A Critique of Revised Basel II. 1. Conclusions. 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). .
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).
The bank’s 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) – ???
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):
Regulatory authorities specify a rule to approximate the ideal capital. This is the required regulatory capital.
Hypothesis 3 ( Approximate Ideal Capital from Below):
Example: In revised Basel II, the rule for required capital is (for illustrative purposes)
Will discuss later in more detail.
Given hypotheses 1 and 2.
for j=1,…,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.
Let hypotheses 1 – 3 hold.
for i = 1,…,m be the regulatory capital for bank i,
Then when considering a new 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.
For my analysis, concentrate on internal ratings/advanced approach.
Risk weights determined based on bank’s internal estimates of PD, LGD and EAD.
These estimates input into a formula for capital (K) held for each asset. Capital K based on:
Discuss each in turn…
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.
Ideal regulatory capital should be state dependent.
Problems with the VaR measure for loss L.
Well-known that VaR:
VaR(LA) = 0 and VaR(L(A+B)/2) = $.50
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.
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  needed 3 factors to fit corporate bond prices.
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???
Formula for K implies that losses (returns) are normally distributed.
Inconsistent with evidence:
Capital determination based on book values of assets.
This ignores capital gains/losses on assets over the 1-year horizon.
Gordy  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.
P. Kupiec constructs a model – Black/Scholes/Merton 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.
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  argues operational risk is of two types: system or agency based.
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.
Liquidity risk only included implicitly in
Better and more direct ways of doing this are available, see Jarrow and Protter .