The Microeconomic
Foundations of Basel II
Erik Heitfield*
Board of Governors of the Federal Reserve System
20th and C Street, NW
Washington, DC 20551 USA
[email protected]
* 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
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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
The Basel Capital
Accords
Basel I
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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
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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
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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
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
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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
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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)
•
•
•
•
Corporate and industrial
Qualifying revolving exposures (credit cards)
Residential mortgages
Project finance
Risk-weight functions differ by exposure
class. Classes include
The Asymptotic Single
Risk Factor Framework
Value-at-Risk Capital Rule
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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
Loss Distribution at 1-Year Horizon
Probability

Insolvent
Solvent
Portfolio Loss
K
Decentralized Capital Rule
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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
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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
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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
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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
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Consider two subportfolios, A and B,
such that L = LA + LB,
Capital can be assigned separately to
each subportfolio.
The A-IRB
Capital Formula
Merton Model
Obligor i defaults if its normalized
asset return Yi falls below the default
threshold .
where
Merton Model
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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
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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
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Value vs. Maturity for BBB $1NPV Loan
by Grade at 1-Year Horizon
1.20
Market Value at Horizon
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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
1.15
1.10
1.05
1.00
0.95
0.90
0.85
1
2
3
4
5
Maturity
Value vs. Maturity for B $1NPV Loan
by Grade at 1-Year Horizon
1.20
Market Value at Horizon
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1.15
AA
A
BBB
BB
B
CCC
1.10
1.05
1.00
0.95
0.90
0.85
1
2
3
Maturity
4
5
Maturity Adjustment
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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
Capital (% of Exposure)
30.00%
25.00%
20.00%
15.00%
10.00%
M = 2.5
LGD = 45%
5.00%
0.00%
0.00%
5.00%
10.00%
Probability of Default
15.00%
20.00%
The A-IRB Capital Rule
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Basel II risk weight functions use a mix of
bank-reported and supervisory parameters
Bank-reported parameters
•
•
•
•
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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
Guarantor
Obligor
Substitution Approach
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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
Capital (% of Exposure)
12.00%
10.00%
LGD = 45%
M=1
Unhedged
8.00%
6.00%
Guarantor PD=1.00%
4.00%
2.00%
0.00%
0.00%
Guarantor PD=0.03%
1.00%
2.00%
3.00%
Obligor PD
4.00%
5.00%
Substitution Approach
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Shortcomings of the substitution approach
• Provides no incentive to hedge high-quality
exposures
• Not risk sensitive for low-quality hedged
exposures
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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
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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
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Model allows for
• Guarantors with high sensitivity to
systematic risk
• “Wrong way” risk between obligors and
guarantors
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Three correlation parameters
Joint Default Probabilities
Joint default probability is generally much lower
than either marginal default probability
Obligor PD
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%
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
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12.00%
Capital (% of Exposure)
ASRF provides
incentive to hedge risk
for all types of
obligors
ASRF is more risksensitive for both high
and low quality
obligors and
guarantors
ASRF may or may not
generate lower capital
charges than
substitution
Unhedged
10.00%
8.00%
6.00%
Guarantor PD=1.00%
4.00%
Guarantor PD=0.03%
2.00%
0.00%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
Obligor PD
ASRF Approach
12.00%
Capital (% of Exposure)

Substitution Approach
10.00%
Unhedged
8.00%
6.00%
Guarantor PD=1.00%
4.00%
Guarantor PD=0.03%
2.00%
0.00%
0.00%
1.00%
2.00%
3.00%
Obligor PD
4.00%
5.00%
Summary
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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
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Basel II’s IRB capital functions use a mix of bankreported and “hard wired” parameters
The ASRF framework can be used to generate
capital rules for complex credit exposures
• Hedged loans
• Loan backed securities
References
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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