The Microeconomic The Microeconomic Foundations of Basel IIFoundations of Basel II

Erik Heitfield*Erik Heitfield*Board of Governors of the Federal Reserve SystemBoard of Governors of the Federal Reserve System

2020thth and C Street, NW and C Street, NWWashington, DC 20551 USAWashington, DC 20551 USA

Erik.Heitfield@frb.govErik.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…How did we get from here…

““[T]he new framework is intended to align regulatory capital requirements [T]he new framework is intended to align regulatory capital requirements more closely with underlying risks, and to provide banks and their more closely with underlying risks, and to provide banks and their supervisors with several options for the assessment of capital adequacy.”supervisors with several options for the assessment of capital adequacy.”

-- William McDonough-- William McDonough

……to here?to here?

Today’s TalkToday’s Talk

The Basel Capital AccordsThe Basel Capital Accords The asymptotic-single-risk-factor The asymptotic-single-risk-factor

frameworkframework The advanced-internal-ratings-based The advanced-internal-ratings-based

capital functioncapital function• Asset correlation assumptionsAsset correlation assumptions• Adjustment for maturity effectsAdjustment for maturity effects

Application: the treatment of credit Application: the treatment of credit derivatives and financial guaranteesderivatives and financial guarantees

The Basel Capital The Basel Capital AccordsAccords

Basel IBasel I Signed by members of the Basel Committee on Signed by members of the Basel Committee on

Banking Supervision in 1988Banking Supervision in 1988 Establishes two components of regulatory capitalEstablishes 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 riskWeighs assets to broadly reflect underlying risk Capital divided by risk-weighted assets is called Capital divided by risk-weighted assets is called

the the risk-based capital ratiorisk-based capital ratio Basel I imposes two restrictions on risk-based Basel I imposes two restrictions on risk-based

capital ratioscapital 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 IIBasel II

Goal: to more closely align regulatory Goal: to more closely align regulatory capital requirements with underlying capital requirements with underlying economic riskseconomic risks

TimelineTimeline• Work begun in 1999Work begun in 1999• Third quantitative impact study completed in Third quantitative impact study completed in

December 2002December 2002• Third consultative package released for Third consultative package released for

comment in May 2003comment in May 2003• Completion targeted for early 2004Completion targeted for early 2004

Basel II – Three PillarsBasel II – Three Pillars

I.I. Minimum capital requirements cover Minimum capital requirements cover credit risk and operational riskcredit risk and operational risk

II.II. Supervisory standards allow Supervisory standards allow supervisors to require buffer capital supervisors to require buffer capital for risks not covered under Pillar Ifor risks not covered under Pillar I

III.III. Disclosure requirements are intended Disclosure requirements are intended to enhance market disciplineto enhance market discipline

Credit Risk Capital ChargesCredit Risk Capital Charges

Basel II extends the risk-based capital ratio Basel II extends the risk-based capital ratio introduced in Basel Iintroduced in Basel I

Risk weights will reflect fine distinctions Risk weights will reflect fine distinctions among risks associated with different among risks associated with different exposuresexposures

Three approaches to calculating risk Three approaches to calculating risk weightsweights• Standardized approachStandardized approach• Foundation internal-ratings-based approachFoundation internal-ratings-based approach• Advanced internal-ratings-based approachAdvanced internal-ratings-based approach

Advanced IRB ApproachAdvanced IRB Approach Risk-weight functions map bank-reported risk Risk-weight functions map bank-reported risk

parameters to exposure risk weightsparameters to exposure risk weights Bank-reported risk parameters includeBank-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 Risk-weight functions differ by exposure class. Classes includeclass. 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 The Asymptotic Single Risk Factor FrameworkRisk Factor Framework

Value-at-Risk Capital RuleValue-at-Risk Capital Rule

Portfolio is solvent if the value of assets exceeds Portfolio is solvent if the value of assets exceeds the value of liabilitiesthe value of liabilities

Set Set KK so that capital exceeds portfolio losses at a so that capital exceeds portfolio losses at a one-year assessment horizon with probability one-year assessment horizon with probability αα

Loss Distribution at 1-Year Horizon

Portfolio Loss

Pro

babi

lity

Solvent Insolvent

K

Decentralized Capital RuleDecentralized Capital Rule The capital charge assigned to an exposure The capital charge assigned to an exposure

reflects its marginal contribution to the reflects its marginal contribution to the portfolio-wide capital requirementportfolio-wide capital requirement

The capital charge assigned to an exposure is The capital charge assigned to an exposure is independent of other exposures in the bank independent of other exposures in the bank portfolioportfolio

The portfolio capital charge is the sum of The portfolio capital charge is the sum of charges applied to individual exposurescharges applied to individual exposures

The ASRF FrameworkThe ASRF Framework

In a general setting, a VaR capital rule In a general setting, a VaR capital rule cannot be decentralized because the cannot be decentralized because the marginal contribution of a single exposure marginal contribution of a single exposure to portfolio risk depends on its correlation to portfolio risk depends on its correlation with all other exposureswith all other exposures

Gordy (2003) shows that under stylized Gordy (2003) shows that under stylized assumptions a decentralized capital rule assumptions a decentralized capital rule can satisfy a VaR solvency targetcan satisfy a VaR solvency target

Collectively these assumptions are called Collectively these assumptions are called the the asymptotic-single-risk-factorasymptotic-single-risk-factor (ASRF) (ASRF) frameworkframework

ASRF AssumptionsASRF Assumptions Cross-exposure Cross-exposure

correlations in losses correlations in losses are driven by a single are driven by a single systematic risk factorsystematic risk factor

The portfolio is The portfolio is infinitely-fine-grainedinfinitely-fine-grained (i.e. idiosyncratic risk (i.e. idiosyncratic risk is diversified away)is diversified away)

For most exposures For most exposures loss rates are loss rates are increasing in the increasing in the systematic risk factorsystematic risk factor

ASRF Capital RuleASRF Capital Rule

The The thth percentile of percentile of XX is is

Set capital to the Set capital to the thth percentile of percentile of LL to to ensure a portfolio solvency probability of ensure a portfolio solvency probability of

Plug the Plug the thth percentile of percentile of XX into c( into c(xx))

ASRF Capital RuleASRF Capital Rule

Consider two subportfolios, Consider two subportfolios, AA and and BB, , such that such that L = LL = LA A + L+ LBB,,

Capital can be assigned separately to Capital can be assigned separately to each subportfolio.each subportfolio.

The A-IRBThe A-IRBCapital FormulaCapital Formula

Merton ModelMerton Model

Obligor Obligor ii defaults if its normalized defaults if its normalized asset return asset return YYii falls below the default falls below the default threshold threshold . .

wherewhere

Merton ModelMerton Model

The conditional expected loss function for The conditional expected loss function for exposure exposure ii given given XX is is

Plugging the 99.9Plugging the 99.9thth percentile of X into percentile of X into ccii(x) (x) yields the core of the Basel II capital ruleyields the core of the Basel II capital rule

Asset CorrelationsAsset Correlations The asset correlation parameter The asset correlation parameter measures measures

the importance of systematic riskthe importance of systematic risk Under Basel II Under Basel II is “hard wired” is “hard wired” Asset correlation parameters were calibrated Asset correlation parameters were calibrated

using data from a variety of sources in the US using data from a variety of sources in the US and Europeand Europe

For corporate exposures, For corporate exposures, depends on obligor depends on obligor characteristicscharacteristics• Asset correlation declines with obligor PDAsset correlation declines with obligor PD• SMEs receive a lower asset correlationSMEs receive a lower asset correlation

Maturity AdjustmentMaturity Adjustment Base capital function Base capital function

reflects only default reflects only default losses over a one-year losses over a one-year horizonhorizon

The market value of The market value of longer maturity loans longer maturity loans are more sensitive to are more sensitive to declines in credit declines in credit quality short of defaultquality short of default

Higher PD loans are Higher PD loans are less sensitive to less sensitive to market value declinesmarket value declines

Value vs. Maturity for BBB $1NPV Loan by Grade at 1-Year Horizon

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1 2 3 4 5

Maturity

Mar

ket

Val

ue a

t H

oriz

on

Value vs. Maturity for B $1NPV Loan by Grade at 1-Year Horizon

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1 2 3 4 5

Maturity

Mar

ket

Val

ue a

t H

oriz

on

AA

A

BBB

BB

B

CCC

Maturity AdjustmentMaturity Adjustment Maturity adjustment function rescales base Maturity adjustment function rescales base

capital function to reflect maturity effectscapital function to reflect maturity effects

bb((PDPD) determines the effect of maturity on ) determines the effect of maturity on relativerelative capital charges for a given PD capital charges for a given PD

bb((PDPD) is decreasing in PD) is decreasing in PD Note thatNote that K K((PD,LGD,1PD,LGD,1)) = K = K((PD,LGDPD,LGD))

The A-IRB Capital Rule for The A-IRB Capital Rule for Corporate ExposuresCorporate Exposures

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

0.00% 5.00% 10.00% 15.00% 20.00%

Probability of Default

Ca

pit

al (

% o

f E

xp

os

ure

)

M = 2.5LGD = 45%

The A-IRB Capital RuleThe A-IRB Capital Rule Basel II risk weight functions use a mix of Basel II risk weight functions use a mix of

bank-reported and supervisory parametersbank-reported and supervisory parameters Bank-reported parametersBank-reported parameters

• Probability of defaultProbability of default• Loss given defaultLoss given default• MaturityMaturity• Exposure at defaultExposure at default

““Hard wired” parametersHard wired” parameters• Asset correlationsAsset correlations• Maturity adjustment functionsMaturity adjustment functions• VaR solvency thresholdVaR solvency threshold

How should Basel II treat How should Basel II treat guarantees and credit guarantees and credit

derivatives?derivatives?

Credit Risk MitigationCredit Risk Mitigation

Banks can hedge the credit risk Banks can hedge the credit risk associated with an exposureassociated with an exposure• Financial guaranteesFinancial guarantees• Single-name credit default swapsSingle-name credit default swaps

Bank Obligor

Guarantor

Substitution ApproachSubstitution Approach Basel II allows a bank that purchases Basel II allows a bank that purchases

credit protection to use the PD associated credit protection to use the PD associated with the guarantor instead of that with the guarantor instead of that associated with the obligorassociated with the obligor

When When PDPDgg<<PDPDoo the substitution approach the substitution approach allows banks to receive a lower capital allows banks to receive a lower capital charge for hedged exposurescharge for hedged exposures

The substitution approach is The substitution approach is notnot derived derived from an underlying credit risk modelfrom an underlying credit risk model

Substitution ApproachSubstitution Approach

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.00% 1.00% 2.00% 3.00% 4.00% 5.00%

Obligor PD

Ca

pita

l (%

of E

xpo

sure

)

LGD = 45%M = 1

Guarantor PD=0.03%

Guarantor PD=1.00%

Unhedged

Substitution ApproachSubstitution Approach

Shortcomings of the substitution approachShortcomings of the substitution approach• Provides no incentive to hedge high-quality Provides no incentive to hedge high-quality

exposuresexposures• Not risk sensitive for low-quality hedged Not risk sensitive for low-quality hedged

exposuresexposures SolutionSolution

• The same ASRF framework used to derive The same ASRF framework used to derive capital charges for unhedged loans can be capital charges for unhedged loans can be used to derive capital charges for hedged loansused to derive capital charges for hedged loans

ASRF/Merton ApproachASRF/Merton Approach

A Merton model describes default by both A Merton model describes default by both the obligor (o) and the guarantor (g)the obligor (o) and the guarantor (g)

Two risk factors drive default correlationsTwo risk factors drive default correlations• XX affects all exposures in the portfolio affects all exposures in the portfolio• ZZ affects only the obligor and the guarantor affects only the obligor and the guarantor

ASRF/Merton ApproachASRF/Merton Approach

Model allows forModel allows for• Guarantors with high sensitivity to Guarantors with high sensitivity to

systematic risksystematic risk• ““Wrong way” risk between obligors and Wrong way” risk between obligors and

guarantorsguarantors Three correlation parametersThree correlation parameters

Joint Default ProbabilitiesJoint Default Probabilities

Guarantor PD 0.03% 0.05% 0.10% 0.50% 1.00% 2.00% 5.00% 10.00%

0.03% 0.00% 0.00% 0.00% 0.01% 0.01% 0.02% 0.02% 0.03%

0.05% 0.00% 0.00% 0.01% 0.01% 0.02% 0.03% 0.04% 0.04%

0.10% 0.00% 0.01% 0.01% 0.02% 0.04% 0.05% 0.07% 0.08%

0.50% 0.01% 0.01% 0.02% 0.08% 0.12% 0.17% 0.27% 0.35%

1.00% 0.01% 0.02% 0.04% 0.12% 0.19% 0.29% 0.48% 0.65%

2.00% 0.02% 0.03% 0.05% 0.17% 0.29% 0.46% 0.81% 1.16%

Obligor PD

Joint default probability is generally much lower Joint default probability is generally much lower than either marginal default probabilitythan either marginal default probability

ρog = 60%

ASRF/Merton ApproachASRF/Merton Approach

Plugging the 99.9Plugging the 99.9thth percentile of percentile of XX into the conditional expected loss into the conditional expected loss function for the hedged exposure function for the hedged exposure yields an ASRF capital ruleyields an ASRF capital rule

ASRF/Merton vs. SubstitutionASRF/Merton vs. Substitution ASRF provides ASRF provides

incentive to hedge risk incentive to hedge risk for all types of obligorsfor all types of obligors

ASRF is more risk-ASRF is more risk-sensitive for both high sensitive for both high and low quality and low quality obligors and obligors and guarantorsguarantors

ASRF may or may not ASRF may or may not generate lower capital generate lower capital charges than charges than substitutionsubstitution

Substitution Approach

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.00% 1.00% 2.00% 3.00% 4.00% 5.00%

Obligor PD

Ca

pita

l (%

of E

xpo

sure

)

ASRF Approach

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0.00% 1.00% 2.00% 3.00% 4.00% 5.00%

Obligor PD

Ca

pit

al (

% o

f E

xp

os

ure

)

Guarantor PD=0.03%

Guarantor PD=0.03%

Guarantor PD=1.00%

Guarantor PD=1.00%

Unhedged

Unhedged

SummarySummary Basel II is intended to more closely align Basel II is intended to more closely align

regulatory capital requirements with underlying regulatory capital requirements with underlying economic riskseconomic risks

The ASRF framework produces a simple capital The ASRF framework produces a simple capital rule thatrule that• Achieves a portfolio VaR targetAchieves a portfolio VaR target• Is decentralizedIs decentralized

Basel II’s IRB capital functions use a mix of bank-Basel II’s IRB capital functions use a mix of bank-reported and “hard wired” parametersreported and “hard wired” parameters

The ASRF framework can be used to generate The ASRF framework can be used to generate capital rules for complex credit exposurescapital rules for complex credit exposures• Hedged loansHedged loans• Loan backed securitiesLoan backed securities

ReferencesReferences Basel Committee on Banking Supervision (2003), “Third Basel Committee on Banking Supervision (2003), “Third

Consultative Paper” http://www.bis.org/bcbs/bcbscp3.htm Consultative Paper” http://www.bis.org/bcbs/bcbscp3.htm

Gordy, M. (2003), “A risk-factor model foundation for Gordy, M. (2003), “A risk-factor model foundation for ratings-based bank capital rules,” ratings-based bank capital rules,” Journal of Financial Journal of Financial IntermediationIntermediation 12(3), pp. 199-232 12(3), pp. 199-232

Heitfield, E. (2003), “Using guarantees and credit Heitfield, E. (2003), “Using guarantees and credit derivatives to reduce credit risk capital requirements under derivatives to reduce credit risk capital requirements under the new Basel Capital Accord,” in the new Basel Capital Accord,” in Credit Derivatives: the Credit Derivatives: the Definitive GuideDefinitive Guide, J. Gregory (Ed.), Risk Books, J. Gregory (Ed.), Risk Books

Pykhtin, M. and A. Dev (2002), “Credit risk in asset Pykhtin, M. and A. Dev (2002), “Credit risk in asset securitizations: an analytical model,” securitizations: an analytical model,” RiskRisk May 2003, pp. May 2003, pp. 515-520515-520