Back-testing during times of crisis

1. Rabobank Nederland Back-testing during times of crisis Rabobank: Group Risk Management

2. 2 Rabobank Nederland Agenda Introduction Current back-testing framework Impact economic cycle Example of the issue Current situation of the approach, results & findings Future steps Conclusions

3. Introduction Many defaults have been observed lately: (averaged as defaults declared depend on meeting days at court) Defaults fluctuate over time. Back-testing gets more attention Hypothesis: back-testing will be influenced by the economic cycle 3 Rabobank Nederland

4. Current back-testing framework Rating philosophy: Strive for TTC PD estimated throughout economic Cycle Rabobank has TTC with point in time aspects Rating bucket characteristics: Predefined buckets are filled with comparable facilities A constant PD is assigned to each homogenous bucket

5. Current back-testing framework

6. Impact of the economic cycle Due to the economic cycle, credit risk is cyclical: more defaults at downturns while less defaults at upturns We focus on cyclicality in the default risk: PD (and not in severity of the loss: LGD) Cyclicality has a systematic component, i.e., it affects many counterparties at the same time: the default behaviour of all clients will be affected

7. Impact of the economic cycle - What is the influence of the economic cycle on the back-testing of PD models? - How should the economic cycle be taken into account when back-testing a PD model?

8. Impact of the economic cycle

9. Impact of the economic cycle The point-in-time (PIT) PD is the likelihood that a loan will not be repaid and, thus, will fall into default within the coming year. (unobservable) This is also called expected annual default frequency The through-the-cycle (TTC) DF is the annual default frequency estimated on the long run. The estimates take into consideration upturns and downturns in the economy (unobservable) The number of defaults is the realized number of clients who default within one year (observable)

10. Impact of the economic cycle Assume: 1000 clients; The PIT PD is 4% (expectation of number of defaults is 40), while the realized number of defaults can vary.

11. Impact of the economic cycle

12. Current status solution Main objective is testing the (TTC-) PDs (model) Derive true TTC DF from annual number of defaults and Macro economic factor (e.g. unemployment rate, ? GDP�) Compare with TTC PD model estimation Assumption: PD from model is pure TTC PD

13. Current status solution

14. Current status solution � Back-testing unobservable PIT PDs number of defaults (from real data)

15. Current status solution - Logistic Model

16. Current status solution � Methodology Score card TTC PD estimate Macro � variable Number of defaults unobserved PIT PDs & true TTC DF misspecification �0

17. Current status solution � Maximum Likelihood

18. Current status solution �misspecification

19. Current status solution - testing represents the difference between the true TTC DF and the TTC PD estimate from Rabobank�s internal model. Confidence intervals are created: TTC PD estimate

20. Current status solution - Power of Back-testing

21. Current status solution � Simulation (I) Score card TTC PD estimate Macro � variable create PIT PDs # of defaults misspecification Derive with ML PIT PDs & true TTC DF �0

22. Current status solution � Simulation (II)

23. Current status solution � Simulation (III) Macro � variable Length of time series unobservable PIT PDs number of defaults Portfolio size (number of clients) number of defaults

24. Current status solution � Simulation (IV) unobservable PIT PDs number of defaults

25. Current status solution � Simulation (V) Repeat the process of power simulation 10,000 times Under 95% confidence interval One simulation gives a or an 10,000 simulations give a Rejection Rate: Rejection Rate of lower than 5% indicates

26. Current status solution: Result Simulation (I)

27. Current status solution: Result Simulation (II)

28. Current status solution: findings Simulation (I)

29. Current status solution: findings Simulation (II)

30. Current status solution: Result Simulation (III)

31. Current status solution: Result Simulation (IV)

32. Current status solution: findings Simulation (III)

33. Current status solution: Macro factor real world

34. Current status solution: When to use new method? (I)

35. Current status solution: When to use new method? (II)

36. Future steps

37. Conclusions

38. Questions