Assessing the impact of IDR on bank’s regulatory capital Eduardo Epperlein & Alan Smillie PRMIA-ISDA Seminar 11 Se

1. Assessing the impact of IDR on bank’s regulatory capital Eduardo Epperlein & Alan SmilliePRMIA-ISDA Seminar 11 September 2007 The analysis and conclusions set forth are those of the authors. Citi is not responsible for any statement or conclusion herein, and opinions or theories presented herein do not necessarily reflect the position of the institution.

2. Outline • Part I: Capitalizing Market Risk (“the rules ”) • Part II: Modelling IDR (“the maths”) • Part III: Impact of IDR (“the shock”)

3. Capitalizing Market Risk - Background • In 2005 BIS* requires banks to capitalize Trading Book default risk “to a soundness standard comparable to that of the IRB based approach to credit risk” • This is Incremental Default Risk (IDR) • IDR model required for new VaR model approvals • Firms with existing VaR model approval (includes most large banks) have until 2010 to implement IDR * “The Application of Basel II to Trading Activities and the Treatment of Double Default Risk”, BIS 2005, www.bis.org/publ/bcbs116.pdf

4. Capitalizing Market Risk – Current Rules • Basic Market Risk Capital = 3 x VaRMarket(99%, 10-day) • Not too clear what ‘3’ multiplier means, but is broadly accepted by industry • Range of methods to model VaRMarket subject to regulatory approval • Specific Risk Surcharge (SRS) • Applied if banks do not capture event risk in VaRMarket • Total Market Risk Capital = Basic + SRS

5. Capitalizing Market Risk – The New Standard • Interim Regulatory IDR: VaRDefault(99.9%, 1 year) • “to a soundness standard comparable to that of the IRB based approach to credit risk” • Interim Regulatory Total Capital: VaRDefault(99.9%, 1 year) + 3 x VaRMarket(99%, 10-day) • Specific Risk Surcharge is abandoned • No diversification between VaRDefault and VaRMarket • Draft rules permit the assumption of “constant level of risk” rather than buy-and-hold for 1 year • more on this later

6. Capitalizing Market Risk – Industry Response • Two main concerns: • Sets a far higher standard for default risk (99.9%, 1 year, no diversification) than market risk (99%, 10 days, diversification, 3 multiplier) • Regulators creating an incentive to ignore non-default risk in the Trading Book • Rules prescribe perfect correlation between default losses and market losses • Not realistic, fails the use test

7. Capitalizing Market Risk – Industry Response • Industry* put forward an alternative proposal • The current rules can be interpreted as implying a 60-day horizon and 99.9% confidence level 3 x VaRMarket (10-day, 99%) ≈ VaRMarket(60-day, 99.9%) • So set a common standard for default risk and market risk: Total Capital = VaRTotal(60-day, 99.9%) where • Needs a joint model of market and credit risk * “Industry Technical Paper on Incremental Default Risk”, ISDA, LIBA & IIF 2007, www.isda.org/speeches/pdf/Industry-TechnicalPaperonIDRCFINAL26Jan07.pdf

8. Outline • Part I: Capitalizing Market Risk (“the rules”) • Part II: Modelling IDR (“the maths”) • Part III: Impact of IDR (“the shock”)

9. Modelling IDR – Basic Approach • Compute the default loss distribution on the Trading Book • Start a with a Banking Book-style one factor model for PD • Main difference is shorter holding period for the Trading Book • Modelling Challenges • How to measure PD over short (< 1 year) horizon? • How to aggregate default losses with market losses? • Borrow from Banking Book • Models of LGD • Model of default correlation

10. Modelling IDR – Buy-and-Hold vs. Constant Level of Risk • Traditional credit risk models assume buy and hold for at least a year • Not realistic for the Trading Book • Instead assume positions are held for some ‘liquidity period’ of < 1 year • given PDs over the liquidity period, we can compute loss distribution • What happens next? • Assume that Trading Book is an ongoing business, • Bank ‘rebalances’ its portfolio every liquidity period • Constant Level of Risk

11. Modelling IDR – example of Buy and Hold vs. Constant Level of Risk Buy and Hold Constant Level of Risk

12. Modelling IDR – Short Horizon PD • What impact does ‘constant level of risk’ have? • Set the capital horizon at 1, assume some liquidity horizon t < 1 • - If default intensity is linear, none at all • - If default intensity is convex, reduces default risk

13. Modelling IDR – Short Horizon PD • Study* based on Moody’s rating data shows: • PD is very convex for investment grade issuers • PD is convex for high yield issuers • PD is concave for junk issuers * “Assessing Alternative Assumptions on Default Risk Capital in the Trading Book”, Dunn et al 2006, www.isda.org/c_and_a/ppt/Default-Risk-Capital-Alternative-Assumptions.doc

14. Modelling IDR – Short Horizon PD • Study* based on the EDF market based metric of creditworthiness shows same effect * “Extension of the Moody’s KMV Study on Surprise Defaults”, Moody’s-KMV 2006

15. Modelling IDR – Impact of Short Horizon PD • Interesting effect, but the impact is not that large • Assume a one year capital horizon • For a sample trading portfolio, going from Buy-and-Hold to 3-month and 1-month Constant Level of Risk reduced risk by ≈ 10% and ≈ 20% respectively • Why? • Because default risk is driven by HY exposures, which are less convex

16. Modelling IDR – Other Modelling Issues • Aggregation with Market Risk • A large proportion of IDR is concentration risk, uncorrelated with systemic factors • How is systemic credit risk correlated with market risks (credit spreads, equities, base rates...)? • Applying different liquidity horizons consistently • How to account for exposures to the same issuer with different levels of liquidity

17. Outline • Part I: Capitalizing Market Risk (“the rules”) • Part II: Modelling IDR (“the maths”) • Part III: Impact of IDR (“the shock”)

18. Impact of IDR – ISDA experiment • 7 Banks computed Trading Book reg cap according to: • Current Rules • Regulators’ Draft Principles • Industry Proposal • Each used their own best estimate of how they would implement IDR • Differences exist between banks’ portfolios • Some differences between banks’ models

19. Impact of IDR – ISDA results • Results are normalized so that current VaR-based capital equals 100% • Specific Risk Surcharge forms only a small proportion of existing VaR-based regulatory capital • Under industry’s proposed rules capital increases by one third • Applying IDR as per draft principles increases regulatory capital dramatically

20. Impact of IDR – Discussion • Current specific risk surcharge is small, firms have little regulatory capital incentive to manage this risk • Draft principles go too far in the opposite direction: • By design, draft principles set a much higher standard (1 year confidence level, no diversification) for default risk than for other market risks • Leads to very substantial increase in Trading Book regulatory capital, which is now driven almost entirely by default risk • Creates the perverse incentive for banks to focus only on default risk. Market risk would subsequently have relatively little impact on Trading Book capital • Under industry proposals impact of IDR is material, but proportional to true magnitude of default risk relative to other risk types