The Microeconomic Foundations of Basel II

1. The Microeconomic Foundations of Basel II Erik Heitfield* Board of Governors of the Federal Reserve System20th and C Street, NWWashington, DC 20551 USAErik.Heitfield@frb.gov * The views expressed in this presentation are my own, and nod not necessarily reflect the opinions of the Federal Reserve Board or its staff.

2. How did we get from here… “[T]he new framework is intended to align regulatory capital requirements more closely with underlying risks, and to provide banks and their supervisors with several options for the assessment of capital adequacy.” -- William McDonough …to here?

3. Today’s Talk • The Basel Capital Accords • The asymptotic-single-risk-factor framework • The advanced-internal-ratings-based capital function • Asset correlation assumptions • Adjustment for maturity effects • Application: the treatment of credit derivatives and financial guarantees

4. The Basel Capital Accords

5. Basel I • Signed by members of the Basel Committee on Banking Supervision in 1988 • Establishes two components of regulatory capital • Tier 1: book equity, certain equity-like liabilities • Tier 2: subordinated debt, loan loss reserves • Weighs assets to broadly reflect underlying risk • Capital divided by risk-weighted assets is called the risk-based capital ratio • Basel I imposes two restrictions on risk-based capital ratios • 4% minimum on tier 1 capital • 8% minimum on total (tier 1 + tier 2) capital

6. Basel II • Goal: to more closely align regulatory capital requirements with underlying economic risks • Timeline • Work begun in 1999 • Third quantitative impact study completed in December 2002 • Third consultative package released for comment in May 2003 • Completion targeted for early 2004

7. Basel II – Three Pillars • Minimum capital requirements cover credit risk and operational risk • Supervisory standards allow supervisors to require buffer capital for risks not covered under Pillar I • Disclosure requirements are intended to enhance market discipline

8. Credit Risk Capital Charges • Basel II extends the risk-based capital ratio introduced in Basel I • Risk weights will reflect fine distinctions among risks associated with different exposures • Three approaches to calculating risk weights • Standardized approach • Foundation internal-ratings-based approach • Advanced internal-ratings-based approach

9. Advanced IRB Approach • Risk-weight functions map bank-reported risk parameters to exposure risk weights • Bank-reported risk parameters include • Probability of default (PD) • Loss given default (LGD) • Maturity (M) • Exposure at default (EAD) • Risk-weight functions differ by exposure class. Classes include • Corporate and industrial • Qualifying revolving exposures (credit cards) • Residential mortgages • Project finance

10. The Asymptotic Single Risk Factor Framework

11. Value-at-Risk Capital Rule • Portfolio is solvent if the value of assets exceeds the value of liabilities • Set K so that capital exceeds portfolio losses at a one-year assessment horizon with probability α

12. Decentralized Capital Rule • The capital charge assigned to an exposure reflects its marginal contribution to the portfolio-wide capital requirement • The capital charge assigned to an exposure is independent of other exposures in the bank portfolio • The portfolio capital charge is the sum of charges applied to individual exposures

13. The ASRF Framework • In a general setting, a VaR capital rule cannot be decentralized because the marginal contribution of a single exposure to portfolio risk depends on its correlation with all other exposures • Gordy (2003) shows that under stylized assumptions a decentralized capital rule can satisfy a VaR solvency target • Collectively these assumptions are called the asymptotic-single-risk-factor (ASRF) framework

14. ASRF Assumptions • Cross-exposure correlations in losses are driven by a single systematic risk factor • The portfolio is infinitely-fine-grained (i.e. idiosyncratic risk is diversified away) • For most exposures loss rates are increasing in the systematic risk factor

15. ASRF Capital Rule • The th percentile of X is • Set capital to the th percentile of L to ensure a portfolio solvency probability of  • Plug the th percentile of X into c(x)

16. ASRF Capital Rule • Consider two subportfolios, A and B, such that L = LA + LB, • Capital can be assigned separately to each subportfolio.

17. The A-IRBCapital Formula

18. Merton Model Obligor i defaults if its normalized asset return Yi falls below the default threshold . where

19. Merton Model • The conditional expected loss function for exposure i given X is • Plugging the 99.9th percentile of X into ci(x) yields the core of the Basel II capital rule

20. Asset Correlations • The asset correlation parameter  measures the importance of systematic risk • Under Basel II  is “hard wired” • Asset correlation parameters were calibrated using data from a variety of sources in the US and Europe • For corporate exposures,  depends on obligor characteristics • Asset correlation declines with obligor PD • SMEs receive a lower asset correlation

21. Maturity Adjustment • Base capital function reflects only default losses over a one-year horizon • The market value of longer maturity loans are more sensitive to declines in credit quality short of default • Higher PD loans are less sensitive to market value declines

22. Maturity Adjustment • Maturity adjustment function rescales base capital function to reflect maturity effects • b(PD) determines the effect of maturity on relative capital charges for a given PD • b(PD) is decreasing in PD • Note that K(PD,LGD,1) = K(PD,LGD)

23. The A-IRB Capital Rule for Corporate Exposures M = 2.5LGD = 45%

24. The A-IRB Capital Rule • Basel II risk weight functions use a mix of bank-reported and supervisory parameters • Bank-reported parameters • Probability of default • Loss given default • Maturity • Exposure at default • “Hard wired” parameters • Asset correlations • Maturity adjustment functions • VaR solvency threshold

25. How should Basel II treat guarantees and credit derivatives?

26. Credit Risk Mitigation Banks can hedge the credit risk associated with an exposure • Financial guarantees • Single-name credit default swaps Bank Obligor Guarantor

27. Substitution Approach • Basel II allows a bank that purchases credit protection to use the PD associated with the guarantor instead of that associated with the obligor • When PDg<PDo the substitution approach allows banks to receive a lower capital charge for hedged exposures • The substitution approach is not derived from an underlying credit risk model

28. Substitution Approach LGD = 45%M = 1 Unhedged Guarantor PD=1.00% Guarantor PD=0.03%

29. Substitution Approach • Shortcomings of the substitution approach • Provides no incentive to hedge high-quality exposures • Not risk sensitive for low-quality hedged exposures • Solution • The same ASRF framework used to derive capital charges for unhedged loans can be used to derive capital charges for hedged loans

30. ASRF/Merton Approach • A Merton model describes default by both the obligor (o) and the guarantor (g) • Two risk factors drive default correlations • X affects all exposures in the portfolio • Z affects only the obligor and the guarantor

31. ASRF/Merton Approach • Model allows for • Guarantors with high sensitivity to systematic risk • “Wrong way” risk between obligors and guarantors • Three correlation parameters

32. Joint Default Probabilities Joint default probability is generally much lower than either marginal default probability ρog = 60%

33. ASRF/Merton Approach Plugging the 99.9th percentile of X into the conditional expected loss function for the hedged exposure yields an ASRF capital rule

34. ASRF/Merton vs. Substitution • ASRF provides incentive to hedge risk for all types of obligors • ASRF is more risk-sensitive for both high and low quality obligors and guarantors • ASRF may or may not generate lower capital charges than substitution Unhedged Guarantor PD=1.00% Guarantor PD=0.03% Unhedged Guarantor PD=1.00% Guarantor PD=0.03%

35. Summary • Basel II is intended to more closely align regulatory capital requirements with underlying economic risks • The ASRF framework produces a simple capital rule that • Achieves a portfolio VaR target • Is decentralized • Basel II’s IRB capital functions use a mix of bank-reported and “hard wired” parameters • The ASRF framework can be used to generate capital rules for complex credit exposures • Hedged loans • Loan backed securities

36. References • Basel Committee on Banking Supervision (2003), “Third Consultative Paper” http://www.bis.org/bcbs/bcbscp3.htm • Gordy, M. (2003), “A risk-factor model foundation for ratings-based bank capital rules,” Journal of Financial Intermediation 12(3), pp. 199-232 • Heitfield, E. (2003), “Using guarantees and credit derivatives to reduce credit risk capital requirements under the new Basel Capital Accord,” in Credit Derivatives: the Definitive Guide, J. Gregory (Ed.), Risk Books • Pykhtin, M. and A. Dev (2002), “Credit risk in asset securitizations: an analytical model,” Risk May 2003, pp. 515-520