Title: The Microeconomic Foundations of Basel II
1The Microeconomic Foundations of Basel II
- Erik Heitfield
- Board of Governors of the Federal Reserve
System20th and C Street, NWWashington, DC 20551
USAErik.Heitfield_at_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.
2- How did we get from here
- The 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?
3Todays 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
4The Basel Capital Accords
5Basel 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
6Basel 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
7Basel 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
8Credit 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
9Advanced 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
10The Asymptotic Single Risk Factor Framework
11Value-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 a
12Decentralized 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
13The 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
14ASRF 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
15ASRF 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)
16ASRF Capital Rule
- Consider two subportfolios, A and B, such that L
LA LB, - Capital can be assigned separately to each
subportfolio.
17The A-IRBCapital Formula
18Merton Model
- Obligor i defaults if its normalized asset
return Yi falls below the default threshold ?. - where
19Merton 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
20Asset 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
21Maturity 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
22Maturity 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)
23The A-IRB Capital Rule for Corporate Exposures
M 2.5LGD 45
24The 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
25How should Basel II treat guarantees and credit
derivatives?
26Credit Risk Mitigation
- Banks can hedge the credit risk associated with
an exposure - Financial guarantees
- Single-name credit default swaps
Bank
Obligor
Guarantor
27Substitution 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 PDgltPDo 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
28Substitution Approach
LGD 45M 1
Unhedged
Guarantor PD1.00
Guarantor PD0.03
29Substitution 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
30ASRF/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
31ASRF/Merton Approach
- Model allows for
- Guarantors with high sensitivity to systematic
risk - Wrong way risk between obligors and guarantors
- Three correlation parameters
32Joint Default Probabilities
Joint default probability is generally much lower
than either marginal default probability
?og 60
33ASRF/Merton Approach
- Plugging the 99.9th percentile of X into the
conditional expected loss function for the hedged
exposure yields an ASRF capital rule
34ASRF/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 PD1.00
Guarantor PD0.03
Unhedged
Guarantor PD1.00
Guarantor PD0.03
35Summary
- 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 IIs 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
36References
- 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