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The Microeconomic Foundations of Basel II. Erik Heitfield* Board of Governors of the Federal Reserve System 20 th and C Street, NW Washington, DC 20551 USA Erik.Heitfield@frb.gov.
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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.
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?
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
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
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
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
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
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
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
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
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
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
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)
ASRF Capital Rule • Consider two subportfolios, A and B, such that L = LA + LB, • Capital can be assigned separately to each subportfolio.
Merton Model Obligor i defaults if its normalized asset return Yi falls below the default threshold . where
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
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
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
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)
The A-IRB Capital Rule for Corporate Exposures M = 2.5LGD = 45%
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
How should Basel II treat guarantees and credit derivatives?
Credit Risk Mitigation Banks can hedge the credit risk associated with an exposure • Financial guarantees • Single-name credit default swaps Bank Obligor Guarantor
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
Substitution Approach LGD = 45%M = 1 Unhedged Guarantor PD=1.00% Guarantor PD=0.03%
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
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
ASRF/Merton Approach • Model allows for • Guarantors with high sensitivity to systematic risk • “Wrong way” risk between obligors and guarantors • Three correlation parameters
Joint Default Probabilities Joint default probability is generally much lower than either marginal default probability ρog = 60%
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
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%
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
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