1. Scenario Generation & Multi-Period Portfolio Credit Risk Analysis Oct-17 2014 Dr. Juan M. Licari Senior Director Juan.Licari@moodys.com Dr. Gustavo Ordoñez-Sanz Director Gustavo.Ordonez-Sanz@moodys.com

2. Multi-period Credit Portfolio Models 1

3. Multi-period Credit Portfolio Models Rationale & Drawbacks 3 »Portfolio life-time analysis: With average maturity (or duration) of the portfolio assets being longer than a year, any profitability or new deal analysis would benefit from multi-year modelling capabilities »Accuracy: Even for 1 year horizon, increasing frequency (e.g. monthly, quarterly) of calculation improves accuracy »Time-varying exposures: Exposure today might differ from exposure at default (or when downgrade occurs) Practical challenges: »Complexity: More realism always bring more complexity »Run-time: Multi-period Monte Carlo models tend to require vast amounts of processing power

4. Multi-period Credit Portfolio Models Proposed Analytical Framework 4 »Accurate: Solutions are “exact” (up to numerical error) »Fast: Calculations can be performed in seconds (often milliseconds) (1) Expected Loss is an example of widely used analytical solution for credit portfolio models. Popular metric because: »Trivial to compute »Decomposes easily to each issuer/debtor in the portfolio: (2) Loss Volatility adds important information to the EL metric Key Building Blocks: (A) Scenario Generation + (B) Law of Total Variance & MGF analysis + (C) Conditional Independence

5. Multi-period Credit Portfolio Models Multi-period Credit Portfolio Modelling - Key Results 5 »Analytical Loss Volatility –Multi-period Stress testing – calculate uncertainty around forecasted ST losses –Risk Contributions to Loss Volatility – decompose volatility in the same way as EL –“Instantaneous” risk-based pricing (RAROC) – Fast portfolio profitability analysis –Optimal portfolio allocation – Find the investment allocation that minimises the loss volatility for a given level of expected return »Conditional Expectations –Tail Risk Contributions (EC Allocation) – contribution of each instrument in portfolio to any level of loss –Reverse Stress Testing – Find macroeconomic scenarios (or distribution) that produce a given level of loss –Optimal Importance Sampling – Accelerate Monte Carlo simulations to calculate VaR/EC

6. Macroeconomic Scenario Generation 2

7. 7 Large Scale Macro Models: Laurence Klein (Nobel 1980) Demand-Supply systems of equations. Pros: Explicit modeling of industries and macro sectors. Cons: Not connected to economic theory of consumer behaviour and production. Dynamic Stochastic General Equilibrium Models (DSGE): Sargent (Nobel 2011), Prescott (Nobel 2004), Lucas (Nobel 1995) Modern macro models with micro foundations. Used widely across central banks and think tanks. Pros: Feedback effects and optimal responses can be explicitly modeled. Cons: Limited to key macro series and very math-intensive once extended. VARs and Structural VARs: Sims (Nobel 2011) Data driven models, work-horse models for short-term forecasting. Pros: Easier to implement, maintain and simulate. Ideal for satellite models. Cons: Not connected to economic theory.

8. 8 Macroeconomic Scenario Generation (cont.) Bayesian Estimation – Prior & Posterior Distributions – Simulations

9. 9 Rank Ordering of Macroeconomic Scenarios Target 1: Max Drop in GDP growth Histogram across 2.5M simulations Target 1: Max Drop in GDP growth Scatter over Final Rank Order Target 1: Max Drop in GDP growth Scatter over Marginal Rank Order Max quarterly drop in GDP Growth Cumulative Proportion Max quarterly drop in GDP Growth Cumulative Proportion Max quarterly drop in GDP Growth

10. 10 Rank Ordering of Macroeconomic Scenarios (cont.) Target 2: Max Cumulative Drop in GDP growth Histogram across 2.5M simulations Target 2: Max Cumulative Drop in GDP growth Scatter over Final Rank Order Target 2: Max Cumulative Drop in GDP growth Scatter over Marginal Rank Order Max cumulative drop in GDP Growth Cumulative Proportion Max cumulative drop in GDP Growth Cumulative Proportion Max cumulative drop in GDP Growth

11. 11 Rank Ordering of Macroeconomic Scenarios (cont.) Target 12: Max Cumulative Drop in Investment growth Histogram across 2.5M simulations Target 17: Max Cumulative Drop in HPI growth Histogram across 2.5M simulations Target 23: Max Unemployment Rate Histogram across 2.5M simulations Target 24: Max Proportional Increase in Unemployment Rate Histogram across 2.5M simulations Max cumulative drop in HPI Growth Max Unemployment Rate Max proportional increase in Unemployment Rate Max cumulative drop in Investment Growth

12. 12 Rank Ordering of Macroeconomic Scenarios (cont.) Overall Target Scatter over Final Rank Order Overall Target Histogram across 2.5M simulations Cumulative Proportion Final Weighted Score

13. 13 Rank Ordering of Macroeconomic Scenarios (cont.)

14. 14 Modelling Market and Credit Risk Drivers (1)Swaps and Sovereign Curves (term structure models) Nelson-Siegel approach (2)Stock Market Returns, Historical and Implied Volatilities Global Equity Factor (GEF) related to global economic conditions (3)CDS Spreads by Sector and Rating category Time series model with Global Credit Factor (GCF) (4)Credit Migration Transition matrices for credit portfolios, two stage approach: (i) probit model combined with (ii) quantile and time-series analysis

15. 15 Modelling Market and Credit Risk Drivers (cont.) Credit Migration

16. Credit PD Models (conditional on Macro Scenarios) US Auto Lending & Mortgage Markets 3

17. Credit Models – A Vintage/Cohort Approach 17 Performance Data – Vintage Segmentation – History and Forecasts Two examples: First Mortgages & Total Auto, US National Level, Quarterly Vintages

18. US Auto Models – Exposure Lifecycle 18 First Vintage: 2007Q1 Number of Accounts over Age (Quarters since Origination) First Vintage: 2007Q1 Outstanding Balance (Mil. $ - NSA) over Age (Quarters since Origination) Mid-age Vintage: 2012Q3 Number of Accounts over Age (Quarters since Origination) Mid-age Vintage: 2012Q3 Outstanding Balance (Mil. $ - NSA) over Age (Quarters since Origination) Age (# of quarters since origination) Balance (Mil. USD) Number Balance (Mil. USD)

19. US Auto PD Model – Historic Performance 19 First Vintage: 2007Q1 Default Rate (#) over Age (Quarters since Origination) Mid-age Vintage: 2012Q3 Default Rate (#) over Age (Quarters since Origination) Default Rate (#) over Vintage, observed at different ages 07Q308Q410Q111Q2 12Q3 Age (# of quarters since origination) Vintage Observed PDs

20. US Auto PD Model – Fixed-Effects Panel Data Estimation 20 Predicted PDs Observed PDs Histogram of Residuals Residual

21. US Auto PD Model – Projections – 2012Q3 Vintage 21 2012Q3 Vintage at +Q5 Default Rate (#) over Simulations (ordered by macro ranking) +Q1 +Q2 +Q3 +Q4 +Q5 +Q6 +Q7 +Q8 +Q9 2012Q3 Vintage at +Q5: Histogram of Default Rates (#) Summary Stats for Predicted PDs - 2012Q3 Vintage at +Q5 Predicted PDs Simulation ID - Ranked Age (# of quarters since origination)

22. US Auto PD Model – Projections – 2014Q3 Vintage Dynamic Forecast – Example of PD Projections for a “Future” Vintage 22 +Q1 +Q2 +Q3 +Q4 +Q5 +Q6 +Q7 +Q8 +Q9 Predicted PDs Age (# of quarters since origination)

23. US Auto Exposure Model – Projections 23 Historic Number of Accounts over Vintage, observed at age=2 07Q308Q410Q1 11Q2 12Q3 Vintage Number of Accounts Future Vintage 2014Q3 observed at +Q5: Histogram for Outstanding Balance Balance Future Vintage 2014Q3 observed at +Q5: Histogram for Outstanding Number Number

24. US Mortgage PD Model – Historic Performance 24 First Vintage: 2007Q1 PD over Age Mid-age Vintage: 2012Q3 Default Rate (#) over Age (Quarters since Origination) Default Rate (#) over Vintage, observed at different ages 07Q308Q410Q111Q2 12Q3 Age (# of quarters since origination) Vintage Observed PDs

25. US Mortgage PD Model – Projections – 2012Q3 Vintage 25 2012Q3 Vintage at +Q5 Default Rate (#) over Simulations (ordered by macro ranking) +Q1 +Q2 +Q3 +Q4 +Q5 +Q6 +Q7 +Q8 +Q9 2012Q3 Vintage at +Q5: Histogram of Default Rates (#) Summary Stats for Predicted PDs - 2012Q3 Vintage at +Q5 Predicted PDs Simulation ID - Ranked (# of quarters since origination)

26. US Mortgage PD Model – Projections – 2014Q3 Vintage Dynamic Forecast – Example of PD Projections for a “Future” Vintage 26 +Q1 +Q2 +Q3 +Q4 +Q5 +Q6 +Q7 +Q8 +Q9 Predicted PDs (# of quarters since origination)

27. US Mortgage Exposure Model – Projections 27 Historic Number of Accounts over Vintage, observed at age=2 07Q308Q410Q1 11Q2 12Q3 Vintage Number of Accounts Future Vintage 2014Q3 observed at +Q5: Histogram for Outstanding Balance Balance Future Vintage 2014Q3 observed at +Q5: Histogram for Outstanding Number Number

28. Multi-period Credit Analytics Key Results 4

29. Analytical Solutions – Can we do better than EL? 29

30. Definitions – Cont. Note that it is easy to split the losses due to default: From losses due to downgrades (+ credit spreads / pre-payment / etc.): And all the results that follow can be split accordingly. 30

31. Conditional Moment Generating Function Conditional Expectations. Analytical framework that allows to calculate conditional expectations on a given loss level. Based on Thompson & McLeod (2006): “Analytic calculation of conditional default and risk contributions using the Ensemble method”. But extended to: »More than one period »Credit migrations »Credit spreads, pre-payment risk, IR, FX, etc. Requires the calculation of the MGF: 31 Loss Volatility. Can be computed analytically, assuming conditional independent defaults (on scenario) and the Law of Total Variance:

32. US Mortgage – Analytical Loss Volatility 32 Period EL ($m) Analytical Volatility ($m) Monte Carlo Volatility ($m) Cumulative EL ($m) Cumulative Analytical Volatility ($m) Cumulative Monte Carlo Volatility ($m) Q12556230.2230.12556230.2230.1 Q22484303.0303.15039 485.0 484.8 Q32424357.5357.47464782.7782.4 Q42381405.7405.698451120.0 Q52355450.6450.312200 1906.61905.2 Q62336491.2492.014536149581495.0 Q72318530.6530.0168542348.12346.0 Q82297567.3566.2191502819.42816.3 Q92275598.6597.1214253315.13310.7

33. US Mortgage – Loss Distribution 33

34. US Auto Lending – Analytical Loss Volatility 34 Period EL ($m) Analytical Volatility ($m) Monte Carlo Volatility ($m) Cumulative EL ($m) Cumulative Analytical Volatility ($m) Cumulative Monte Carlo Volatility ($m) Q1132180.3 132180.3 Q2132296.296.42644152.4152.5 Q31309110.0109.93953235.2235.5 Q41287123.1123.25239329.6329.7 Q51265135.2135.36503 436.0436.1 Q61243145.5145.67747552.1552.3 Q71225155.1155.28972677.3677.4 Q81210164.6164.710182810.6810.7 Q91197172.1 11379950.3950.4

35. US Auto – Loss Distribution 35

36. Corporate bond/CDS portfolio The examples shown in the following slides are based on a toy portfolio consisting of: »95 long bond positions on 95 bonds ($1-25m in each): 36 Aaa, 26 Aa, 34 A »5 short bond (5 long CDS) positions ($5-8m in each): 3 Aaa, 1 Aa, 1A »The calculations are run over 4 years and it is assumed that all bonds redeem after that date. »Instruments are marked-to-market at the end of each period taking into account changes to the credit spreads, IR and FX and any downgrades (or upgrades) »EDF implied transition matrices »100% LGD assumed »1m MC runs »Figures are reported in $m 36

37. Corporate – Analytical Loss Volatility – Intra-period 37 Port Volatility Analytical Default EL Analytical Transitions EL Analytical Default Volatility MC Default Volatility Analytical Transitions Volatility MC Transitions Volatility Period 10.4020.232.772.7880.6680.68 Period 22.7716.0011.6011.5873.4873.49 Period 37.3311.6022.6222.7267.3067.31 Period 411.827.2728.8428.8262.06 *Note that both Default and Transition losses incorporate the effect of changing IR, FX and Credit Spreads

38. Corporate – Analytical Loss Volatility – Cumulative 38 Port Volatility Analytical Default EL Analytical Transitions EL Analytical Default MC DefaultAnalytical Transitions MC Transitions Period 10.4020.272.772.7880.6680.68 Period 23.1636.2413.18 153.33153.92 Period 310.4947.8333.91 219.66220.78 Period 422.3155.1128.8459.75280.48282.07 *Note that both Default and Transition losses incorporate the effect of changing IR, FX and Credit Spreads

39. Risk Contributions to Loss Volatility We can calculate the contributions to portfolio volatility analytically. So we can manage our portfolio With 39

40. US Mortgage – Risk Contributions to Loss Volatility 40

41. US Auto Lending – Risk Contributions to Loss Volatility 41

42. Expectations Conditional on Loss Level 42

43. US Auto Lending – Tail-Risk Contributions (EC Allocation) 43

44. 44 Analytical Reverse Stress Testing The solution also give us the distribution for states of the world

45. US Auto Lending – Uniform distribution of Z 45

46. Concluding Remarks and Future Research Topics 5

47. Risk Adjusted Pricing (RAROC) 47 Analytical calculation of the portfolio volatility up to the new deal’s maturity allows us to instantaneously price. The Sharpe ratio of the new portfolio with the new deal (or deals) should be larger than without: BUY

48. Portfolio Optimisation 48

49. Optimal Importance Sampling 49

50. moodysanalytics.com © 2014 Moody’s Corporation, Moody’s Investors Service, Inc., Moody’s Analytics, Inc. and/or their licensors and affiliates (collectively, “MOODY’S”). All rights reserved. CREDIT RATINGS ISSUED BY MOODY'S INVESTORS SERVICE, INC. (“MIS”) AND ITS AFFILIATES ARE MOODY’S CURRENT OPINIONS OF THE RELATIVE FUTURE CREDIT RISK OF ENTITIES, CREDIT COMMITMENTS, OR DEBT OR DEBT-LIKE SECURITIES, AND CREDIT RATINGS AND RESEARCH PUBLICATIONS PUBLISHED BY MOODY’S (“MOODY’S PUBLICATIONS”) MAY INCLUDE MOODY’S CURRENT OPINIONS OF THE RELATIVE FUTURE CREDIT RISK OF ENTITIES, CREDIT COMMITMENTS, OR DEBT OR DEBT-LIKE SECURITIES. MOODY’S DEFINES CREDIT RISK AS THE RISK THAT AN ENTITY MAY NOT MEET ITS CONTRACTUAL, FINANCIAL OBLIGATIONS AS THEY COME DUE AND ANY ESTIMATED FINANCIAL LOSS IN THE EVENT OF DEFAULT. CREDIT RATINGS DO NOT ADDRESS ANY OTHER RISK, INCLUDING BUT NOT LIMITED TO: LIQUIDITY RISK, MARKET VALUE RISK, OR PRICE VOLATILITY. CREDIT RATINGS AND MOODY’S OPINIONS INCLUDED IN MOODY’S PUBLICATIONS ARE NOT STATEMENTS OF CURRENT OR HISTORICAL FACT. MOODY’S PUBLICATIONS MAY ALSO INCLUDE QUANTITATIVE MODEL- BASED ESTIMATES OF CREDIT RISK AND RELATED OPINIONS OR COMMENTARY PUBLISHED BY MOODY’S ANALYTICS, INC. CREDIT RATINGS AND MOODY’S PUBLICATIONS DO NOT CONSTITUTE OR PROVIDE INVESTMENT OR FINANCIAL ADVICE, AND CREDIT RATINGS AND MOODY’S PUBLICATIONS ARE NOT AND DO NOT PROVIDE RECOMMENDATIONS TO PURCHASE, SELL, OR HOLD PARTICULAR SECURITIES. NEITHER CREDIT RATINGS NOR MOODY’S PUBLICATIONS COMMENT ON THE SUITABILITY OF AN INVESTMENT FOR ANY PARTICULAR INVESTOR. MOODY’S ISSUES ITS CREDIT RATINGS AND PUBLISHES MOODY’S PUBLICATIONS WITH THE EXPECTATION AND UNDERSTANDING THAT EACH INVESTOR WILL, WITH DUE CARE, MAKE ITS OWN STUDY AND EVALUATION OF EACH SECURITY THAT IS UNDER CONSIDERATION FOR PURCHASE, HOLDING, OR SALE. MOODY’S CREDIT RATINGS AND MOODY’S PUBLICATIONS ARE NOT INTENDED FOR USE BY RETAIL INVESTORS AND IT WOULD BE RECKLESS FOR RETAIL INVESTORS TO CONSIDER MOODY’S CREDIT RATINGS OR MOODY’S PUBLICATIONS IN MAKING ANY INVESTMENT DECISION. IF IN DOUBT YOU SHOULD CONTACT YOUR FINANCIAL OR OTHER PROFESSIONAL ADVISER. ALL INFORMATION CONTAINED HEREIN IS PROTECTED BY LAW, INCLUDING BUT NOT LIMITED TO, COPYRIGHT LAW, AND NONE OF SUCH INFORMATION MAY BE COPIED OR OTHERWISE REPRODUCED, REPACKAGED, FURTHER TRANSMITTED, TRANSFERRED, DISSEMINATED, REDISTRIBUTED OR RESOLD, OR STORED FOR SUBSEQUENT USE FOR ANY SUCH PURPOSE, IN WHOLE OR IN PART, IN ANY FORM OR MANNER OR BY ANY MEANS WHATSOEVER, BY ANY PERSON WITHOUT MOODY’S PRIOR WRITTEN CONSENT. All information contained herein is obtained by MOODY’S from sources believed by it to be accurate and reliable. Because of the possibility of human or mechanical error as well as other factors, however, all information contained herein is provided “AS IS” without warranty of any kind. MOODY'S adopts all necessary measures so that the information it uses in assigning a credit rating is of sufficient quality and from sources MOODY'S considers to be reliable including, when appropriate, independent third-party sources. However, MOODY’S is not an auditor and cannot in every instance independently verify or validate information received in the rating process or in preparing the Moody’s Publications. To the extent permitted by law, MOODY’S and its directors, officers, employees, agents, representatives, licensors and suppliers disclaim liability to any person or entity for any indirect, special, consequential, or incidental losses or damages whatsoever arising from or in connection with the information contained herein or the use of or inability to use any such information, even if MOODY’S or any of its directors, officers, employees, agents, representatives, licensors or suppliers is advised in advance of the possibility of such losses or damages, including but not limited to: (a) any loss of present or prospective profits or (b) any loss or damage arising where the relevant financial instrument is not the subject of a particular credit rating assigned by MOODY’S. To the extent permitted by law, MOODY’S and its directors, officers, employees, agents, representatives, licensors and suppliers disclaim liability for any direct or compensatory losses or damages caused to any person or entity, including but not limited to by any negligence (but excluding fraud, willful misconduct or any other type of liability that, for the avoidance of doubt, by law cannot be excluded) on the part of, or any contingency within or beyond the control of, MOODY’S or any of its directors, officers, employees, agents, representatives, licensors or suppliers, arising from or in connection with the information contained herein or the use of or inability to use any such information. NO WARRANTY, EXPRESS OR IMPLIED, AS TO THE ACCURACY, TIMELINESS, COMPLETENESS, MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE OF ANY SUCH RATING OR OTHER OPINION OR INFORMATION IS GIVEN OR MADE BY MOODY’S IN ANY FORM OR MANNER WHATSOEVER. MIS, a wholly-owned credit rating agency subsidiary of Moody’s Corporation (“MCO”), hereby discloses that most issuers of debt securities (including corporate and municipal bonds, debentures, notes and commercial paper) and preferred stock rated by MIS have, prior to assignment of any rating, agreed to pay to MIS for appraisal and rating services rendered by it fees ranging from $1,500 to approximately $2,500,000. MCO and MIS also maintain policies and procedures to address the independence of MIS’s ratings and rating processes. Information regarding certain affiliations that may exist between directors of MCO and rated entities, and between entities who hold ratings from MIS and have also publicly reported to the SEC an ownership interest in MCO of more than 5%, is posted annually at www.moodys.com under the heading “Shareholder Relations — Corporate Governance — Director and Shareholder Affiliation Policy.” For Australia only: Any publication into Australia of this document is pursuant to the Australian Financial Services License of MOODY’S affiliate, Moody’s Investors Service Pty Limited ABN 61 003 399 657AFSL 336969 and/or Moody’s Analytics Australia Pty Ltd ABN 94 105 136 972 AFSL 383569 (as applicable). This document is intended to be provided only to “wholesale clients” within the meaning of section 761G of the Corporations Act 2001. By continuing to access this document from within Australia, you represent to MOODY’S that you are, or are accessing the document as a representative of, a “wholesale client” and that neither you nor the entity you represent will directly or indirectly disseminate this document or its contents to “retail clients” within the meaning of section 761G of the Corporations Act 2001. MOODY’S credit rating is an opinion as to the creditworthiness of a debt obligation of the issuer, not on the equity securities of the issuer or any form of security that is available to retail clients. It would be dangerous for “retail clients” to make any investment decision based on MOODY’S credit rating. If in doubt you should contact your financial or other professional adviser.