The Microeconomic Foundations of Basel II Erik Heitfield* Board of Governors of the Federal Reserve...
-
Upload
martin-york -
Category
Documents
-
view
219 -
download
0
Transcript of The Microeconomic Foundations of Basel II Erik Heitfield* Board of Governors of the Federal Reserve...
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
[email protected]@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