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Intuitively we all know that people with higher credit risk scores tend to get more favorable loan terms. Since a higher credit risk score corresponds to lower chance of delinquency, a lender can grant: a higher credit line, a more favorable APR or a mix of those and other loan terms. Some people might wonder if there is a way to quantify the relationship between a credit risk score and the loan terms in a more mathematically rigorous way. For example, what is an appropriate credit limit for a given score band? Early in my career I worked a lot with mathematical optimization. This optimization used a software product called Marketswitch (later purchased by Experian). One caveat of optimization is in order to choose an optimal decision you must first simulate all possible decisions. Basically, one decision cannot be deemed better than another if the consequences of those decisions are unknown. So how does this relate to credit risk scores? Credit scores are designed to give lenders an overall view of a borrower’s credit worthiness. For example, a generic risk score might be calibrated to perform across: personal loans, credit cards, auto loans, real estate, etc. Per lending category, the developer of the credit risk score will provide an “odds chart;” that is, how many good outcomes can you expect per bad outcome. Here is an odds chart for VantageScore® 3 (overall - demi-decile). Score Range How Many Goods for 1 Bad 823-850 932.3 815-823 609.0 808-815 487.6 799-808 386.1 789-799 272.5 777-789 228.1 763-777 156.1 750-763 115.6 737-750 85.5 723-737 60.3 709-723 45.1 693-709 33.0 678-693 24.3 662-678 18.3 648-662 14.1 631-648 10.8 608-631 7.9 581-608 5.5 542-581 3.5 300-542 1.5 Per the above chart, there will be 932.3 good accounts for every one “bad” (delinquent) account in the score range of 823-850. Now, it’s a simple calculation to turn that into a bad rate (i.e. what percentage of accounts in this band will go bad). So, if there are 932.3 good accounts for every one bad account, we have (1 expected bad)/(1 expected bad + 932.3 expected good accounts) = 1/(1+932.3) = 0.1071%. So, in the credit risk band of 823-850 an account has a 0.1071% chance of going bad. It’s very simple to apply the same formula to the other risk bands as seen in the table below. Score Range How Many Goods for 1 Bad Bad Rate 823-850 932.3 0.1071% 815-823 609.0 0.1639% 808-815 487.6 0.2047% 799-808 386.1 0.2583% 789-799 272.5 0.3656% 777-789 228.1 0.4365% 763-777 156.1 0.6365% 750-763 115.6 0.8576% 737-750 85.5 1.1561% 723-737 60.3 1.6313% 709-723 45.1 2.1692% 693-709 33.0 2.9412% 678-693 24.3 3.9526% 662-678 18.3 5.1813% 648-662 14.1 6.6225% 631-648 10.8 8.4746% 608-631 7.9 11.2360% 581-608 5.5 15.3846% 542-581 3.5 22.2222% 300-542 1.5 40.0000%   Now that we have a bad percentage per risk score band, we can define dollars at risk per risk score band as: bad rate * loan amount = dollars at risk. For example, if the loan amount in the 823-850 band is set as $10,000 you would have 0.1071% * $10,000 = $10.71 at risk from a probability standpoint. So, to have constant dollars at risk, set credit limits per band so that in all cases there is $10.71 at risk per band as indicated below. Score Range How Many Goods for 1 Bad Bad Rate Loan Amount $ at Risk 823-850 932.3 0.1071%  $   10,000.00  $   10.71 815-823 609.0 0.1639%  $     6,535.95  $   10.71 808-815 487.6 0.2047%  $     5,235.19  $   10.71 799-808 386.1 0.2583%  $     4,147.65  $   10.71 789-799 272.5 0.3656%  $     2,930.46  $   10.71 777-789 228.1 0.4365%  $     2,454.73  $   10.71 763-777 156.1 0.6365%  $     1,683.27  $   10.71 750-763 115.6 0.8576%  $     1,249.33  $   10.71 737-750 85.5 1.1561%  $        926.82  $   10.71 723-737 60.3 1.6313%  $        656.81  $   10.71 709-723 45.1 2.1692%  $        493.95  $   10.71 693-709 33.0 2.9412%  $        364.30  $   10.71 678-693 24.3 3.9526%  $        271.08  $   10.71 662-678 18.3 5.1813%  $        206.79  $   10.71 648-662 14.1 6.6225%  $        161.79  $   10.71 631-648 10.8 8.4746%  $        126.43  $   10.71 608-631 7.9 11.2360%  $          95.36  $   10.71 581-608 5.5 15.3846%  $          69.65  $   10.71 542-581 3.5 22.2222%  $          48.22  $   10.71 300-542 1.5 40.0000%  $          26.79  $   10.71   In this manner, the output is now set credit limits per band so that we have achieved constant dollars at risk across bands. Now in practice it’s unlikely that a lender will grant $1,683.27 for the 763 to 777 credit score band but this exercise illustrates how the numbers are generated. More likely, a lender will use steps of $100 or something similar to make the credit limits seem more logical to borrowers. What I like about this constant dollars at risk approach is that we aren’t really favoring any particular credit score band. Credit limits are simply set in a manner that sets dollars at risk consistently across bands. One final thought on this: Actual observations of delinquencies (not just predicted by the scores odds table) could be gathered and used to generate a new odds tables per score band. From there, the new delinquency rate could be generated based on actuals. Though, if this is done, the duration of the sample must be long enough and comprehensive enough to include both good and bad observations so that the delinquency calculation is robust as small changes in observations can affect the final results. Since the real world does not always meet our expectations, it might also be necessary to “smooth” the odds-chart so that its looks appropriate.

Published: November 17, 2020 by Guest Contributor

This is the first to a series of blog posts highlighting optimization, artificial intelligence, predictive analytics, and decisioning for lending operations in times of extreme uncertainty.   Like all businesses, lenders are facing tremendous change and uncertainty in the face of the COVID-19 crisis.  While focusing first on how to keep their employees and customers safe during the new normal, they are asking how to make data-driven decisions in this new environment.  It’s only natural that business people are skeptical about whether analytics will work in a situation like today's – in which the data deviate from all historical precedents.  Certainly, nobody predicted, for example, that the number of loans with forbearance requests would increase by over 1000% during each two-week period in March. Can anyone possibly make an optimized decision when things are changing so quickly and when so many things are unknown?   Prescriptive analytics – also known as mathematical optimization – is the practice of developing a business strategy to achieve a business objective subject to capacity and other constraints, often using a demand forecast. For example, banks use optimization software to develop marketing and debt management strategies to run their lending operations.  But what happens when the demand forecast might be wrong, when the constraints change quickly, and when decision-makers cannot agree on a single objective? The reality is that decisionmakers have to balance multiple competing objectives related to many different stakeholders. And, especially during the COVID-19 crisis and the period of change that will certainly follow, they have to do so in the face of uncertainty.   Let's discuss some of the methods that analysts use to control risk while optimizing lending practices during times like these. These techniques, collectively known as robust optimization and robust statistics, help lenders and other business people deal with the uncomfortable reality that we do not know what the future holds.     Consider a hypothetical bank or other lender servicing a portfolio of consumer loans and forecasting its loss performance in this environment. Management probably has several competing objectives: they want to improve service levels on their digital channel, they want to minimize credit and fraud losses, they're facing a reduced operating budget, and they're not certain how many employees they will have and which vendors will be able to provide adequate service levels. Furthermore, they anticipate new and unpredicted changes, and they need to be able to update their strategies quickly.   The mathematics can be quite technical, but Experian’s Marketswitch Optimization is user-friendly software to help businesspeople--not engineers--design and deploy optimal strategies for practices such as Account Management and Loan Originations while facing such a dynamic and uncertain environment. The bank's business analysts (not computer specialists or mathematicians) will use techniques such as these:   With Sensitivity Analysis, the analysts will explore the performance of their optimized Account Management, Collections, and Loan Originations strategies while considering possible changes in input variables.   Optimization Scenarios with Uncertainty (technically known as Stochastic Optimization) allow the managers and analysts to design operational strategies that control risk, particularly the bank’s exposure to probabilistic and worst-case scenarios.   Using Scenario Performance Analysis, the lender's team will validate and test their optimization scenarios against a variety of different data sets to understand how their strategies would perform in each case.   Model Quality Evaluation techniques help the credit risk managers compare model predictions against actual performance during a quickly changing economy.   Model impact analysis (related to Model Risk Management) helps senior leadership assess when it is time to invest in improving its statistical models.   Robust Model Calibration Analysis removes unjustifiable variations in the lender's predictive models to make their predictions more valid as things change over time.   These six advanced analytics techniques are especially helpful when developing business strategies for a time in which some values are unknown—including future unemployment levels, staffing budgets, data reporting practices, interest rates, and customer demands.  Business decisions can—and arguably must—be optimized during times of uncertainty. But during times like these, it is especially important that the analysts understand how and why to account for the uncertainty in both the data and the models.   Lenders, are you optimizing your servicing and debt management strategies? It has never been more important than now to do so--using the advanced techniques available to manage uncertainty mathematically. Learn more about how Marketswitch can help you solve complex business problems and meet organizational objectives. Learn more

Published: April 14, 2020 by Jim Bander

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