A Critique of Revised Basel II

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A Critique of Revised Basel II
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1. Conclusions
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2. XYZ Theory of Regulatory Capital

• Randomness in the economy determined by the
  evolution of a set of state variables.
• State variables include individual bank
  characteristics and business cycle
  characteristics (macro-variables).

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The Banks Optimal Capital

• The banks optimal capital level is defined to be
  that capital which maximizes shareholders
  wealth, independently of regulatory rules.
• Banks may or may not know f( . , . ).
• Larger (international) banks yes
• Smaller (regional banks) ???

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Ideal Regulatory Capital

• Regulatory capital is needed due to costly
  externalities associated with bank failures.
• The ideal regulatory capital is defined to be
  that (hypothetical) capital determined as if
  regulatory authorities had perfect knowledge
  (information).
• Hypothesis 1 (Costly Externalities)
•  
•  
•  

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Ideal Regulatory Capital
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Required Regulatory Capital

• Regulatory authorities specify a rule to
  approximate the ideal capital. This is the
  required regulatory capital.
• Hypothesis 3 ( Approximate Ideal Capital from
  Below)

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Required Regulatory Capital

• Justification
• Believed that many banks choose Xt gt Yt for
  competitive reasons. Then, under hypothesis 1,
  Zt gt Xt gt Yt.
• Rule chosen (shown later) is based on asymptotic
  theory where idiosyncratic risks are
  infinitesimal and diversified away, implies Zt
  gt Yt.
• Rule chosen (shown later) so that ideally,
  probability of failure is less than .001. Implies
  A credit rating or better (Moodys). In practice,
  required capital does not achieve this level for
  many banks, so that for these banks Zt gt Yt.

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Required Regulatory Capital

• Example In revised Basel II, the rule for
  required capital is (for illustrative purposes)
• Will discuss later in more detail.

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Theorem 1

• Given hypotheses 1 and 2.
• Let
• for j1,,N represent a collection of regulatory
  capital rules.
• Let hypothesis 3 hold. Then,
• is a better approximation to Zt than any single
  rule.
• If hypothesis 3 does not hold, then no simple
  ordering of regulatory capital rules is possible
  without additional structure.

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Theorem 1 - implications

• New rules should be implemented without
  discarding existing rules. Implies retention of
  leverage based rules (FDICIA) is prudent.
• Four year parallel run period with yearly
  transitional floors (95, 90,85) within Basel
  II revised framework is prudent.

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Theorem 2

• Let hypotheses 1 3 hold.
• Let
• for i 1,,m be the regulatory capital for bank
  i,
• Then when considering a new rule

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Theorem 2 - implications

• Scaling individual bank capital so that in
  aggregate, industry capital does not decline, is
  prudent. Current scale is 1.06 based on the 3rd
  Quantitative Impact Study. Tentative magnitude.
• Requiring that the regulations be
  restudied/modified if a 10 reduction in
  aggregate capital results after implementation is
  prudent.

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3. The Revised Basel II Capital Rule

• The following analysis is independent of XYZ
  theory.
• Revised Basel II rule illustrated on a previous
  slide.
• In revised Basel II, the risk weightings are
  explicitly adjusted for credit risk, operational
  risk, and market risk. Liquidity risk is only an
  implicit adjustment.

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The Revised Basel II Capital Rule

• Two approaches
• Standard (based on tables and rules given in
  revised Basel II framework).
• Internal ratings/ Advanced approach (based on
  internal models).
• For my analysis, concentrate on internal
  ratings/advanced approach.

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Credit Risk

• Risk weights determined based on banks internal
  estimates of PD, LGD and EAD.
• These estimates input into a formula for capital
  (K) held for each asset. Capital K based on
• Value at Risk (VaR) measure over a 1-year horizon
  with a 0.999 confidence level.
• Asymptotic single-factor model, with constant
  correlation assumption.
• An adjustment for an assets maturity.
• Discuss each in turn

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PD, LGD, EAD

• PD is 1-year long term average default
  probability
• not state dependent.
• LGD is computed based on an economic downturn
• quasi-state dependent.
• EAD is computed based on an economic downturn
• quasi-state dependent.
• These do not change with business cycle.

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PD, LGD, EAD

• Ideal regulatory capital should be state
  dependent.
• Pro Makes bank failures counter-cyclic.
• Con Makes bank capital pro-cyclic. Could
  adversely effect interest rates (investment).
  But, monetary authorities have market based tools
  to reduce this negative impact.

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Problems with VaR

• Problems with the VaR measure for loss L.
• Well-known that VaR
• ignores distribution of losses beyond 0.999
  level, and
• penalizes diversification of assets (provides an
  incentive to concentrate risk).

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Example Concentrating Risk
VaR(LA) 0 and VaR(L(AB)/2) .50
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Given VaR Portfolio Invariance

• Capital K formulated to have portfolio
  invariance, i.e. the required capital for a
  portfolio is the sum of the required capital for
  component assets.
• Done for simplicity of implementation.
• But, it ignores benefits of diversification,
  provides an incentive toward concentrating risk.

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Given VaR Single Risk Factor

• The asymptotic model (to get portfolio
  invariance) has a single risk factor.
• The single risk factor drives the state variables
  vector.
• Inconsistent with evidence, e.g.
• Duffee 1999 needed 3 factors to fit corporate
  bond prices.

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Given VaR Common Correlation

• When implementing the ASRF model, revised Basel
  II assumes that all assets are correlated by a
  simple function of PD, correlation bounded
  between 0.12 and 0.24.
• No evidence to support this simplifying
  assumption???

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Given VaR Normal Distribution for Losses

• Formula for K implies that losses (returns) are
  normally distributed.
• Inconsistent with evidence
• Ignores limited liability (should be lognormal)
• Ignores fat tails (stochastic volatility and
  jumps)

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Given VaR Maturity Adjustment

• Capital determination based on book values of
  assets.
• This ignores capital gains/losses on assets over
  the 1-year horizon.
• Gordy 2003 argues that a maturity adjustment is
  necessary to capture downgrades of credit rating
  in long-dated assets.
• Do not understand. Asset pricing theory has
  downgrade independent of maturity. Maturity
  (duration) adjustment only (roughly) captures
  interest rate risk.

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Significance of Error

• P. Kupiec constructs a model Black/Scholes/Merto
  n economy, correlated geometric B.M.s for
  assets. Considers a portfolio of zero-coupon
  bonds.
• Computes ideal capital, compares to revised Basel
  II framework capital.
• Finds significant differences.
• Conclusion revised Basel II capital rule is a
  (very) rough approximation to the ideal rule.

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Operational Risk

• Basic indicator and standard approach capital is
  proportional to income flow.
• Advanced measurement approach internal models
  approach based on VaR, 1-year horizon, 0.999
  confidence level.
• Jarrow 2005 argues operational risk is of two
  types system or agency based.
• Income flow captures system type risk.
• Agency risk is not captured by income flow. More
  important of the two types. Only possibly
  captured in advanced measurement approach.

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Market Risk

• Standardized and internal models approach.
• Concentrate on internal models approach.
• Internal models approach is VaR based with 10-day
  holding period and 0.99 confidence level with a
  scale factor of 3.
• Why the difference from credit risk?
• Could lead to regulatory arbitrage if an asset
  could be classified as either.

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Liquidity Risk

• Liquidity risk only included implicitly in
• credit risk (via the LGD, EAD being for an
  economic downturn)
• market risk (via the scale factor of 3).
• Better and more direct ways of doing this are
  available, see Jarrow and Protter 2005.