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A Critique of Revised Basel II

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Robert Jarrow

Robert Jarrow

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).

Robert Jarrow

The bankâ€™s optimal capital level is defined to be that capital which maximizes shareholdersâ€™ wealth, independently of regulatory rules.

Banks may or may not know f( . , . ).

Larger (international) banks â€“ yes

Smaller (regional banks) â€“ ???

Robert Jarrow

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):

Robert Jarrow

Robert Jarrow

Regulatory authorities specify a rule to approximate the ideal capital. This is the required regulatory capital.

Hypothesis 3 ( Approximate Ideal Capital from Below):

Robert Jarrow

Justification:

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

Robert Jarrow

Example: In revised Basel II, the rule for required capital is (for illustrative purposes)

Will discuss later in more detail.

Robert Jarrow

Given hypotheses 1 and 2.

Let

for j=1,â€¦,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.

Robert Jarrow

- 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.

Robert Jarrow

Let hypotheses 1 â€“ 3 hold.

Let

for i = 1,â€¦,m be the regulatory capital for bank i,

Then when considering a new rule

Robert Jarrow

- 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.

Robert Jarrow

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.

Robert Jarrow

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.

Robert Jarrow

Risk weights determined based on bankâ€™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 assetâ€™s maturity.
Discuss each in turnâ€¦

Robert Jarrow

PD is 1-year long term average default probability

â€“ not state dependent.

LGD is computed based on an economic downturn

â€“ quasi-state dependent.

EAD is computed based on an economic downturn

â€“ quasi-state dependent.

These do not change with business cycle.

Robert Jarrow

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.

Robert Jarrow

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).

Robert Jarrow

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

Robert Jarrow

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.

Robert Jarrow

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.

Robert Jarrow

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???

Robert Jarrow

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)

Robert Jarrow

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.

Robert Jarrow

P. Kupiec constructs a model â€“ Black/Scholes/Merton economy, correlated geometric B.M.â€™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.

Robert Jarrow

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.

Robert Jarrow

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.

Robert Jarrow

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].

Robert Jarrow