# Presentation: 287222

## 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).

## The Bank’s Optimal Capital

- 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) – ???

## 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):**    **
**                                       ****	**
** **
** **
** **

## Ideal Regulatory Capital

## 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):

## Required Regulatory Capital

- Justification:
- Believed that many banks choose *X**t*  > *Y**t*  for competitive reasons. Then, under hypothesis 1,        *Z**t  **> X**t ** > Y**t*.
- Rule chosen (shown later) is based on asymptotic theory where idiosyncratic risks are infinitesimal and diversified away, implies  *Z**t  **> Y**t*.
- Rule chosen (shown later) so that ideally, probability of failure is less than .001. Implies A credit rating or better (Moody’s). In practice, required capital does not achieve this level for many banks, so that for these banks *Z**t  **> Y**t**.*

## Required Regulatory Capital

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

## Theorem 1

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

## 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.

## 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

## 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.

## 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.

## 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.

## Credit Risk

- 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:
- 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 asset’s maturity.
- Discuss each in turn...

## 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.

## 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.

## 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).

## Example: Concentrating Risk

| Loss | P(LA) | P(LB)
 | P(L(A+B)/2)
 |
| --- | --- | --- | --- |
| $0 | 0.9991 | 0.9991 | 0.9982 |
| $.50 | 0 | 0 | 0.0018 |
| $1 | 0.0009 | 0.0009 | 0.0000 |

*VaR(L**A**) = 0  and  VaR(L**(A+B)/2**)** = $.50*

## 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.

## 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.

## 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???

## 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)

## 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.

## Significance of Error

- 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.

## 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.

## 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.

## 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].