The Microeconomic Foundations of Basel II Erik Heitfield* Board of Governors of the Federal Reserve System 20 th and C Street, NW Washington, DC USA * 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 Basel Capital Accords The asymptotic-single-risk-factor framework The asymptotic-single-risk-factor framework The advanced-internal-ratings-based capital function The advanced-internal-ratings-based capital function Asset correlation assumptionsAsset correlation assumptions Adjustment for maturity effectsAdjustment for maturity effects Application: the treatment of credit derivatives and financial guarantees Application: the treatment of credit derivatives and financial guarantees

The Basel Capital Accords

Basel I Signed by members of the Basel Committee on Banking Supervision in 1988 Signed by members of the Basel Committee on Banking Supervision in 1988 Establishes two components of regulatory capital Establishes two components of regulatory capital Tier 1: book equity, certain equity-like liabilitiesTier 1: book equity, certain equity-like liabilities Tier 2: subordinated debt, loan loss reservesTier 2: subordinated debt, loan loss reserves Weighs assets to broadly reflect underlying risk Weighs assets to broadly reflect underlying risk Capital divided by risk-weighted assets is called the risk-based capital ratio Capital divided by risk-weighted assets is called the risk-based capital ratio Basel I imposes two restrictions on risk-based capital ratios Basel I imposes two restrictions on risk-based capital ratios 4% minimum on tier 1 capital4% minimum on tier 1 capital 8% minimum on total (tier 1 + tier 2) capital8% minimum on total (tier 1 + tier 2) capital

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

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

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

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

The Asymptotic Single Risk Factor Framework

Value-at-Risk Capital Rule Portfolio is solvent if the value of assets exceeds the value of liabilities 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 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 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 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 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 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 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 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 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) 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 For most exposures loss rates are increasing in the systematic risk factor

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

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

The A-IRB Capital Formula

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

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

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

Maturity Adjustment Base capital function reflects only default losses over a one-year horizon 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 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 Higher PD loans are less sensitive to market value declines

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

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

The A-IRB Capital Rule Basel II risk weight functions use a mix of bank-reported and supervisory parameters Basel II risk weight functions use a mix of bank-reported and supervisory parameters Bank-reported parameters Bank-reported parameters Probability of defaultProbability of default Loss given defaultLoss given default MaturityMaturity Exposure at defaultExposure at default “Hard wired” parameters “Hard wired” parameters Asset correlationsAsset correlations Maturity adjustment functionsMaturity adjustment functions VaR solvency thresholdVaR 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 guaranteesFinancial guarantees Single-name credit default swapsSingle-name credit default swaps BankObligor 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 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 PD g <PD o the substitution approach allows banks to receive a lower capital charge for hedged exposures When PD g <PD o 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 The substitution approach is not derived from an underlying credit risk model

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

Substitution Approach Shortcomings of the substitution approach Shortcomings of the substitution approach Provides no incentive to hedge high-quality exposuresProvides no incentive to hedge high-quality exposures Not risk sensitive for low-quality hedged exposuresNot risk sensitive for low-quality hedged exposures Solution Solution The same ASRF framework used to derive capital charges for unhedged loans can be used to derive capital charges for hedged loansThe 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) A Merton model describes default by both the obligor (o) and the guarantor (g) Two risk factors drive default correlations Two risk factors drive default correlations X affects all exposures in the portfolioX affects all exposures in the portfolio Z affects only the obligor and the guarantorZ affects only the obligor and the guarantor

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

Joint Default Probabilities Joint default probability is generally much lower than either marginal default probability ρ og = 60%

ASRF/Merton Approach Plugging the 99.9 th 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 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 is more risk- sensitive for both high and low quality obligors and guarantors ASRF may or may not generate lower capital charges than substitution ASRF may or may not generate lower capital charges than substitution Guarantor PD=0.03% Guarantor PD=1.00% Unhedged

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

References Basel Committee on Banking Supervision (2003), “Third Consultative Paper” Basel Committee on Banking Supervision (2003), “Third Consultative Paper” Gordy, M. (2003), “A risk-factor model foundation for ratings-based bank capital rules,” Journal of Financial Intermediation 12(3), pp Gordy, M. (2003), “A risk-factor model foundation for ratings-based bank capital rules,” Journal of Financial Intermediation 12(3), pp 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 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 Pykhtin, M. and A. Dev (2002), “Credit risk in asset securitizations: an analytical model,” Risk May 2003, pp