Developing WOE Binned Scorecards for Predicting LGD

Transcription

1 Developing WOE Binned Scorecards for Predicting LGD Naeem Siddiqi Global Product Manager Banking Analytics Solutions SAS Institute Anthony Van Berkel Senior Manager Risk Modeling and Analytics BMO Financial Group Copyright 2010 SAS Institute Inc. All rights reserved.

2 Agenda Why Study Objectives Loss Given Default Discussion of Methodology Discussion of Results 2

3 Why? Points based scorecards with discrete bins are a more transparent, interpretable tool. Model risk Increased business scrutiny and input into process Increased regulatory scrutiny Better decision making tool 3

4 Objective of Study A binned variable scorecard can be built for predicting LGD The scorecard will offer as much risk ranking as other models, plus the advantages associated with scorecard format. Willing to trade transparency, interpretability, ease of use with statistical accuracy 4

5 Loss Given Default In general, (100% - Proportion of the balance at default recovered after workout period) For collateral based : recovery_amount col : all payments generated by the liquidation of collateral or all payments of the guarantor discounted to date of default workout_cost col : collateral liquidation costs discounted to date of default collateral_value_post_haircut: estimated liquidation value one year prior to default time (d) 5

6 Estimating LGD Various methods Calculate LGD for each pool/facility based on historical data e.g. long run average or down turn. Use models to predict LGD for each pool based on explanatory variables e.g. Linear regression. Issues : bimodal/unimodal distribution, quality of collateral, long workout periods, measuring cost of recovery, downturn. 6

7 Advantages of Scorecard Format Binning Process Deeper understanding of predictors, leads to better strategies Adjust predictor to target relationships based on business sense, and fix biases. logical. Allows business input. Binning reduces impact of outliers Format easy to understand, explain, audit, diagnose. Better tool for business decision making, easier buy-in from end users. 7

8 Methodology Converted continuous LGD to binary target Standard scorecard development process WOE based interactive binning Logistic regression Transformation to scorecard Validation and benchmarking Produce predictions convertible to LGD 8

9 Data Used Overdraft product October 2009 to October 2011 LGD = (loss/balance at default) 160 Explanatory variables from O/D product, other products at bank, bureau data, application data 11,119 base records 9

10 Project Snapshot 10

11 Convert Continuous LGD to binary An LGD is part good, part bad A case with LGD of 25% equivalent to 75 cases with zero LGD ( Good ) and 25 cases with 100% LGD ( Bad ) Create 2 weighted cases for each original LGD case, weighting based on LGD Multiply each case physically To facilitate WOE based binning, and building a binary target logistic regression scorecard. 11

12 Example of conversion to binary Case LGD Goods Bads Time as customer Total

13 WOE Based Binning Standard WOE formula applied WOE bin = ln (proportion of Goods in bin/proportion of Bads in bin) Business adjustments made to bins, to reflect logical relationships and fix known material biases. Unexplainable relationships ignored, weak variables omitted Grouped variable : Time as Customer Count Goods Bads Bad rate WOE 0 to to to to

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16 Fitting a Model Several models fitted using forward and stepwise regression Final model : 14 variables with net worth, delinquency, balances, transactions, inquiries etc. Data from other products and credit bureau Model transformed into scorecard Variable Attribute Score Bad Rate CSCRNTWT< 32828, _MISSING_ Current Net Worth 32828<= CSCRNTWT< <= CSCRNTWT< <= CSCRNTWT< Number of times 60 Days Past Due in Past 12 Months Number of Active Trades with utilisation >= 90% <= CSCRNTWT CYC2X12M< <= CYC2X12M< <= CYC2X12M< <= CYC2X12M, _MISSING_ actv_util_ge90_nbr< <= actv_util_ge90_nbr< <= actv_util_ge90_nbr< <= actv_util_ge90_nbr< Num Inquiries Last 12 Months 5<= actv_util_ge90_nbr, _MISSING_ inq_12mth< <= inq_12mth< <= inq_12mth< <= inq_12mth< <= inq_12mth< <= inq_12mth, _MISSING_

17 Gains Chart Score Bucket Count Bad Count Good Count Marginal Bad Rate Average Predicted Probability Low Threshold Predicted probability High Threshold Training Dataset Score >= <= Score < <= Score < <= Score < <= Score < <= Score < <= Score < <= Score < <= Score < Validation Dataset Score >= <= Score < <= Score < <= Score < <= Score < <= Score < <= Score < <= Score < <= Score <

18 Out of sample validation 18

19 Benchmarking 19

20 Benchmark 2 100% 90% 80% 70% 60% LOSS 50% $ 40% 30% 20% 10% 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% DEFAULT $ UNDUP TREE RANDOM DUP SCORECARD PLS100 TREE100 20

21 Conclusion LGD scorecard is possible Lower fit stats (e.g. AUC 66% vs 64%) Deemed acceptable given the additional transparency, business input, interpretability, ease of use. Difference not significant given transformation of data during binning Rank ordering holds 21

22 Thank You support.sas.com/resources/papers/proceedings12/ pdf Copyright 2010 SAS Institute Inc. All rights reserved.