1. Convergence of Credit Capital Models ISDA Seminar-July 18, 2006

2. 2 IACPM ISDA Study Objectives For a hypothetical, large corporate portfolio with all data elements specified evaluate the degree of convergence of economic capital estimates across commercially available models and across internal models as implemented by financial institutions –Provide benchmarks to participating firms of methodologies for capital estimation and allocation as practiced by peers –Use results to demonstrate to regulators the degree to which regulatory capital can be estimated using banks internal models

3. 3 Summary Conclusions Economic capital models employed by firms can for the most part be shown to converge in their estimates of portfolio- level capital requirements, given the same data assumptions. Where differences arise, a road map of the modeling assumptions can be used to reconcile these differences.

4. 4 Project Overview Mini-survey to determine modeling practices Development of a representative portfolio of transactions with pre-specified risk parameters –Separating out modeling approaches vs. data assumptions Phase 1:Analysis of overall levels of portfolio capital Phase 2: Sensitivity analysis Phase 3: Allocation to individual exposures

5. 5 Project Structure Joint venture between IACPM and ISDA 28 financial institutions participated Steering Committee for governance Consultant (Rutter Associates) for confidentiality, tabulation of results, and running two vendor models Project results published in February 2006 after a two-year period

6. 6 Models and mini survey results Participants were using three vended models –Moody’s KMV Portfolio Manager (PM) –RiskMetrics Group CreditManager (CM) –Credit Suisse CreditRisk+ (CR+). and internally-developed models Of the 28 participants –12 obtain eco capital directly from vended models –6 obtain eco capital from internal models using the output from vended models –8 obtain eco capital from internally-developed models that are similar to vended models –2 obtain eco capital from internally-developed models that are significantly different from the vended models

7. 7 Test Portfolio 3,000 obligors 2 term loans each → $100 billion portfolio Obligors –61 M-KMV industries (643 NAICS industry codes) –7 countries –8 whole-grade rating buckets Term Loans: –Principal: $1MM to $1,250MM –Tenor: 6 months to 7 years –LGD: 22% to 58% Correlation(R 2 ): 10% to 65%. Contractual spreads: Chosen such that initial MTM value of exposures is approximately par

8. 8 Portfolio exposure by industry

9. 9 Portfolio credit quality

10. 10 LGD exposure distribution

11. 11 Exposure distribution

12. 12 Project Phases 1.Compare aggregate eco capital –“Default Only” and “Mark-to-Market” modes – “Base” and “Production” settings 2.Compare changes in aggregate economic capital associated with changes in data assumptions and risk parameters 3.Compare economic capital attributed to a selection of individual transactions and cohorts

13. 13 Phase 1 – Default Only Mode Initial model results seem to produce very different estimates Default Mode (maturities capped at 1 yr)Expected Loss Eco Capital (99.90% Conf Level PM and Similar Models7904,420 CM and Similar Models5663,817 CR+ and Similar Models5643,387 Basel II (caps, floor, min.03 bps)6073,345 Expected Loss differences greatest for poor quality exposures whose coupons were highest (were priced at par)

14. 14 Phase 1 – Default only mode However, the difference results from the way the models treat the 3-, 6-, 9- and 12-month interest payments if default is simulated to have occurred at the one-year horizon. –PM: Obligor defaults on all coupons; all coupons that were owed between time zero and horizon are included in EAD. –CM and CR+: Obligor pays all of the coupons; loss is limited to principal If PM is run with CM/CR+ assumptions (no coupons) Default Mode (Maturity capped at 1 year) Expected Loss Eco Capital PM with spreads and risk-free rate set to zero5633,791 CM5623,533 CR+5643,662

15. 15 Phase 1 – Mark-to-Market mode Also showed significant differences in estimates MTM mode (full maturities) Expected Loss Eco Capital PM and Similar Models7905,618 CM and Similar Models7614,823 Basel II (caps, floors, min 1 yr maturity,,03 bps) 6074208 Leading to further evaluation of treatment of coupons and correlations

16. 16 Coupon and correlation analysis *Uses PM values as base (PM-CM)/PM Spreads, Coupons & Risk- Free Rates SET EQUAL TO ZERO Industries 61 Industries One Industry “Unassigned” 61 Industries One Industry “Unassigned” Countries 7 Countries One country (“US”) 7 Countries One country (“US”) DEFAULT ONLY MODE EL Difference*34% 0% Eco Cap Difference*25%20%3%-1% MARK TO MARKET MODE EL Difference*8% -34% Eco Cap Difference *25%19% 12%

17. 17 Further analysis of MTM differences Application of LGD to principal and coupons also arises in MTM mode. Point in Time at which Eco Capital is reported PM: Time zero. CM: Horizon Remaining differences result from varying assumptions regarding matching EDF term structure to transition matrices, valuation at horizon

18. 18 PM & similar models CM & similar models CR+ & similar models Basel II Segment Portfolio into IG and NIG10% / 7%16% / 12%14% / NANo Chg Chg all countries to US46% / 43%20% / 19%5% / NANo Chg Chg all industries to “Unassigned”9% / 7%32% / 32%1% / NANo Chg Chg all to “US” and “Unassigned”87% / 80%77% / 76%8% / NANo Chg Increase 1 Telecom from 5MM to 1,005MM 0.1% / 0.4%0.1% / 0.2%0% / NA0.2% / 0.4% from 5MM to 5,005MM1.2% / 2.6%1.7% / 9.1%6% / NA0.8% / 2.2% Increase all PDs by 20%8% / 6% 8% / NA6% / 6% Increase all LGDs by 20%16% / 15%17% / 15%20% / NA20% / 20% Increase all R 2 by 20%15% / 15%15% / 14%15% / NANo Chg Phase 2-sensitivity analysis (DO/MTM)

19. 19 Phase 3- allocation to transactions 23 participants provided risk contributions for 8 individual exposures and 2 cohorts Participants asked to characterize their risk contributions: –Mode: “Default Only” or “Mark-to-Market” –Type of Risk Contribution: “Standard-deviation-based” risk contribution or “Tail-based” risk contribution –Use of risk contribution: Performance measurement or Pricing As expected, risk contributions exhibited significant dispersion.

20. 20 Summary Credit capital models in use by major financial institutions can be shown to converge in overall level of results Differences can be traced to assumptions regarding lost coupons, correlations, and in MTM mode (vs. DO) term structure and horizon valuation assumptions Sensitivity analysis shows generally consistent results (Basel lI proformas by construction invariant to portfolio composition) Allocations to individual exposures reflects varied purposes of these measures and different approaches to risk management