The Microeconomic Foundations of Basel II

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The 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.
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• 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?

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Todays 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

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The Basel Capital Accords
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Basel 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

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Basel 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

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Basel II Three Pillars

1. Minimum capital requirements cover credit risk
   and operational risk
2. Supervisory standards allow supervisors to
   require buffer capital for risks not covered
   under Pillar I
3. Disclosure requirements are intended to enhance
   market discipline

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Credit 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

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Advanced 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

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The Asymptotic Single Risk Factor Framework
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Value-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

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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 is
  independent of other exposures in the bank
  portfolio
• The portfolio capital charge is the sum of
  charges applied to individual exposures

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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
• 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

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ASRF 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

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ASRF 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)

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ASRF Capital Rule

• Consider two subportfolios, A and B, such that L
  LA LB,
• Capital can be assigned separately to each
  subportfolio.

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The A-IRBCapital Formula
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Merton Model

• Obligor i defaults if its normalized asset
  return Yi falls below the default threshold ?.
• where

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Merton 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

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Asset 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

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Maturity 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

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Maturity 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)

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

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How should Basel II treat guarantees and credit
derivatives?
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Credit Risk Mitigation

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

Bank
Obligor
Guarantor
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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
• 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

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Substitution Approach
LGD 45M 1
Unhedged
Guarantor PD1.00
Guarantor PD0.03
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Substitution 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

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ASRF/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

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ASRF/Merton Approach

• Model allows for
• Guarantors with high sensitivity to systematic
  risk
• Wrong way risk between obligors and guarantors
• Three correlation parameters

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Joint Default Probabilities
Joint default probability is generally much lower
than either marginal default probability
?og 60
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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

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ASRF/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
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Summary

• 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

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References

• 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