL SOURCE OF SYSTEMATIC RISK TAKING ACCOUNT FOR BORROWERS HETEROGENEITY AND POTENTIAL CREDIT RISK CONCENTRATION: THE FIRM SECTOR AS AN ADDITIONAL SOURCE OF SYSTEMATIC RISK CONCLUSION REFERENCES APPENDIX : CREDIT RISK MODEL SPECIFICATION THE ASYMPTOTIC MULTIFACTOR CREDIT RISK FRAMEWORK THE ECONOMETRIC ESTIMATION OF THE PORTFOLIO S CREDIT RISK PARAMETERS MEASURING POTENTIAL CONCENTRATION Drecton des Études  SGACP 3
5 How dfferent s the regulatory captal from the economc captal: the case of busness loans portfolos held by major bankng groups n France Mchel DIETSCH 1 and Henr FRAISSE 2 1. Introducton There s a growng concern about the dfferences between rsk weghted assets (RWAs) amounts across banks and across countres. EBA (2012) as well as the Basel Commttee (2012) have recently launched new workng groups to assess the extent of the dfferences and to delver explanatons of ther orgns. Some nternatonal banks have expressed doubts about the relablty of banks RWAs and the consstency and comparablty of captal requrements. Such doubt about the relablty of banks RWAs could have major consequences. In partcular, nvestors could dsregard regulatory captal ratos and requre hgher captal to compensate for the low perceved relablty of the captal rato s denomnator. Then the rsk s that they restrct lendng to banks for whch they have doubts about reported captal adequacy. Prevous papers have provded an overvew of the concerns surroundng the dfferences of rskweghted assets (RWAs) across banks and jursdctons and how ths mght undermne the Basel III captal adequacy framework. They have proposed assessments of the key drvers behnd these dfferences, drawng upon samples of mportant banks n Europe, North Amerca, and Asa Pacfc. Among the man drvers whch have been proposed to explan such dscrepances are the dfferences n regulatory envronment, accountng rules, the poston of the country n the economc cycle whch nfluence the level of the probabltes of default, and, fnally, the dfferences n banks busness models across regons of the world (Le Leslé and Avramova, 2012, Cannata, Casellna and Gud, 2012, and several notes comng from fnancal analyss departments of nternatonal banks). However, the ablty of RWAs to reflect bank portfolos credt rsk could be questoned, at least for two reasons. The frst reason deals wth the the modellng of dependency across oblgors. As emphaszed by the Basel Commttee (BCBS, 2008), ths ssue s a man challenge of portfolo credt rsk measurement. Asset correlatons quantfy ths dependency. Asset correlatons measure the common senstvty of borrowers to systematc rsk factors, whch are macroeconomc, ndustry or geographc factors. If the 1 Autorté de Contrôle Prudentel, Drecton des Etudes, et Unversté de. Strasbourg. Contact : 2 Autorté de Contrôle Prudentel, Drecton des Etudes Drecton des Études  SGACP 4
6 correlaton s hgh, ths senstvty to systematc rsk factors s hgh, and n the case where extreme values of the systematc factors append, losses wll clmb to very hgh levels. Asset correlaton reflects the uncertanty assocated to events whch can produce extremes losses. Thus, asset correlatons are a crucal metrcs n portfolo s credt rsk measurement. As nput parameters nto a credt rsk model, correlatons affect the credt portfolo ValueatRsk (VaR) whch measures credt rsk n a portfolo. Thus, the modelng of ndvdual asset correlatons has a strong mpact on VaR for credt portfolos of heterogeneous borrower sze, suggestng that the omsson of ndvdual dependences can substantally reduce the VaR estmate 3. That sad, to reflect portfolo s credt rsk, asset correlatons should be computed usng nternal data. Credt ratngs alone do not reflect the uncertanty assocated wth forecastng tal credt loss events. However, n the regulatory formulas defnng RWAs, asset correlaton R s entrely determned by the PDs. The second reason deals wth potental concentraton n loans portfolos. Concentraton s another man drver of credt rsk n a portfolo. Concentraton rsk n loan portfolos could come from name concentraton (the ncomplete dversfcaton of dosyncratc borrower rsk) and sector concentraton (the exstence of multple systematc rsk factors, generally related to ndustry or geographc effects). Correlated defaults can be attrbuted to the dependency of credt exposures to common factors that are specfc to some segments of the portfolo or to partcular banks clenteles. If frm heterogenety s defned as heterogenety of rsk factor loadngs across frms, t characterzes loan portfolos due to dfferences n sze 4, sector or localzaton of borrowers. Thus, takng account for potental concentraton effect mples to consder borrowers heterogenety. BCBS (2006) underlnes that concentraton of credt rsk n asset portfolos has been one of the major causes of bank dstress. However, the calbraton of the IRB formulas was allegedly chosen to match the economc rsk n a credt portfolo that should be verywell dversfed across ndustres. Consequently, regulatory formulas do not take nto account borrowers heterogenety and potental concentraton effects comng from potentally correlated defaults across borrowers belongng to the same portfolo s segment and whose fnancal stuaton s drven by systematc rsk factors whch are specfc to ther group. Takng account explctly for concentraton phenomena mples to use multfactor framework. Departures from the underlyng assumptons of the sngle factor model,.e. perfect granularty and a sngle source of systematc rsk could result n substantal devatons of economc captal requrements from regulatory captal requrements. 3 Recent studes n the credt rsk lterature (Tarashev and Zhu, 2007, Hetfeld, 2008, Coval and al. 2009) show that credt rsk models man sources of errors generally come from a msspecfcaton of default dependences. To compute credt rsk n a loans portfolo, t s necessary to characterze the entre jont dstrbuton of payoffs for the loans pool. 4 One should note that IRB formulas actually dffer wth the turnover of the frms and the sze of the exposure. The RWA are computed dfferently whether the busness s classfed n the retal portfolo, the SME portfolo or the corporate portfolo. However, the dfferences n the formulas appled to these portfolos do not stem from the sngle rsk factor theoretcal model underlyng the regulatory framework. Drecton des Études  SGACP 5
7 The am of ths study s to evaluate the ablty of the regulatory captal requrements formula to hedge the portfolo credt rsk. To ths am, we compare the level of captal requrements computed by usng regulatory Basel 2 formula to the level of captal computed by usng a model of portfolo credt rsk whch take nto account multple sources of rsk as well as borrowers heterogenety. Therefore, we have extended the asymptotc sngle rsk factor (ASRF) model to a multfactor framework whch takes account for addtonal systematc rsk factors, such as sze or sector factors. The frst advantage of ths approach s that results obtaned n a multfactor framework are consstent wth results provded by the regulatory approach, allowng drect comparsons of economc and regulatory captal requrements. The second advantage s that takng addtonal rsk factors nto account allows detectng potental dversfcaton benefts n banks loans portfolos, or on the contrary, potental credt rsk concentraton due to correlated defaults. Indeed, credt rsk concentraton could be defned as a stuaton of strong correlated defaults n a portfolo s segment, what nduces a larger number of defaults and hgher losses. In that perspectve, takng account for concentraton mples to decompose the portfolo n segments accordng to the choce of addtonal rsk factors. For nstance, followng ths logc, n ths paper, we segment the portfolo of each bankng group n four sze segment. Then, the concentraton measurement reles on the computaton of the margnal contrbuton of each segment to the portfolo s total losses. If a segment s contrbuton to losses s hgh, that means that losses are concentrated n ths segment, requrng more captal to cover unexpected losses. On the other hand, f the contrbuton s weak, there s a great chance that ths segment contrbutes to portfolo s dversfcaton. To conduct our quanttatve study, we use nformaton about busness loans portfolos contaned n the French Credt Regster ( Fcher Central des Rsques ) on a quarterly bass over the perod. Ths database ncludes all loans of all knds (short term, long term, leasng) wth an amount over Euros provded by French banks to ther busness customers. As a matter of fact, the bulk of busness loans portfolos s bult up by loans to SME. We consder the potental for correlated defaults nsde the portfolo of large bankng groups lendng to busnesses operatng n France, takng successvely sze and sector as addtonal systematc rsk factors. We use ths nformaton to compute captal requrements n each of the sx major bankng groups operatng n the French busness loans market. We compare three captal ratos: a) the regulatory rato usng the Basel II IRB formulas, b) the economc multfactor rato computed by usng a multfactor model whch takes nto account frm sze and frm sector as addtonal rsk sources, and fnally c) an economc sngle factor rato, whch uses the standard ASRF model to compute asset correlatons, and replaces correlatons computed by usng regulatory formulas by asset correlatons computed n ths way. Results show frstly, that the sngle rsk factor regulatory model does not success to capture potental concentraton or dversfcaton effects n strongly granular busness loans portfolos. In ths model, frms heterogenety s only captured by ther ratngs. The ntroducton n the portfolo credt rsk Drecton des Études  SGACP 6
8 modelng of addtonal systematc rsk factors  whch are here frm sze and frm sector show that stuatons of strongly correlated defaults could exst n certan segments of the portfolos or, on the contrary, that some segments could produce a dversfcaton effect. Such stuatons determne an ncrease or a decrease of the captal level requred to cover future unexpected losses, as compared to the regulatory level, dependng of the case. Secondly, on average, Basel II regulatory captal requrements are larger than the economc captal requrements, ether n the sngle or n the multfactor approach. In other words, our results demonstrate that present RWAs formulas do not underestmate portfolo credt rsk, at least when consderng French busness loans portfolos, and that whatever the bankng group. Secton 2 presents the database. Secton 3 presents and justfes the use of the multfactor credt rsk model as a benchmark. Secton 4 shows comparsons of three measures of the captal rato to treat the ssue of RWAs consstency and relablty. Secton 5 concludes. 2. The data In ths paper, we explot the dversty of the portfolos composton across bankng groups. To compute regulatory and economc captal requrements, we use two sources of nformaton. The frst one s the French Credt Regster, (Fcher Central des Rsques, FCR), whch ncludes all loans of all knds (short term, long term, leasng) wth an amount over Euros provded by French banks to busnesses. We have extracted from the FCR all loans suppled by the sx large French bankng groups. We have retaned loans to ndustral and commercal sectors, excludng fnancal sector and state or muncpal servces sector. The perod of the study covers years from 2000 to 2011, ncludng the fnancal crss perod. The FCR provdes also nformaton about frms characterstcs, such as sze, ndustry, geographcal locaton. The second source of nformaton s the Banque de France (BDF) ratngs system ( Cotaton BDF ), for whch the BDF was recognzed as an External Credt Assessment Insttuton (ECAI) 5. The BDF ratngs system provdes ratngs for qute all frms whose turnover s over 0.75 M. However, even f the system provdes ratngs for mcrobusnesses (very small frms wth turnover lower than 0.75 M ), f ther 5 The frm s credt rsk assessment provded by the Banque de France Credt Regster and ratngs system s very safe, due to the fact that the database s very representatve, the threshold level guaranteeng a quasexhaustve coverage of the French busnesses populaton. Another beneft of the ratng system s ts permanent updatng, what allows an nstantaneous evaluaton of rsk. In addton, the Banque de France operates a close montorng of frms knowng fnancal dffcultes, what provdes a soluton to the ssue of mssng accountng nformaton for such frms. Fnally, these databases provde the exclusve possblty to estmate rsk n the real portfolos of the French banks accordngly to the same ratng system. Drecton des Études  SGACP 7
9 exposure s amount s greater than 0.35 M, we do not consder the latter populaton n ths study 6. The BDF ratngs system ncludes twelve ratngs grades. Among them, two refer to default states: ) legal falure, whch s bankruptcy, and ) bank default, whch corresponds n the BDF ratngs system to severe bankng problems ncdents bancares séreux. Takng together these two crterons of default help to catch a set of default stuatons whch s qute close to the set of default stuatons usng the Basel II default crteron, especally n the small busnesses populaton. So, usng ths database, t s possble to compute annual rates of quasbank default and to dstngush them by ratngs grade. In ths study, these default rates were computed dstnctvely for four sze classes: a) very small frms, wth turnover between M 0.75 and M 1.5, b) small frms, wth turnover between M 1.5 and M 10, c) medumszed frms, wth turnover between M 10 and M 50, and d) ntermedate sze frms and large frms, wth turnover over M 50. These emprcal rates of default were used as proxes for probabltes of default (PDs) n the Basel II captal requrements formulas. The permeter of ths study s the populaton of French frms whch fulfll four condtons: ) they have exposures n the Credt Regster, ) the BDF ratng department gves them a ratng (ncludng default grades), ) they get loans from at least one or several of the sx major bankng groups operatng n the French loans to busnesses market, and v) ther annual turnover s over 0.75 M. The populaton contans a very large number of French frms (more than frms on average each year). Table 1 shows the number of n the sample by sze classes. All types of busness loans are ncluded n the total amount, whatever the maturty or the object of loans. The loans amount of the sample s frms represents a total of more than 650 bllon Euros on average over the perod. The market share of the sx studed groups n the French busness s around 70% durng the perod. In addton, busness loans exposures of the studed bankng groups represent on average around 40% of the groups total assets. The sample does not only reflect the realty of the busness loans market but t s also very representatve of the French busnesses populaton. 6 The man reason s that the Banque de France ratngs system covers only that part of ths populaton whch s composed of frms wth exposures amounts hgher than euros. Consequently, relable nformaton about ndvdual credt rsk s mssng for most of the mcro busnesses populaton. Another reason comes from the fundamental heterogenety n terms of credt rsk of the mcro busnesses populaton, whch mxes personal affars such as doctors, lawyers,,  wth very small frms operatng on compettve markets.. Drecton des Études  SGACP 8
10 Table 1: Number of frms by sze n the sample (6 bankng groups) Very small frms Small frms Medumszed frms Intermedate and large frms Total number of frms Total exposures of the sx groups (bn ) Share of the sx groups n total exposures (n%) Source: ACPBDF and Authors computatons. Table 2 shows the dstrbuton of sze and sector composton of loans portfolos across bankng groups. Sgnfcant dfferences across groups appear, especally n what concerns the share of the very small frms or the largest frms (ntermedate sze and large sze frms). Sgnfcant dfferences n ndustry composton across groups also appear. In partcular, some groups are characterzed by a hgh share of those sectors whch are closest to the fnal consumers (retalng, servces to households) whle others lend more to manufacturng and constructon and real estate sectors. Table 2: Dstrbuton of sze and ndustry composton of busness loans portfolos across bankng groups (year 2011) mn mean max Sze classes Very small 16.2% 28.1% 36.1% Small 14.5% 24.2% 28.8% Medumszed 8.3% 19.1% 26.1% Intermedate & large 9.0% 28.6% 61.0% Industres Agrculture 0.5% 1.6% 3.8% Constructon & real estate 14.9% 32.7% 42.4% Manufacturng 14.3% 19.8% 22.9% Retal 7.3% 10.9% 21.7% Wholesale 8.0% 11.1% 15.5% Transport 4.8% 7.1% 10.4% Servce to busness 4.0% 5.2% 12.5% Servces to households 5.6% 11.7% 14.9% Source: ACPBDF and Authors computatons Note: ths table reproduces the mnmum, the mean and the maxmum fracton of exposures across bankng groups and by portfolo segment. For llustraton, n term of exposures, the bankng group the less exposed to the Agrgulture sector hods 0.5% of ts total exposure on ths segment. Drecton des Études  SGACP 9
11 To compute captal ratos, we have used the Basel II formulas n the Internal Ratngs Based Foundaton (IRBF) approach, what means usng the other retal captal requrements formula when the exposure s amount s lower than 1 mllon Euros and the correspondng borrower turnover s below 50 mllon Euros, and usng the corporate captal requrements formula, takng account for sze adjustment when the frm s turnover s lower than 50 mllon Euros, when the exposure s amount s hgher than 1 mllon Euros. In ths paper, we do not use the banks regulatory expected PDs but nstead the observed emprcal rates of default at the one year horzon as proxes for PDs to compute regulatory as well as economc captal requrements. These default rates are computed as the number of frms gong to default state durng the year relatve to the total number of frms n safe condton at the begnnng of the same year. Table 3 presents average annual rates of default at the one year horzon by frm sze, gvng a frst vew of the credt rsk structure n the sample under study. The table shows that the level of the default rates tends to decrease wth frm sze. It shows also that credt qualty tends to vary wth the busness cycle, wth a sgnfcant downgrade n Table 3: Average observed rates of default at the one year horzon by sze n the sample (n %) Very small busnesses Small frms Medumszed frms Intermedate and large sze frms Source: ACPBDF and Authors computatons As mentoned before, n ths paper, we compare captal requrements n busness loans portfolos at the bankng group s level. Therefore, we compute captal requrements at the level of each large bankng group s portfolo (the French Credt Regster allows to dstngush banks portfolos) and we express captal requrements n terms of captal ratos. Now, to assess the ablty of regulatory captal requrements to cover portfolo credt rsk, we need to use other measures of captal requrements as benchmarks. As argued before, our choce s to use a structural credt rsk multfactor model to compute captal requrements n an economc perspectve, takng account for multple sources of rsk. Drecton des Études  SGACP 10
12 3. The methodology To assess the exstence of a potental bas n the estmaton of captal charges assocated wth the prevous regulatory captal requrements formulas, we compare regulatory captal requrements wth captal requrements computed by usng a more comprehensve economc approach provded by a multfactor portfolo credt rsk model. In a multfactor framework, we have to determne the rsk factors. In a frst step, we nclude frm sze as addtonal systematc rsk factor and n a second step we consder frm sector as addtonal factor. The choce of these factors rely on recent research that shows that concentraton exsts n busness loans portfolos and that credt rsk vares n portfolos accordng to ther ndustry and sze composton (Carlng, Ronnegard and Roszbach, 2004, Detsch and Petey, 2004, Duellmann and Scheule, 2003, Hetfeld, Burton and Chomssengphet, 2006, Duellmann and Masschelen, 2006). Recall that regulatory formulas do not consder such factors. However, for the comparson, we compute regulatory captal requrements and economc captal requrements at the same dsaggregated level of portfolo s sze or sector segments we use to mplement the multfactor model. In what follows, frst, we gve a short presentaton of the methodology. A more detaled presentaton s n the appendx of ths paper. Then we explan why the captal requrements measures derved from a multfactor framework can be used as benchmarks A short vew of the multfactor model The multfactor model belongs to the class of structural credt rsk models 7. It s n fact an extended verson of the standard asymptotc sngle rsk factor ASRF model. The extenson conssts to ntroduce addtonal factors varyng across groups of borrowers. We have expanded the model by addng new latent factors of systematc rsk that can be lnked to observable characterstcs of borrowers. Such an extenson to a multfactor model mproves substantally the computaton of the dependency structure (asset correlatons) across exposures n a typcal loans portfolo. Usng ths approach permts n partcular to compare the credt rsk n groups of borrowers gettng ther loans from dfferent bankng groups. The extenson of the ASRF framework allows takng account for potental credt rsk concentraton whch s lnked to borrowers heterogenety. In small portfolos of large exposure concentraton rsk comes from name concentraton. But n large portfolos of busness loans, whch are hghly granular, 7 See appendx for a complete presentaton of the model. Drecton des Études  SGACP 11
13 concentraton rsk arses from correlated defaults among groups of borrowers. Then, measurement of concentraton rsk needs to proceed to an approprate portfolo s segmentaton able to reflect borrowers heterogenety. Here, we adopt as crteron of segmentaton the belongng of an exposure to the busness loans portfolo of one of the fve French bankng groups we consder n ths study. To compute economc captal n ths framework, we proceed n two steps. The frst step s devoted to calculus of portfolos man rsk parameters, and n partcular the dependence structure among exposures measured by asset correlatons. The second step uses MonteCarlo smulaton to buld the probablty dstrbuton functon of losses, determne the total portfolo VaR and compute the level of captal requrements assocated to each addtonal systematc factor whch are n ths study specfc to bankng groups and ther busness model and lendng polcy. Let consder brefly the frst step. As econometrc specfcaton of the multfactor credt rsk model, followng Frey and Mc Nel, 2003, and McNel and Wendn, 2006) we use the methodology of generalzed lnear mxed models (GLMM). Thus, takngs frms credt ratngs hstores to buld tme seres of rates of default by portfolo s segment, we get estmates of portfolo s credt rsk parameters n a multfactor context. The GLMM model mplements n a coherent way the Merton latent factor default modelng approach, n whch the default occurs when the value of the frm s assets become smaller than the value of ts debt, that s, because frm s assets values are dffcult to observe, when the value of a latent varable descrbng the fnancal stuaton of the frm  whch depends on the realzaton of a set of rsk factors  crosses an unobservable threshold whch determnes the default. In ths framework, the default rate s modeled as: P ( default γ ) = Φ[ x' μ + z' γ ] t t r n whch the default rate depends on ) a fxed effect measured by the borrower s nternal ratng (μ r ), and ) random effects (γ t ), whch are related to a general latent factor (the state of the economy), augmented by a set of factors correspondng to a gven segmentaton of the portfolo. t t The GLMM model produces estmates of default thresholds consdered as fxed effects and covarance matrxes of a set of latent random effects correspondng to the set of systematc factors. The estmaton of such parameters allows computng economc captal as buffer of losses n portfolos exposed to dfferent systematc rsk factors. Let consder now the second step. In the structural credt rsk framework, measurng concentraton rsk calls for allocatng economc captal between segments of borrowers,.e. to compute margnal contrbutons of dfferent segments to portfolos total losses. A portfolo s segmentaton s bult by dentfyng groups of borrowers wth the same observable characterstcs whch expose them to the same Drecton des Études  SGACP 12
14 rsk factors. In a multfactor context, captal allocaton can be mplemented at the segment level such that t s possble to nvestgate the heterogenety n captal allocaton nduced by the varous rsk factors. Thus, a sngle factor homogeneous framework could nduce a msrepresentaton of the concentraton rsk even n large portfolos of retal exposures. Whle they are calbrated usng a sngle factor framework, Basel 2 IRB regulatory formulas of captal requrements could be of lmted nterest n allocatng captal. The computaton of the portfolo s valueatrsk (VaR) and margnal rsk contrbutons are made by usng a methodology proposed by Tasche (2009), whch grounds on an mportance samplng based smulaton of expected condtonal losses. Ths methodology has the advantage to take nto account the mpact of borrowers heterogenety on economc captal charges and captal allocaton The multfactor model as benchmark for captal requrements measurement At ths stage, t s mportant to note that there s a relatonshp between regulatory captal requrements and economc captal requrements derved from a multfactor model. In fact, the Basel II rsk weght formulas were calbrated usng a smplfed verson of a portfolo credt rsk model, the Asymptotc Sngle Rsk Factor (ASRF) model. In ths framework (see Gordy, 2003), bank s total captal requrements s computed by usng two parameters whch refer to frm s ndvdual rsk, whch are the probablty of default (PD) and the loss gven default (LGD), and a thrd parameter  the asset correlaton R whch measures the senstvty of borrowers to a common sngle systematc rsk factors, whch s a macroeconomc undetermned rsk factor. The asset correlaton reflects the fact that default rates are volatle and that ths volatlty depends on ther senstvty to a systematc rsk factor. If the correlaton s hgh, ths senstvty s strong and, n case of realzatons of extreme unfavorable value of the systematc rsk factor, losses wll clmb to hgher levels. Thus, more generally, asset correlatons reflect the potental for jont defaults n a portfolo. Followng ths approach, n Basel II rsk weghtng formulas, under the IRB approach, RWAs depend upon these three credt rsk parameters. So, regulatory RWAs are consstent measures of credt rsk. However, as mentoned before, two calbraton choces determne potental dfferences between regulatory captal requrements and economc captal requrements, what justfes to compare the two types of measures. Frstly, n the regulatory formulas of Basel II, asset correlatons R are entrely determned by the PDs. In the ASRF model, asset correlatons measure the senstvty of loans to a macroeconomc rsk factor and they should vary from one portfolo to another one, dependng on the composton of the portfolo. But, n practce, Basel II provdes banks wth the formulas to compute R, nstead to leave them computng ths rsk parameter usng nternal nformaton. Consequently, RWAs depend strongly upon the value of the asset correlatons and the man dfference between regulatory captal requrements and economc captal Drecton des Études  SGACP 13
15 requrements computed by usng banks nternal data comes from the value of assets correlatons. So, one ssue arses to know f the regulatory asset correlatons computed by usng regulatory formulas and the related regulatory captal requrements  are dfferent from the economc asset correlatons computed by usng banks nternal data. Secondly, n the ASRF model, there s a sngle general undetermned credt rsk factor whch represents the state of the economy. However, borrowers are not equally senstve to common systematc rsk factors. In addton, borrowers fnancal heath s lnked to multple sources of credt rsk whch are more or less specfc to the rsk segment to whch they belong. Takng account for borrowers heterogenety oblges to expand the standard sngle rsk factor model and to adopt a multfactor framework. In a multfactor framework, groups of borrowers are exposed to addtonal systematc rsk factors whch are specfc to ther segment. It s mportant to emphasze that these addtonal rsk factors could renforce or attenuate the nfluence of the general systematc rsk factor. Moreover, a multfactor model allows detectng potental concentraton (dversfcaton) effects comng from the strong (weak) dependence of borrowers to rsk factors whch are specfc to ther own rsk segment. In case of realzaton of unfavorable value of one systematc rsk factor, the number of defaults wll ncrease and losses wll clmb to hgher levels. In such a case, the contrbuton to the portfolo s segment whch s exposed to ths rsk factor wll rase, nducng an ncrease n total losses. More generally, f the sensblty of exposures to the systematc rsk factor whch s specfc to ther segment s hgh, the relatve contrbuton of ths segment to the portfolo s total losses wll be hgh, what corresponds to a stuaton of credt rsk concentraton n that segment. So, n a portfolo composed of several segments, usng a multfactor model allows to compute the margnal contrbuton of each segment to total losses and observe ether the mpact of ths segment on the concentraton of losses or, on the contrary, the role the segment plays n the dversfcaton of the portfolo credt rsk. In practce, ths margnal contrbuton can be expressed under the form of a captal rato by relatng captal requrements needed to cover potental unexpected losses produced to ths segment (computed at a gven percentle  for nstance 99.9%  of the probablty dstrbuton functon of losses) to total exposures of the segment. In ths way, we can assess portfolo s concentraton and dversfcaton n terms of captal rato as a common metrcs, showng how sze and sector factors could contrbute to ncrease or decrease the level of captal requrements relatve to the level gven by a sngle rsk factor model. Drecton des Études  SGACP 14
16 4. The results: comparsons of regulatory and economc captal ratos To conduct our analyss, we do not have access to complete detaled bankng groups nternal nformaton, and, n partcular, to banks nternal rate of defaults. However, usng BDF ratngs hstores of French frms as well as nformaton about ther debts provded by the French Credt Regster gves us the opportunty to use an asf approach and to compute very consstently nternal asset correlatons and economc captal requrements. A major advantage of ths approach s to consder a sngle rsk metrc the BDF ratngs across banks. Recall that data whch are used to mplement the econometrc analyss and compute portfolos credt rsk parameters (among them the dependence structure shown by the covarance matrxes of rsk factors) are: ) the tme seres of observed rates of default n the dfferent segments for each bankng group over the perod 8, and ) the loans amounts n the French Credt Regster. The emprcal rates of default were used as proxes for probabltes of default (PDs) n the Basel II captal requrements formulas. We use ths nformaton to compute captal requrements n each of the sx French major bankng groups. In each case, we compare three captal ratos:  the regulatory rato usng the Basel II IRB Foundaton formulas,  the economc multfactor rato computed by usng a multfactor model whch takes nto account frm sze and frm sector as addtonal rsk sources,  the economc sngle factor rato computed by usng the standard ASRF model n whch the rsk factor s a general undetermned factor e.g. not constraned by the regulatory formula. It s nterestng to compute also the sngle factor rato, because the dfference between captal requrements measures provded by the standard sngle factor model and the regulatory model reles drectly on the value of asset correlaton whch s computed usng portfolos default rates dynamc n the ASRF model whle, as mentoned before, t s gven by regulatory formulas n the regulatory model. On the other sde, the dfference between captal requrements provded by the sngle rsk ASRF model and the multfactor model llustrates the role the addtonal rsk factors play n the determnaton of portfolos losses. In the multfactor framework as well as n the sngle factor framework, total portfolo s requred captal s computed by smulaton of the rsk factors gven default thresholds and rsk factor senstvtes, whch are the outputs of an econometrc model explanng the volatlty of default rates over the perod. Gven the credt rsk parameters and a set of smulated rsk factors, defaults n each subportfolo defned by crossng four sze segments  or eght ndustres  wth sx ratng grades are produced by 8 As mentoned before, n the BDF ratngs system, two ratngs refer to default states: ) legal falure, whch s bankruptcy, and ) bank default, whch corresponds n the BDF ratngs system to severe bankng problems ncdents bancares séreux. We took the two forms of default to compute annual rates of default and to dstngush them by ratngs grade. Drecton des Études  SGACP 15
17 drawng from a bnomal probablty wth the number of frms n each subportfolo and the condtonal default probablty defned by econometrc analyss result as parameters. Exposures are then defned as the average of frms total loans amounts wthn classes crossng ratng and szes,.e. we assume at ths stage homogenety n exposures wthn portfolos segments. In what follows, frst, we wll present results we obtaned when decomposng the busness loans portfolo of each major bankng group n four sze segment, takng frm sze as addtonal systematc rsk factor. Then, we present results obtaned when takng frm sector as addtonal systematc rsk factor. 4.1 Takng account for borrowers heterogenety and potental credt rsk concentraton: the frm sze as an addtonal source of systematc rsk Here, we consder frm sze as a rsk factor. The bankng groups portfolos were dvded n the four sze classes we defned prevously, that s:  a) very small frms, wth turnover between M 0.75 and M 1.5,  b) small frms, wth turnover between M 1.5 and M 10,  c) medumszed frms, wth turnover between M 10 and M 50,  d) ntermedate and large frms, wth turnover over M 50. Usng ths segmentaton, we compute captal ratos assocated to each segment consderng three models: the sngle factor model, the multfactor model and the regulatory model. All nformaton concerns the perod and s treated on an early bass. It s lkely that the portfolos under consderaton are hghly granular due to ther sze. Therefore, dfferences n captal requrements would come from credt rsk concentraton whch corresponds to stuatons of strongly correlated defaults. If oblgors were homogenous n terms of credt rsk, captal ratos should not dffer across oblgors and/or portfolos segments. On the contrary, f oblgors are heterogeneous, a hgher captal rato n a gven segment would ndcate potental rsk concentraton. A straghtforward source of heterogenety s credt ratng whch s accounted for n the econometrc analyss by the estmaton of default thresholds. Sze could be an addtonal source of credt rsk heterogenety n SME portfolos. If there s concentraton rsk, captal ratos should vary along ths source of rsk. Thus, the heterogenety n captal charges wll manly come from the rsk factors affectng the dfferent portfolos segments. Drecton des Études  SGACP 16
18 However, table 2 has shown that, apparently, there s not a consderable potental for credt rsk concentraton when consderng the sze of the portfolos and the dstrbuton of exposures nto sze classes n the large bankng groups operatng n France. Indeed, there are patent dfferences n terms of portfolos sze and the composton of the portfolo vares from one group to another one. Notce that one excepton could come from the hgher share of ntermedate and large frms segment. But, all n all, these observatons suggest that the evoluton of potental credt losses n large portfolos mght be sustanable when consderng concentraton rsk. It s what our results tends to verfy. Table 4 shows the covarance matrxes of random effects n the sze model at the aggregate level of a global portfolo composed of all exposures of the sx bankng groups. The covarance matrxes show average values of covarances over the tme perod, takng account for default rates volatlty over tme. Table 4 shows also the mnmum and maxmum values of covarances across bankng groups 9. There s a consderable systematc component drvng the volatlty of default rates. Indeed, the varance assocated to the "general" factor, whch s the random ntercept n the GLMM model, has very hgh values. Secondly, the sze class wth the largest random effect s the very small busnesses class, wth an order of magntude hgher to the general factor. The random effects assocated to the other sze classes are generally small or equal to zero. Moreover, the general and the sze specfc rsk factors are negatvely and qute strongly correlated. Ths reflects lower rsk levels, ths negatve correlaton dampenng the fluctuatons of the general rsk factor. Sze factors and general factors tend to compensate to generate a lower level of credt rsk. Thus, results suggest a very low potental for rsk concentraton on most of sze segments. Fnally, the estmated covarance matrces of random effects do not suggest a contnuous and convex relatonshp between rsk and sze at the aggregate level. 9 Results at the ndvdual bankng group level not presented here  show that all covarance matrces share qute the same pattern when consderng the sze factors. However, dfferences across banks may exst, manly n what concerns the medumszed frms segment.such dfferences mean ether that banks are makng dfferent portfolo s choces or that they encounter dfferent envronmental condtons Drecton des Études  SGACP 17
19 Table 4: Covarance matrces results A: portfolo composed of all exposures Very small Small Medumszed Intermedate & large General Very small Small Medumszed Intermedate & large General B: mnmum values Very small Small Medumszed Intermedate & large General Very small Small Medumszed Intermedate & large General C: maxmum values Very small Small Medumszed Intermedate & large General Very small Small Medumszed Intermedate & large General Source: ACPBDF, Drectorate Research Notes: for llustraton : n the top panel A, corresponds to the correlaton of borrowers belongng to the very small busnesses portfolo to the systematc rsk factor related to ths sub portfolo. A hgh level of correlaton corresponds to a hgh level of concentraton wthn the segment corresponds to the correlaton between the general systemc factor and the sze specfc systemc factor. A large negatve value captures a dversfcaton effect mtgatng the rsk wthn the portfolo. Panel B and C reproduce the mnmum and maxmum values of the components of the correlaton matrx across bankng groups. Table 5 shows the dstrbuton of: () the rato of regulatory captal requrements over captal requrements gven by a multfactor model, and () the rato of regulatory captal requrements over captal requrements gven by a sngle factor model across bankng groups 10. A rato hgher than 1 means that regulatory captal requrements are larger than economc requrements. Another vew s to consder that a rato hgher than 1 n one gven segment demonstrates that dversfcaton effects comng 10 Here, captal ratos represent average values of ratos over the perod. They are computed usng the average rsk parameters (rate of default, covarances) values over the perod. Ths perod ncludes two downturn epsodes, such that these average values could be consdered as throughthecycle values. These values and especally correlatons, can change n case of realzaton of extreme events. However, two remarks could be made on ths ssue. Frstly, because our methodology uses mportance samplng technques, values of probablty dstrbuton of losses could be consdered as stressed values. Secondly, t s possble to obtan stressed values of credt rsk parameters by changng the observaton wndow n order to measure the nfluence of bad years or bad realzatons of the addtonal sze or sector rsk factors. Drecton des Études  SGACP 18
20 from the dependence structure n ths segment are hgh. The result could come ether from low value of covarance of random effect n ths segment or from compensaton between the rsk factor specfc to the sze segment and the general factor. Notce that the regulatory captal ratos are computed usng the IRB formulas of Basel II. The other retal formulas were used for the segments of mcrofrms, very small frms and small frms, whle the corporate formula was used for the medumszed frms segments. Man results come as follows. Table 5: Dstrbuton of the ratos of regulatory to economc captal dstrbuton across bankng groups, by sze of frms Sze of frms n the portfolo Multfactor model Sngle factor model mn mean max mn mean Max very small 2,0 3,4 6,5 1,5 1,8 2,0 small 1,2 1,5 2,7 1,3 1,6 1,9 medumszed 0,9 2,1 4,6 2,2 2,7 3,5 ntermedate & large 1,4 1,8 2,0 1,4 1,8 2,0 Notes 1. Left panel: rato between, on the one hand, regulatory captal requrements, and, on the other hand, captal requrements derved from the multfactor model; rght panel: rato between, on the one hand, regulatory captal requrements, and, on the other hand, captal requrements derved from the sngle factor model model. 2. Regulatory captal ratos are computed accordngly to the other retal basel formula for the very small and small busnesses and accordngly to the corporate Basel 2 formula for the other frm sze classes. Source: ACPBDF, Drectorate Research Frstly, at the aggregate level for each group, the regulatory captal rato does not underestmate credt rsk. It remans true when lookng at specfc portfolo segments. Indeed, the level of captal requrements computed usng the multfactor model are lower than the regulatory captal requrements computed usng the Basel II formulas, except for the portfolo s segment composed of loans to medumszed frms n some bankng groups where regulatory captal rato s lower than economc captal ratos (see for nstance the mnmum value of 0.9 n that sze segment). Ths result shows that, n practce, even f sze concentraton effects, whch the regulatory approach of captal requrements does not take nto account, could exst, the aggregate level of regulatory captal requred to cover total portfolos unexpected losses do cover de facto potental concentraton effects. However, n the (rare) cases where the level of the regulatory captal rato s lower than the level provded by the sze multfactor model, regulatory formulas could nduce dstortons n the captal allocaton across sze segments. The soluton to ths problem would be to complement the regulatory captal requrements to take nto account results provded by a multfactor approach. Drecton des Études  SGACP 19
21 Secondly, the comparson of the ratos of regulatory requrements to economc captal requrements computed by usng the sngle rsk model shows that the regulatory formulas overestmate asset correlaton. In other terms, regulatory approach overestmates the senstvty of exposures to the busness cycle approxmated by the general systematc rsk factor. Thrdly, the comparson of the ratos of regulatory captal requrements to economc captal requrements gven by a multfactor factor and a sngle model shows that the latter s n most cases lower than the former. Thus, takng nto account addtonal factors specfc to sze segments shows tends to lower n most case the economc captal requrements. Therefore, credt rsk concentraton due to a sze effect appears to be lmted. Moreover, the value of the ratos are close from one sze to another one, what means that, on average, t seems better to manage portfolos composed of exposures of all szes than to manage portfolos concentrated on one or a lttle number of szes. Ths result whch holds for qute all bankng groups n all sze segments vares n ntensty across groups. Indeed, the dsperson of the ratos shows clearly the exstence of dvergences between bankng groups when consderng the level of economc captal. The potental for dversfcaton gven by the sze rsk factor vares across bankng groups and banks are not equally effcent n managng the composton of ther portfolos by frm sze or, at least, they do not have the same opportuntes to extract dversfcaton benefts. Table 2 does show dfferences n the allocaton of credt by frm sze across bankng groups. Therefore, ths result s partly the consequence of dfferent bankng groups polcy n terms of suppled loans amount by frm. But, another mportant factor explanng the dfferences of captal rato comes from the dfferences n the dependence structure between oblgors by sze Takng account for borrowers heterogenety and potental credt rsk concentraton: the frm sector as an addtonal source of systematc rsk The prevous secton tred to detect potental concentraton lnked to frm sze n bankng groups busness loans portfolos. Here, we present results consderng potental concentraton comng from sector systematc rsk factors. To proceed, we segment portfolos exposures by ndustry and use the same methodology we used to consder sze effects. If concentraton s strong wthn a sector, ths sector wll strongly contrbute to the potental losses and hgher level of captal wll be requred. Table 6 shows the covarance matrces of random effects n the sze model at the aggregate level of a global portfolo composed of all exposures of the sx bankng groups. Table 4 shows also the mnmum Drecton des Études  SGACP 20
Capital asset pricing model, arbitrage pricing theory and portfolio management
Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securtyspecfc rsk
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationVasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio
Vascek s Model of Dstrbuton of Losses n a Large, Homogeneous Portfolo Stephen M Schaefer London Busness School Credt Rsk Electve Summer 2012 Vascek s Model Important method for calculatng dstrbuton of
More informationPortfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets holdtomaturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationReporting Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (including SME Corporate), Sovereign and Bank Instruction Guide
Reportng Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (ncludng SME Corporate), Soveregn and Bank Instructon Gude Ths nstructon gude s desgned to assst n the completon of the FIRB
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationTransition Matrix Models of Consumer Credit Ratings
Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationThe Current Employment Statistics (CES) survey,
Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probabltybased sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationBank Credit Conditions and their Influence on Productivity Growth: Companylevel Evidence
Bank Credt Condtons and ther Influence on Productvty Growth: Companylevel Evdence Rebecca Rley*, Chara Rosazza Bondbene* and Garry Young** *Natonal Insttute of Economc and Socal Research & Centre For
More informationSIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA
SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands Emal: e.lagendjk@tnw.tudelft.nl
More informationDI Fund Sufficiency Evaluation Methodological Recommendations and DIA Russia Practice
DI Fund Suffcency Evaluaton Methodologcal Recommendatons and DIA Russa Practce Andre G. Melnkov Deputy General Drector DIA Russa THE DEPOSIT INSURANCE CONFERENCE IN THE MENA REGION AMMANJORDAN, 18 20
More informationThe impact of hard discount control mechanism on the discount volatility of UK closedend funds
Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closedend funds Abstract The mpact
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationStress test for measuring insurance risks in nonlife insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n nonlfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationStart me up: The Effectiveness of a SelfEmployment Programme for Needy Unemployed People in Germany*
Start me up: The Effectveness of a SelfEmployment Programme for Needy Unemployed People n Germany* Joachm Wolff Anton Nvorozhkn Date: 22/10/2008 Abstract In recent years actvaton of meanstested unemployment
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management
ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces
More informationGender differences in revealed risk taking: evidence from mutual fund investors
Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More informationRiskbased Fatigue Estimate of Deep Water Risers  Course Project for EM388F: Fracture Mechanics, Spring 2008
Rskbased Fatgue Estmate of Deep Water Rsers  Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationTraffic State Estimation in the Traffic Management Center of Berlin
Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationWORKING PAPER SERIES TAKING STOCK: MONETARY POLICY TRANSMISSION TO EQUITY MARKETS NO. 354 / MAY 2004. by Michael Ehrmann and Marcel Fratzscher
WORKING PAPER SERIES NO. 354 / MAY 2004 TAKING STOCK: MONETARY POLICY TRANSMISSION TO EQUITY MARKETS by Mchael Ehrmann and Marcel Fratzscher WORKING PAPER SERIES NO. 354 / MAY 2004 TAKING STOCK: MONETARY
More informationI. SCOPE, APPLICABILITY AND PARAMETERS Scope
D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable
More informationManagement Quality and Equity Issue Characteristics: A Comparison of SEOs and IPOs
Management Qualty and Equty Issue Characterstcs: A Comparson of SEOs and IPOs Thomas J. Chemmanur * Imants Paegls ** and Karen Smonyan *** Current verson: November 2009 (Accepted, Fnancal Management, February
More informationCovariatebased pricing of automobile insurance
Insurance Markets and Companes: Analyses and Actuaral Computatons, Volume 1, Issue 2, 2010 José Antono Ordaz (Span), María del Carmen Melgar (Span) Covaratebased prcng of automoble nsurance Abstract Ths
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationTHE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE
THE DETERMINANTS OF THE TUNISIAN BANKING INDUSTRY PROFITABILITY: PANEL EVIDENCE Samy Ben Naceur ERF Research Fellow Department of Fnance Unversté Lbre de Tuns Avenue Khéreddne Pacha, 002 Tuns Emal : sbennaceur@eudoramal.com
More informationA Model of Private Equity Fund Compensation
A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationAn Empirical Study of Search Engine Advertising Effectiveness
An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan RmmKaufman, RmmKaufman
More informationReturn decomposing of absoluteperformance multiasset class portfolios. Working Paper  Nummer: 16
Return decomposng of absoluteperformance multasset class portfolos Workng Paper  Nummer: 16 2007 by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume
More informationPortfolio Risk Decomposition (and Risk Budgeting)
ortfolo Rsk Decomposton (and Rsk Budgetng) Jason MacQueen RSquared Rsk Management Introducton to Rsk Decomposton Actve managers take rsk n the expectaton of achevng outperformance of ther benchmark Mandates
More informationPROFIT RATIO AND MARKET STRUCTURE
POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons
More informationENTERPRISE RISK MANAGEMENT IN INSURANCE GROUPS: MEASURING RISK CONCENTRATION AND DEFAULT RISK
ETERPRISE RISK MAAGEMET I ISURACE GROUPS: MEASURIG RISK COCETRATIO AD DEFAULT RISK ADIE GATZERT HATO SCHMEISER STEFA SCHUCKMA WORKIG PAPERS O RISK MAAGEMET AD ISURACE O. 35 EDITED BY HATO SCHMEISER CHAIR
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationEvaluating credit risk models: A critique and a new proposal
Evaluatng credt rsk models: A crtque and a new proposal Hergen Frerchs* Gunter Löffler Unversty of Frankfurt (Man) February 14, 2001 Abstract Evaluatng the qualty of credt portfolo rsk models s an mportant
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120
Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng
More informationFixed income risk attribution
5 Fxed ncome rsk attrbuton Chthra Krshnamurth RskMetrcs Group chthra.krshnamurth@rskmetrcs.com We compare the rsk of the actve portfolo wth that of the benchmark and segment the dfference between the two
More informationThe Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15
The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the
More informationGRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 NORM
GRAVITY DATA VALIDATION AND OUTLIER DETECTION USING L 1 NORM BARRIOT JeanPerre, SARRAILH Mchel BGI/CNES 18.av.E.Beln 31401 TOULOUSE Cedex 4 (France) Emal: jeanperre.barrot@cnes.fr 1/Introducton The
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationMethod for assessment of companies' credit rating (AJPES S.BON model) Short description of the methodology
Method for assessment of companes' credt ratng (AJPES S.BON model) Short descrpton of the methodology Ljubljana, May 2011 ABSTRACT Assessng Slovenan companes' credt ratng scores usng the AJPES S.BON model
More informationCriminal Justice System on Crime *
On the Impact of the NSW Crmnal Justce System on Crme * Dr Vasls Sarafds, Dscplne of Operatons Management and Econometrcs Unversty of Sydney * Ths presentaton s based on jont work wth Rchard Kelaher 1
More informationMacro Factors and Volatility of Treasury Bond Returns
Macro Factors and Volatlty of Treasury Bond Returns Jngzh Huang Department of Fnance Smeal Colleage of Busness Pennsylvana State Unversty Unversty Park, PA 16802, U.S.A. Le Lu School of Fnance Shangha
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationA Simplified Method for Calculating the Credit Risk of Lending Portfolios
A Smplfed Method MOETARY for Calculatng AD ECOOMIC the Credt STUDIES/DECEMBER Rsk of Lendng Portfolos 000 A Smplfed Method for Calculatng the Credt Rsk of Lendng Portfolos Akra Ieda, Kohe Marumo, and Toshnao
More informationThe Shortterm and Longterm Market
A Presentaton on Market Effcences to Northfeld Informaton Servces Annual Conference he Shortterm and Longterm Market Effcences en Post Offce Square Boston, MA 0209 www.acadanasset.com Charles H. Wang,
More informationBrigid Mullany, Ph.D University of North Carolina, Charlotte
Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationExhaustive Regression. An Exploration of RegressionBased Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of RegressonBased Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More informationTrafficlight extended with stress test for insurance and expense risks in life insurance
PROMEMORIA Datum 0 July 007 FI Dnr 07117130 Fnansnspetonen Författare Bengt von Bahr, Göran Ronge Traffclght extended wth stress test for nsurance and expense rss n lfe nsurance Summary Ths memorandum
More informationCahiers de la Chaire Santé
Cahers de la Chare Santé The nfluence of supplementary health nsurance on swtchng behavour: evdence from Swss data Auteurs : Brgtte Dormont, PerreYves Geoffard, Karne Lamraud N 4  Janver 2010 1 The nfluence
More informationSimon Acomb NAG Financial Mathematics Day
1 Why People Who Prce Dervatves Are Interested In Correlaton mon Acomb NAG Fnancal Mathematcs Day Correlaton Rsk What Is Correlaton No lnear relatonshp between ponts Comovement between the ponts Postve
More informationQuantification of qualitative data: the case of the Central Bank of Armenia
Quantfcaton of qualtatve data: the case of the Central Bank of Armena Martn Galstyan 1 and Vahe Movssyan 2 Overvew The effect of nonfnancal organsatons and consumers atttudes on economc actvty s a subject
More informationThe systemic importance of financial institutions 1
Nkola Tarashev nkola.tarashev@bs.org Claudo Boro claudo.boro@bs.org Kostas Tsatsarons ktsatsarons@bs.org The systemc mportance of fnancal nsttutons 1 Prudental tools that target fnancal stablty need to
More informationUK Letter Mail Demand: a Content Based Time Series Analysis using Overlapping Market Survey Statistical Techniques
10170 Research Group: Econometrcs and Statstcs 2010 UK Letter Mal Demand: a Content Based Tme Seres nalyss usng Overlappng Market Survey Statstcal Technques CTHERINE CZLS, JENPIERRE FLORENS, LETICI VERUETEMCKY,
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationEmployment and Trade in France
Please cte ths paper as: Kramarz, F. (2011), Employment and Trade n France: A FrmLevel Vew (19952004), OECD Trade Polcy Workng Papers, No. 124, OECD Publshng. http://dx.do.org/10.1787/5kg3mkgh4cznen
More informationChapter 11 Practice Problems Answers
Chapter 11 Practce Problems Answers 1. Would you be more wllng to lend to a frend f she put all of her lfe savngs nto her busness than you would f she had not done so? Why? Ths problem s ntended to make
More informationTwo Faces of IntraIndustry Information Transfers: Evidence from Management Earnings and Revenue Forecasts
Two Faces of IntraIndustry Informaton Transfers: Evdence from Management Earnngs and Revenue Forecasts Yongtae Km Leavey School of Busness Santa Clara Unversty Santa Clara, CA 950530380 TEL: (408) 5544667,
More informationHigh Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets)
Hgh Correlaton between et Promoter Score and the Development of Consumers' Wllngness to Pay (Emprcal Evdence from European Moble Marets Ths paper shows that the correlaton between the et Promoter Score
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationWORKING PAPERS. The Impact of Technological Change and Lifestyles on the Energy Demand of Households
ÖSTERREICHISCHES INSTITUT FÜR WIRTSCHAFTSFORSCHUNG WORKING PAPERS The Impact of Technologcal Change and Lfestyles on the Energy Demand of Households A Combnaton of Aggregate and Indvdual Household Analyss
More informationProceedings of the Annual Meeting of the American Statistical Association, August 59, 2001
Proceedngs of the Annual Meetng of the Amercan Statstcal Assocaton, August 59, 2001 LISTASSISTED SAMPLING: THE EFFECT OF TELEPHONE SYSTEM CHANGES ON DESIGN 1 Clyde Tucker, Bureau of Labor Statstcs James
More informationTESTING FOR EVIDENCE OF ADVERSE SELECTION IN DEVELOPING AUTOMOBILE INSURANCE MARKET. Oksana Lyashuk
TESTING FOR EVIDENCE OF ADVERSE SELECTION IN DEVELOPING AUTOMOBILE INSURANCE MARKET by Oksana Lyashuk A thess submtted n partal fulfllment of the requrements for the degree of Master of Arts n Economcs
More informationIdentifying Workloads in Mixed Applications
, pp.395400 http://dx.do.org/0.4257/astl.203.29.8 Identfyng Workloads n Mxed Applcatons Jeong Seok Oh, Hyo Jung Bang, Yong Do Cho, Insttute of Gas Safety R&D, Korea Gas Safety Corporaton, ShghungSh,
More informationFragility Based Rehabilitation Decision Analysis
.171. Fraglty Based Rehabltaton Decson Analyss Cagdas Kafal Graduate Student, School of Cvl and Envronmental Engneerng, Cornell Unversty Research Supervsor: rcea Grgoru, Professor Summary A method s presented
More informationDiscount Rate for Workout Recoveries: An Empirical Study*
Dscount Rate for Workout Recoveres: An Emprcal Study* Brooks Brady Amercan Express Peter Chang Standard & Poor s Peter Mu** McMaster Unversty Boge Ozdemr Standard & Poor s Davd Schwartz Federal Reserve
More informationRequIn, a tool for fast web traffic inference
RequIn, a tool for fast web traffc nference Olver aul, Jean Etenne Kba GET/INT, LOR Department 9 rue Charles Fourer 90 Evry, France Olver.aul@ntevry.fr, JeanEtenne.Kba@ntevry.fr Abstract As networked
More informationIs the home bias in equities and bonds declining in Europe?
Drk Schoenmaker (Netherlands), Thjs Bosch (Netherlands) Is the home bas n equtes and bonds declnng n Europe? Abstract Fnance theory suggests that nvestors should hold an nternatonally dversfed portfolo.
More information1.1 The University may award Higher Doctorate degrees as specified from timetotime in UPR AS11 1.
HIGHER DOCTORATE DEGREES SUMMARY OF PRINCIPAL CHANGES General changes None Secton 3.2 Refer to text (Amendments to verson 03.0, UPR AS02 are shown n talcs.) 1 INTRODUCTION 1.1 The Unversty may award Hgher
More information