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Application of data envelopment analysis to calculating probability of default for high rated portfolio Urszula Grzybowska i Marek Karwański Katedra Informatyki Wydział Zastosowań Informatyki i Matematyki SGGW w Warszawie FENS 2014 Lublin 14-16.05.2014 1

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Plan of the talk Introduction Motivation Description of models and methods Data Results Conclusions 2

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Introduction According to the Capital Requirements Directive (2006, 2009, 2010,2013) banks applying the internal-rating based approach have to estimate probabilities of default (PDs) for their obligors. PDs are a core input to modern credit risk models. In credit risk estimation an obligor is assigned to one of several rating classes. The obligors with the same credit quality are assigned to the same risk group. There are from 8 to 18 rating categories that describe credit quality of agents. Following S&P the highest and the best rating category is AAA. An obligation rated AAA is judged to be the best quality, with the smallest degree of investment risk. On the other edge of the scale is category D, which is assigned to an obligation where a default has already occurred. 3

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Introduction One of the obstacles connected with PD estimation is the low number of defaults, especially in high rating grades. High rating categories might experience many years without any default. A substantial part of bank assets consists of portfolios with low default rate, especially high rated portfolios are LDP. 4

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Low default portfolio - definition Low default portfolio (LDP) is a portfolio with only few defaults or a portfolio free from any defaults 5

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Probability of a Low Default Portfolio A. Forrest’s (2005); K. Pluto and D. Tasche’s (2005); N. M. Kiefer (2006) ; M. Burgt’s (2007); D. Tasche’s (2009); Basel Committee on Banking Supervision proposed several methods to estimate PD for LDP: 6

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The model of K. Pluto and D. Tasche’s Assume that three rating classes are given: A, B and C. We assume that no default occurred. Let p A be the unknown probability of default for grade A, p B - probability of default of grade B, and p C of grade. The probabilities should reflect the decreasing credit- worthiness of the grades, in the sense of the following inequality: p A ≤ p B ≤ p C 7

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Confidence regions for PDs 8 The confidence region for p A can be described as the set of all admissible values of p A with the property that the probability of not observing any default during the observation period is not less than 1 −α (for instance for α= 90%). Let n A, n B, n C be the size of groups A, B and C respectively. Then, using the formula for probability of no success in Bernoulli trials we get confidence intervals for desired probabilities: The only key assumption is a correct ordinal rating of the borrowers.

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Motivation The aim of our research is to propose a method of rating which is based on efficiency measure given by DEA. We will compare the DEA driven results with results obtained by PCM and a clustering method. 9

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DEA- its origin and applications Data Envelopment Analysis (DEA) is an OR approach for evaluating the performance of a set of peer entities called Decision Making Units (DMU). The first article on DEA application by Cooper, Charnes and Rhodes was published in 1978. The work on the subject originated in the eraly 1970s in response to the thesis effort of Rhodes. The aim of the thesis was to evaluate the educational programs for disadvantaged students. 10

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DEA as a Benchmarking Tool Benchmarking can be described as a process of defining valid measures of performance comparison among peer units, using them to determine the relative positions of the peer units and, ultimately, establishing a standard of excellence. 11

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Applications of DEA DEA can be applied to a wide variety of activities. It can be used to evaluate the performance of: Governental agencies; Hospitals; Universities; Non-profit organizations; Banks; Firms. 12

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Basic DEA Benchmarking Information DEA gives Efficiency rating, or score, for each DMU: Θ Efficiency reference set: peer group Target for the inefficient DMU Information on how much inputs can be decreased or outputs increased to make the unit efficient – improving productivity and performance 13

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DEA Model 14 inputs outputs DMU

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Basic CCR model in its dual form – Farrel Model (1978) 15

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The BCC-0 model 16

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Variable selection Inputs: Assets turnover Total Liabilities/Total Assets (Debt Ratio) Outputs: Return on assets (ROA) Return on equity (ROE) Current ratio (CR) Operating profit margin (OPM) 17

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Data 17 Building companies traded on Warsaw Stock Exchange (the the financial reports covered two years: 2001 and 2002) 76 Production companies traded on WSE (the financial reports covered two years: 2011 and 2012) 18

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Applied methods We performed DEA, PCM and cluster analysis to distinguish groups of homogeneous elements - rating classes. 19

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Group Number of elements in a group Company 17 BUDIMEX. BUDOPOL, INSTAL_K, MOST_EXP, MOST_PK, POLNORD, ULMA 28 AWBUD, CENNOWTE, ELBUDOWA, ELKOP. ENERGOPL, ENMONTPD MOST_ZAB, RESBUD 32KOPEX, PEMUG Results of DEA BCC-0. Example 1 20

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CompanyPCM score DEA Group Efficiency rating MOST_EXP206,001 1 ULMA190,231 1 BUDIMEX180,391 1 MOST_ZAB149,842 0,68 ELKOP134,622 0,74 CENNOWTE134,492 0,997 ENERGOPL134,492 0,998 ENMONTPD122,892 0,74 KOPEX117,133 0,68 PEMUG108,203 0,756 MOST_PK97,471 1 ELBUDOWA87,722 0,994 INSTAL_K87,171 1 POLNORD83,61 1 RESBUD71,202 0,933 AWBUD70,862 0,99 BUDOPOL62,2451 1 Company PCM score DEA Group Efficiency rating MOST_EXP206,001 1 ULMA190,231 1 BUDIMEX180,391 1 MOST_ZAB149,842 0,68 ELKOP134,622 0,74 CENNOWTE134,492 0,997 ENERGOPL134,492 0,998 ENMONTPD122,892 0,74 KOPEX117,133 0,68 PEMUG108,203 0,756 MOST_PK97,471 1 ELBUDOWA87,722 0,994 INSTAL_K87,171 1 POLNORD83,601 1 RESBUD71,202 0,933 AWBUD70,862 0,99 BUDOPOL62,24511 21

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Results of DEA BCC-0. Example 2 76 Production companies traded on WSE 23

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Group Number of elements Companies 19 ZELMER, PGE, EKO_EXP, HYDROTOR, PANITERE, BERLING, WINDMOB, AC, MENNICA 213 SONEL, BSCDRUK, APATOR, CIGAMES, CITYINTE, STALPROD, ESSYSTEM, PULAWY, MEGAR, WAWEL, ZYWIEC, POLICE, IZOL_JAR 315 KETY, POLNA, PEPEES, BIOMAXIM, NOVITA ZUK, RELPOL, IZOSTAL, BUDVAR, STOMIL_S ALKAL, HUTMEN, INTERCAR, KPPD, DUDA 412 INTEGER, TAURON, MOJ, POZBUD, BORYSZEW, PROJPRZM, PATENTUS, INVICO, FORTE, ZPUE, DEBICA, LOTOS 510 GROCLIN, LENTEX, RAFAMET, PLASTBOX, FASING, FERRO, RAFAKO, SYNEKTIK, ERG AMICA 617 GRAJEWO, MUZA, KOELNER, RAWLPLUG, VISTULA, ARMATURA, SUWARY, GRAAL, WOJAS, ENERGOIN, MIESZKO, PAMAPOL, ZPC_OTM, FERRUM, ZUE, SNIEZKA, WIELTON 24

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25 LPCompanyPCM scoreRanking PCM DEA group Ward group Eliptical- Seriation (1) score Eliptical- Seriation (4) score 71ZELMER1029,4111 [GR=1] 7576 48PGE566,26421 [GR=2] 49 28INTEGER521,1534 [GR=1] 73 65TAURON433,2044 [GR=1] 69 24GRAJEWO391,1156 [GR=1] 7475 42MUZA379,8966 [GR=2] 40 41MOJ379,8674 [GR=2] 3435 25GROCLIN358,8285 [GR=1] 67 34KOELNER356,0396 [GR=1] 71 57RAWLPLUG355,99106 [GR=1] 72 66VISTULA333,50116 [GR=1] 65 36LENTEX326,93125 [GR=2] 37 56RAFAMET315,23135 [GR=2] 52 5ARMATURA303,81146 [GR=1] 70 52POZBUD301,09154 [GR=2] 57

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Conclusions DEA seems to be a promising tool, alternative to traditional scoring models. It enables ranking of agents. It can be used for distinguishing classes of homogeneous object, e.g., rating classes. The rsults obtained with help of DEA differ from results obtained with clustering methods. 32

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