LGD Risk Resolved please do not quote or distribute

1. LGD Risk Resolvedplease do not quote or distribute Jon Frye Federal Reserve Bank of Chicago Mike Jacobs Office of the Comptroller of the Currency FR-Chicago Quantitative Congress October 15, 2010 Any views expressed are the authors’ and do not necessarily represent the views of the management of the Federal Reserve Bank of Chicago, the Federal Reserve System, the Office of The Comptroller of the Currency or the U.S. Department of the Treasury.

2. An important question to ask If you are on a bank exam and find that the bank has a complicated model of X, ask how well they do X with a simple model.

3. Reasons to ask that • Instead of, "This is how we do it," you focus on measuringtheresults. This is a much cooler topic. • You find out if the complicated model works before you try to understand it. A better use of time, yes? • The bank might find that a simpler model works just as well. We did. The bank should be grateful. 3

4. Why this is fun • The bank might never have done this. • You can help them make progress. • The bank might say it is impossible to measure the performance of a risk model. • This can be entertaining to hear. • Some day, banks will manage risk based on evidence. • You'll be able to say that you played a role. 4

5. Outline of today's talk What's new in LGD Risk Resolved Soup-to-nuts summary Greek alphabet soup:  = "Rho", a number [] = "Phi", a function 5

6. What's new in LGD-RR 1. The LGD adjustment 2. Credit loss (not LGD) models 3. Testing a model 4. Model of a finite portfolio 5. Negative test results 6. This is practical and scientific

7. The LGD adjustment It works OK Every loan has LGD risk 7

8. Credit loss models • The topic of LGD-RR is credit loss. • LGD is not the main topic. • Credit risk is a high percentile of the distribution of credit loss. • The credit loss model running at most banks works in a particular way. • Our "LGD adjustment" causes this model to produce the best model of credit loss. • "Best" = "simplest that survives testing" 8

9. Testing a model This is the holiest of holies in statistics. A complicated model tests a simple one. A complicated model • fits old data better than a simple model • (this explains superstition, by the way), • but can mislead when it encounters new data. • Jargon: "Over-fitting the model," or "Type 1 Error." A test finds out if the complicated model is "better enough" to reject a simple model. 9

10. Finite portfolios—1 • LGD-RR seeks the distribution of credit loss in a homogeneous portfolio: • every firm has the same probability of default; • every pair of firms has the same correlation; • every exposure has the same expected LGD. • LGD-RR starts with a particularly simple case: a large homogeneous portfolio. • This has an infinite number firms. • AKA, "asymptotically fine-grained" portfolio. 10

11. Finite portfolios—2 This map shows our flow of logic: 11

12. Negative test results—1 The simpler model is the "null hypothesis." The null is loss with the LGD adjustment. Alternatives use more complicated LGD models. A null hypothesis is either rejected (an alternative makes a "statistically significant" improvement on the null) or not. Our tests do not reject the null hypothesis. 12

13. Negative test results—2 • This is completely opposite most research. • Usually, research produces significant results. • The researcher finds something new that matters. • We cannot significantly improve the null. • We don't think anyone can. • We think the LGD adjustment isn't that bad. • We think there isn't enough data to show otherwise. • But of course, we don't know. • Anyone can gain fame and glory by showing that Frye and Jacobs are just plain wrong. 13

14. This is practical • The LGD adjustment uses PD, , and EL. • Banks have estimates of PD, , and EL. • We estimate them the same way banks do. • We don't require new estimators or estimates. • A bank could put the LGD adjustment into its loss model with not much bother. 14

15. And, this is scientific It works well enough for the data we have, like quantum electrodynamics and relativity. It is a falsifiable hypothesis, which is again like QED and relativity. If a credit loss model has not been tested against Frye-Jacobs, it is suspect. At the least, Frye and Jacobs will suspect it. 15

16. Soup-to-nuts summary of LGD-RR 1. The normal CDF 2. The Vasicek default model 3. The Modest Means loss model 4. MM + two strong assumptions  the LGD adjustment 5. Default rates and LGD rates 6. Alternative LGD models 7. Testing cell-by-cell 8. Testing all cells together 16

17. The normal CDF CDF = "cumulative distribution function" Normal = standard normal random variable The CDF is symbolized []; it is an "S" curve. 17

18. The Vasicek default model In a large homogenous portfolio, • the default rate is "" of a linear function of z, • where z is an unobserved variable that characterizes systemic credit stress. 18

19. The Modest Means loss model In a large homogenous portfolio, the loss rate is "" of a linear function of z: This is simpler than the common model: 19

20. MM plus two strong assumptions 1. Default has a Vasicek distribution. 2. The same Z affects both default and LGD. Then, cLGD is the ratio of loss to default: This is the Frye-Jacobs LGD adjustment. 20

21. Default rates and LGD rates 21

22. The alternatives are more flexible Each of the five Alternatives can produce greater or less LGD risk than the LGD adjustment. 22

23. Testing cell-by-cell Significance: LnL > 1.92 23

24. Testing all cells together 24

25. Summary of LGD-RR We propose an LGD adjustment. • It attributes LGD risk to every exposure. • LGD risk is sensitive to PD, , and ELGD. • Banks need these parameters anyway. Tests do not reject the LDG adjustment. The LGD adjustment can be used: • to introduce LGD risk to existing models • as a null hypothesis in future research. 25