Basel Accords

History of Bank Regulation

• Pre-1988

• 1988: BIS Accord (Basel I)

• 1996: Amendment to BIS Accord

• 1999: Basel II first proposed

• Basel III in response to the recent global financial crisis

Pre-1988• Banks were regulated using balance sheet measures

such as the ratio of capital to assets• Definitions and required ratios varied from country

to country• Enforcement of regulations varied from country to

country• Bank leverage increased in 1980s• Off-balance sheet derivatives trading increased• LDC debt was a major problem • Basel Committee on Bank Supervision set up

1988: BIS Accord

• Capital regulations under Basel I came into effect in December 1992 (after development and consultations since 1988).

• The aims were: – to require banks to maintain enough capital to

absorb losses without causing systemic problems,– to level the playing field internationally (to avoid

competitiveness conflicts).

1988: BIS Accord

• The assets: capital ratio must be less than 20. Assets includes off-balance sheet items that are direct credit substitutes such as letters of credit and guarantees

• Cooke Ratio: Capital must be 8% of risk weighted amount. At least 50% of capital must be Tier 1.

Types of Capital

• Tier 1 Capital: common equity, non-cumulative perpetual preferred shares

• Tier 2 Capital: cumulative preferred stock, certain types of 99-year debentures, subordinated debt with an original life of more than 5 years

Risk-Weighted Capital• A risk weight is applied to each on-balance- sheet asset

according to its risk (e.g. 0% to cash and govt bonds; 20% to claims on OECD banks; 50% to residential mortgages; 100% to corporate loans, corporate bonds, etc.)

• For each off-balance-sheet item we first calculate a credit equivalent amount and then apply a risk weight

• Risk weighted amount (RWA) consists of– sum of risk weight times asset amount for on-balance sheet

items– Sum of risk weight times credit equivalent amount for off-

balance sheet items

Credit Equivalent Amount

• The credit equivalent amount is calculated as the current replacement cost (if positive) plus an add on factor

• The add on amount varies from instrument to instrument (e.g. 0.5% for a 1-5 year swap; 5.0% for a 1-5 year foreign currency swap)

Add-on Factors (% of Principal)

Remaining Maturity (yrs)

Interest rate

Exch Rate and Gold

Equity

Precious Metals except gold

Other Commodities

<1 0.0 1.0 6.0 7.0 10.0

1 to 5 0.5 5.0 8.0 7.0 12.0

>5 1.5 7.5 10.0 6.0 15.0

Example: A $100 million swap with 3 years to maturity worth $5 million would have a credit equivalent amount of $5.5 million

The Math

j

N

i

M

jjii CwLwRWA

1 1

*

On-balance sheet items: principal times risk weight

Off-balance sheet items: credit equivalent amount times risk weight

For a derivative Cj = max(Vj,0) + ajLj where Vj is value, Lj is principal and aj is add-on factor

G-30 Policy Recommendations

• Influential publication from derivatives dealers, end users, academics, accountants, and lawyers

• 20 recommendations published in 1993

Netting

• Netting refers to a clause in derivatives contracts that states that if a company defaults on one contract it must default on all contracts

• In 1995 the 1988 accord was modified to allow banks to reduce their credit equivalent totals when bilateral netting agreements were in place

Netting Calculations• Without netting exposure is

• With netting exposure is

• Net Replacement Ratio

N

jjV

1

)0,max(

N

jjV

1

0,max

Netting without Exposure

Netting with ExposureNRR

Netting Calculations continued

• Credit equivalent amount modified from

• To

N

jjjj LaV

1

])0,[max(

N

j

N

jjjj LaV

1 1

)NRR6.04.0()0,max(

1996 Amendment

• Implemented in 1998

• Requires banks to measure and hold capital for market risk for all instruments in the trading book including those off balance sheet (This is in addition to the BIS Accord credit risk capital)

The Market Risk Capital

• The capital requirement is

• Where k is a multiplicative factor chosen by regulators (at least 3), VaR is the 99% 10-day value at risk, and SRC is the specific risk charge for idiosyncratic risk related to specific companies

SRCVaR k

Problem with Basel I

• Regulatory arbitrage was rampant • Basel I gave banks the ability to control the amount of

capital they required by shifting between on-balance sheet assets with different weights, and by securitising assets and shifting them off balance sheet – a form of disintermediation

• Banks quickly accumulated capital well in excess of the regulatory minimum and capital requirements, which, in effect, had no constraining impact on bank risk taking.

Basel II

• Implemented in 2007

• Three pillars– New minimum capital requirements for

credit and operational risk – Supervisory review: more thorough and

uniform– Market discipline: more disclosure

New Capital Requirements

• Risk weights based on either external credit rating (standardized approach) or a bank’s own internal credit ratings (IRB approach)

• Recognition of credit risk mitigants

• Separate capital charge for operational risk

Basel II: Pillar 1• Pillar 1 of the Basel II system defines minimum capital

to buffer unexpected losses. • Total RWA (risk weighted assets) are based on a

complex system of risk weighting that applies to– ‘credit’ – ‘market’ (MR) – ‘operational’ risk (OR)

• These risks are calculated separately and then added:

RWA= {12.5(OR+MR) + 1.06w(i)A(i)}

USA vs European Implementation

• In US Basel II applies only to large international banks

• Small regional banks required to implement “Basel 1A’’ (similar to Basel I), rather than Basel II

• European Union requires Basel II to be implemented by securities companies as well as all banks

New Capital RequirementsStandardized Approach

Bank and corporations treated similarly (unlike Basel I)

Rating AAA to AA-

A+ to A-

BBB+ to BBB-

BB+ to BB-

B+ to B-

Below B-

Unrated

Country 0% 20% 50% 100% 100% 150% 100%

Banks 20% 50% 50% 100% 100% 150% 50%

Corporates 20% 50% 100% 100% 150% 150% 100%

New Capital RequirementsIRB Approach for corporate, banks and

sovereign exposures• Basel II provides a formula for translating PD (probability of

default), LGD (loss given default), EAD (exposure at default), and M (effective maturity) into a risk weight

• Under the Advanced IRB approach banks estimate PD, LGD, EAD, and M

• Under the Foundation IRB approach banks estimate only PD and the Basel II guidelines determine the other variables for the formula

Model for Loan Portfolio• We map the time to default for company i, Ti, to a

new variable Ui and assume

where F and the Zi have independent standard normal distributions

• Define Qi as the cumulative probability distribution of Ti

• Prob(Ui<U) = Prob(Ti<T) when N(U) = Qi(T)

iiii ZaFaU 21

The Model continued

ncorrelatio copula the is where

Prob

companies all for same the are s' and s' the Assuming

Prob

Hence

Prob

1

)()(

1

)()(

1)(

1

2

1

2

FTQNNFTT

aQ

a

FaTQNNFTT

a

FaUNFUU

i

i

iii

i

ii

The Model continued

• The worst case default rate for portfolio for a time horizon of T and a confidence limit of X is

• The VaR for this time horizon and confidence limit is

where L is loan principal and R is recovery rate

1

)()]([ 11 XNTQNNWCDR(T,X)

),()1(),( XTWCDRRLXTVaR

Key Model in Basel II IRB (Gaussian Copula)

• The 99.9% worst case default rate is

PD – probability of default

• We are 99.9% certain not to exceed WCRD next year

.NPDN

NWCDR--

1

)9990()( 11

The Loss on the Portfolio• There is 99.9% chance that the loss on the

portfolio will be less than

– EADi – exposure given default, i.e. the dollar amount that is expected to be owed by the ith counterparty at the time of default

– LGDi – loss given default, i.e. the percentage of EAD expected to be lost at default

WCDRLGDEAD year) 1%,99.99( ii

i VaR

The Expected Loss and Capital Requirements

• The expected loss from default is:

• The capital requirement is worst case loss minus the expected loss:

PDLGDEADEL ii

i

PD)(WCDRLGDEAD ii

i

The Model Used by Regulators:The loss probability density function and the

capital required by a financial institution

0 1 2 3 4

E xpectedL oss

X % W orst C ase Loss

R equired C apital

L oss over tim e horizon

0 1 2 3 4

E xpectedL oss

X % W orst C ase Loss

R equired C apital

L oss over tim e horizon

Numerical Results for WCDR

PD=0.1% PD=0.5% PD=1% PD=1.5% PD=2%

=0.0 0.1%

0.5% 1.0% 1.5% 2.0%

=0.2 2.8% 9.1% 14.6% 18.9% 22.6%

=0.4 7.1% 21.1% 31.6% 39.0% 44.9%

=0.6 13.5% 38.7% 54.2% 63.8% 70.5%

=0.8 23.3% 66.3% 83.6% 90.8% 94.4%

Dependence of on PD

• For corporate, sovereign and bank exposure

(For small firms is reduced)

]e[112.0e1

e110.24

e1

e10.12ρ PD50

50

PD50

50

PD50

PD 0.1% 0.5% 1.0% 1.5% 2.0%

WCDR 3.4% 9.8% 14.0% 16.9% 19.0%

Capital Requirements

RWA of 8%Capital that so

Capital the times12.5 are assets weighted-risk The

ln(PD)]0.05478[0.11852b

andmaturity effective theis whereb1.51

b2.5)(M1 MA

adjustmentmaturity --MA where

MAPD)(WCDRLGDEADCapital

2

M

Retail Exposures

PD-

PDPD

e.

e

e

e

e

PDWCDRLGDEAD

35

35

35

35

35

1300.03

1

110.16

1

103.0

exposures retailother For

0.04 exposures retail revolvingFor

0.15 mortgages lresidentiaFor

)(Capital

casesboth in EAD andLGD, PD, estimate Banks

.approaches IRB Advanced and Foundationbetween n distinctio no is There

Two Types of Losses and Two Types of Capital under Basel II

• Expected Loss (EL)• Unexpected losses (UL)

UL(T) = VaR(,T) –EL(T)

• Regulatory capital (Tier 1 and 2) is applied to EL which are expected to occur but are of smaller consequence.

• Economic capital is for UL which are low frequency but have significant magnitude. UL is very sensitive to the shape of the loss distribution.

UL is Connected to VaR and Inherits its Shortcomings

• UL of the portfolio can be great than sum of the ULs of its components. This is because VaR is not sub-additive.

• “Star-Treck” problem of VaR: “How do we estimate something where we have never even gone before.” VaR depends on the tail of the loss distribution for which we have no data. 99.99% cutoff is arbitrary.

• VaR is know to depend on the number of samples generated in Mode Carlo simulations. The greater sampling increases the number of outlier observations and “stretches out” the tail.

If you want to reduce UL – simulate less.

Components of Credit Risk Losses

•If each element comes from a distribution, there are issues of Jensen’s inequality. That means that inputs are correlated with each other.

•Foundation IRB (F-IRB) vs Advanced IRB (A-IRB): In the former, LGD is mandated by regulator.

Granularity and Aggregation

• n=210 = 1024 normalized assets

• Portfolio P: w = 1/n, mean 0, variance =

• Expected loss:

• As the assets get clubbed into portfolios, within portfolio diversification needs to be offset by higher correlations across groups; correlation must be a function of granularity (not fixed).

Σww'σ2

Table: Expected loss, unexpected loss and Value-at-Risk for varying levels of granularity and

aggregation•The first column shows the number of business units• The second column gives the number of assets within each portfolio. •Each asset has a standard normal distribution. :Corr” is the average pairwise correlation between portfolio values.

Credit Risk Mitigants

• Credit risk mitigants (CRMs) include collateral, guarantees, netting, the use of credit derivatives, etc

• The benefits of CRMs increase as a bank moves from the standardized approach to the foundation IRB approach to the advanced IRB approach

Adjustments for Collateral• Two approaches

– Simple approach: risk weight of counterparty replaced by risk weight of collateral

– Comprehensive approach: exposure adjusted upwards to allow to possible increases; value of collateral adjusted downward to allow for possible decreases; new exposure equals excess of adjusted exposure over adjusted collateral; counterparty risk weight applied to the new exposure

Guarantees

• Traditionally the Basel Committee has used the credit substitution approach (where the credit rating of the guarantor is substituted for that of the borrower)

• However this overstates the credit risk because both the guarantor and the borrower must default for money to be lost

• Alternative proposed by Basel Committee: capital equals the capital required without the guarantee multiplied by 0.15+160×PDg where PDg is probability of default of guarantor

Operational Risk Capital

• Basic Indicator Approach: 15% of gross income

• Standardized Approach: different multiplicative factor for gross income arising from each business line

• Internal Measurement Approach: assess 99.9% worst case loss over one year.

Supervisory Review Changes

• Similar amount of thoroughness in different countries

• Local regulators can adjust parameters to suit local conditions

• Importance of early intervention stressed

Market Discipline

• Banks will be required to disclose

– Scope and application of Basel framework– Nature of capital held– Regulatory capital requirements– Nature of institution’s risk exposures

Comparison of Basel I and Basel II

Solvency II• Similar three pillars to Basel II• Pillar I specifies the minimum capital

requirement (MCR) and solvency capital requirement (SCR)

• If capital falls below SCR the insurance company must submit a plan for bringing it back up to SCR.

• If capital; drops below MCR supervisors are likely to prevent the insurance company from taking new business

Solvency II continued

• Internal models vs standardized approach

• One year 99.5% confidence for internal models

• Capital charge for investment risk, underwriting risk, and operational risk

• Three types of capital

Problems With Basel II

• Portfolio invariance.• Single global risk factor.• Financial system “promises” are not treated

equally—regulatory arbitrage facilitated by “complete markets” in credit (the CDS market particularly).

• Pro-cyclicality.• Subjective inputs.• Unclear and inconsistent definitions.

Example of Regulatory Arbitrage• Bank A lends $1000 to a BBB rated company, 100%

risk weighted, by buying a bond and would have to hold $80 capital. Bank A holds a promise by the company to pay a coupon and redeem at maturity.

• Bank A buys a CDS from Bank B on the bond, shorting the bond and passing the promise to redeem from the company to Bank B.

• Because B is a bank, which carries a 20% capital weight, Bank A reduces its required capital to 20% of $80, or $16.

• Bank B underwrites the risk with a reinsurance company outside of the banking system; the promise to redeem is now outside the banks and the BIS capital rules don’t apply.

Example of Regulatory Arbitrage(cont.)

• Bank B’s capital required for counterparty risk is only 8% of an amount determined as follows: – the CDS spread price of say $50 (500bps)– plus a regulatory surcharge coefficient of 1.5% of the face value of

the bond (i.e. $15) – all multiplied by the 50% weighting for off balance sheet

commitments. That is, $2.60 (i.e. 0.08*$65*0.5).

• So jointly the banks have managed to reduce their capital required from $80 to $18.60 – a 70.6% fall.

• In effect, in this example, the CDS contracts make it possible to reduce risky debt to some combination of the lower bank risk weight and a small weight that applies to moving the risk outside of the bank sector

There is little point in defining an ex ante risk bucket of company bond as 100% risk weighted in the first place.

Shifting the Promises– Example of Regulatory Arbitrage (cont.)