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PD models in CSOB Scoring Models for Individuals Retail portfolio Scoring Function ππππππ = π1 π₯π1 + π2 π₯π2 + π3 π₯π3 + β― + ππ π₯ππ = πβ² ππ Vector of borrowerβs characteristics: ππ = π₯π1 π₯π2 β¦ π₯π2 Vector of unknown parameters (weights): π = π1 π2 β¦ ππ Internal model versus crystal ball How to assess creditworthiness of each borrower? To whom I can borrow? Who should be rejected from loan providing? Who will not be able to repay his loan? Scoring β classing/ ordering people Score: 0, 12, 38, 44, 48,67, 78, 93,101, 112, 230, 330,560 Risk Drivers for retail portfolio β’ Borrowerβs specific characteristics β’ Age of borrower β’ Marital Status β’ Occupation, income β’ Loanβs specific information β’ Type of loan β’ Monthly instalment β’ Transactions information (in case if available) β’ Drawings β’ Payment balance β’ External /Macro β’ Unemployment rate β’ Czech Banking Credit Bureau Data Weight of evidence and information value definition WoE=ln(P(c/Good))-ln(P(c/Bad) P(Good/c) P(Good) ln(P(c/Good))-ln(P(c/Bad)=ln - ln P(Bad) P(Bad/c) WeE = A Posteriory log odds β A priory log odds Interpretation: the improvement of forecast through the information of category c. IV = πͺ π=π πΎππ¬π (P(c/Good))βP(c/Bad)) Interpretation: a high value of IV indicates a high discriminative power of a variable You cannot predict everything β’ Unacceptable risk (DR β 37%) β’ Decline on spot β’ No products allowed Score 0 Score 2 33% 25% Score 3 Score 4 Score 5 Score 6 14% 8% 0% 20% β’ Medium risk β’ Manual review β’ Proceed with caution β’ Income (800 mln) β’ Debt (0 mln) β’ Region (Capital region) β’ High score + Default β Fraud! Model 60% Score 1 β’ Low risk portfolio β’ Automatically accepted β’ No manual review Basel Accord To set higher risk management and internal control standards for banks To introduce more risk-sensitive approach to the regulatory capital requirements β’ 1988: 1st Capital Accord β Basel I (BCBS, BIS) β’ 1999: Basel II 1st Consultative Paper β’ 2004: The New Capital Accord - Basel II β’ 2006: EU Capital Adequacy Directive β’ 2008: Basel II effective for banks β’ 2010: Basel III following the crisis (effective 2013-2019) The main principles of Basel Accord (example) Bank A Bank B Liabilities Assets Deposits 900 Capital 100 Total 1000 Loans Total Liabilities 1000 1000 After credit Loss of $ 125 m Deposits 900 Capital -25 Total 875 Loans Total Assets Deposits 600 Capital 400 Total 1000 Loans 1000 Total 1000 Loans 875 Total 875 After credit Loss of $ 125 m 875 875 Capital negative ο¨ insolvency Bankβs assets are not enough to repay its deposits To cease the operations or recapitalized/bailed out Deposits 600 Capital 275 Total 875 Capital positive ο¨ solvent Continues the operations Banks operate on thin margins(difference in margins between deposits and loans). Some amount of leverage (usage of borrowed capital) is a must. But high leverage is a risk. The main principles of Basel Accord: losses over time The expected part of the losses β EL , based on the long term history, should be covered from annual revenues. EL β is the cost of doing business, the credit pricing has to absorb EL The unexpected part β UL, if not covered by revenues, must be charged against the capital. The main principles of Basel Accord: Expected Loss (EL) and Unexpected Loss (UL) In good years losses might be less than expected, but in bad years the bank needs a sufficient capital buffer. The goal of regulation: to set up a procedure estimating the potential unexpected loss (UL) on a regulatory level β 99.9% of potential losses should be covered by the outcome of internal models. Rating System and its Performance External versus Internal Rating Category Rating Highest Quality AAA Very Good Quality AA β’ Moodyβs (1906) Good Quality A β’ Standard&Poorβs (S&P, 1916) Medium Quality BBB β’ Fitch, etc Low Medium Quality BB Poor Quality B Speculative Quality C Default D β’ External - Rating Agencies: β’ Internal Rating system βdiffer from FI to FI β’ Basel requirement: at least 7 rating grades β’ WHY Internal Rating? β’ External ratings represent the quality of particular debt issue/ internal rating evaluate clientβs quality β’ External Ratings are available only for large corporates, sovereigns/ Internal Ratings assess all medium, small business segments β’ Conflict of interest: External Agencies earn their income providing rating service from fees, which are paid by corporate clients Probability of Default and Default rates β’ Qualitative measure of default likeliness β’ Number in a range: 0<PD<1 or 0%<PD<100% β’ DR = D during observation period/(Total ND at the beginning of observation period) β’ DR is empirical realization of PD β’ PD is individual characteristic of client, DR is characteristics of clientsβ sample / portfolio β’ Benefits of PD: β’ Objective Information, which can be used in comparison of different clients in different portfolios and benchmarked with external default data β’ PD is useful for credit pricing: the higher PD, the higher risk, hence credit premium ought to be higher β’ PD enables calculation of the economic capital: the higher PD, the higher capital requirements β’ Cohorts: 2005 2007 2006 Outcome period Cumulative Accuracy Profile (CAP)and Accuracy Ratio (AR) β I CAP curve β line in the rectangle [0,1]x [0,1], plots cumulative distribution of defaulted debtors πΆπ· - ordered from worse rating to the best against cumulative distribution of all debtors πΆπ -ordered from worse rating to the best ο£ CD Intuition: bad clients have to be assigned to the worst Rating grades πΆπ (π π ) - for given rating π π - percentage of all debtors with rating π π or worse πΆπ· (π π ) - for given rating π π - percentage of all debtors with rating π π or worse Random Model: straight line which halves the quadrant β rating system contains no information about debtorβs credit quality; assign x% of defaulters among x% debtors with the worst rating (no discrimination) Perfect Model: all defaulters get a worse rating than the non-defaulted debtors and CAP raises straight to 1 and stays there. Cumulative Accuracy Profile (CAP)and Accuracy Ratio (AR) - II ππ ππ ο£ CD CAP curve can be summarized into a single number β The Accuracy Ratio β AR or (Gini Coefficient, or Power Statistics) ππ π΄π = ππ ππ - the area between CAP rating model and CAP random model; ππ - the area between CAP perfect model and CAP rating model; 0 <= AR <= 1 Intuition: the closer AR to 1, the more CAP curve to the upper left, the higher is the discriminative power of a rating model Discriminative Power of the Rating System PD models for Legal Entities Corporate/SME portfolio Model Selection: Logit Regression Advantages: 1. Output from Logistic regression can be interpreted directly as probability of default (PD) 2. Easy check β dependence between explanatory variables and default risk π¦πβ latent (unobservable variable): π¦π - observable output default event Logistic distribution Interpretation of Logistic coefficients: the odds β the relation of probability of default to the survival probability changes by π π½π when explanatory variable π₯π changes by 1 unit. Note: other models are also in use such as probit, survival model, decision trees, neural networks, panel data models, etc. Data Collection: Risk Drivers for Legal Entities Firm Credit Risk Operating (NonFinancial) Risks Financial Risk Internal (Company Level) Risks Industry Risks External Risks Operating Risks β’ External Risks β’ β’ β’ β’ β’ β’ National Development (Macroeconomic Factors: Private Consumption, Government Spending, Inflation, etc) International Development (Exchange Rates, Fiscal Policy, Monetary Policy, etc.) Economic Factors (business cycle, investment, import, export, etc.) Political Factors (terrorism, civil wars) Social Factors (demography, education) Cultural Factors, Regulatory Framework, Technology, Environment) β’ Industry Risks β’ β’ β’ β’ β’ β’ β’ Risks Emanating from External Environment (tariff barriers, changes of consumer preferences) Industry Specific Risks (new entrance, price wars, bargaining power of suppliers and buyers) Risks Emanating from Industry Drivers (demand factors) Industry Cycle Stages: pioneering, rapid growth, maturity, Stabilization, Decline Permanence of Industry Government Support Industry Profitability (completion among existing firms, threat of new, threat of substitute products) Data Processing 1995 β’ Data Cleaning 1996 N default sales Net sales 1 0 -1230 N/A 2 1 N/A 3 N/A N/A β¦.. 1997 Horizontal cleaning: repeated rows, errors in specific cells, non representative firms (too large, too smallβ¦) non annual financial statements collected default information is missing β row should be deleted N/A Vertical cleaning: if specific variable has high number of missing values β column should be deleted β’ Treatment of missing Values β’ Substitute by mean or median (neutral) value some of the input variables β’ Treatment of Outliers β’ Replace extreme values by an appropriate cut-off value or percentile β’ Transformation of Explanatory Variables β’ Standardization or/and normalization Single Factor Analysis: the choice of input variables (Long List) 1. The expected dependence between the financial ratio and probability of default 2. Test of linearity assumption: 2.1. Divide the indicators into groups that contains the same number of observations, for instance by percentile 2.2. Default rate (π·π π ) in each group; π·π 2.3. Empirical log odd within each group ππ( π ) 1βπ·π π 2.4. Estimate linear regression of log odds on the mean values π₯π of the each group of indicators. 3. Test whether the postulated dependency in step 1. coincides with the linearity in step 2. Model building: Training Sample versus Validation Sample The whole portfolio, 5 cohorts Splitted portfolio, 70 : 30 Source: Hayden (2002) Training Sample serves for developing of final model Validation Sample serves for out-of-sample evaluation of final model Model building: Pairwise correlation (Pirsonβs correlation) Short list creation of variables potentially appropriate for the final model: Variable 1 is highly correlated with Variable 2 (both measuring leverage) but AR Var 1 < AR Var 2=> Var 1 is dropped from multivariate analysis Variable 10 is highly correlated with Variable 11 (both measuring profitability) but AR Var 10 < AR Var 11=> Var 10 is dropped from multivariate analysis Model Building : Multivariate Analysis Total number of different combinations variables in the model : 212 = 4 096 models=> try backward /forward selection. Step by step elimination of insignificant variables until remaining variables have high significance level. True parameters are different from zero with a probability of 90% (*), 95% (**), or 99%(***) (low p-value to reject H0:coef=0.) Model 1: Variable 9 has opposite sigh in the regression than it was expected hypothetically. Var 9 is correlated with group of other variables: Var 10,11,12 => remove Var 9 from the model Model 2: Variable 6 became highly insignificant => removed from the final model. Model Building : Performance Modelβs Robustness: test statistics, AR, HL in the development sample and validation sample are close enough Goodness of Fit: Brier test, Hosmer-Lemenshow test (high p-value)
