Transcript Basel Accords
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) <1 1 to 5 >5 Interest rate 0.0
0.5
1.5
Exch Rate and Gold 1.0
5.0
7.5
Equit y 6.0
8.0
10.0
Precious Metals except gold 7.0
7.0
6.0
Other Commoditie s 10.0
12.0
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
RWA
i N
1
w i L i
j M
1
w
*
C j j
On-balance sheet items: principal times risk weight Off-balance sheet items: credit equivalent amount times risk weight For a derivative
C j
= max(
V j
,0) +
a j L j
value,
L j
is principal and
a j
where is add-on factor
V j
is
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
j N
1 max(
V j
, 0 ) •
With netting exposure is
max
j N
1
V j
, 0 •
Net Replacement Ratio
NRR Exposure with Netting Exposure without Netting
Netting Calculations continued
•
Credit equivalent amount modified from
j N
1 [max(
V j
, 0 )
a j L j
] •
To
max(
j N
1
V j
, 0 )
j N
1
a j L j
( 0 .
4 0 .
6 NRR )
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
k
VaR SRC •
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
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) + 1.06
w(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 Requirements
Standardized Approach Bank and corporations treated similarly (unlike Basel I) Rating AAA to AA A+ to A 0% 20% BBB+ to BBB 50% BB+ to BB B+ to B 100% 100% Below B Unrated 150% 100% Country Banks 20% 50% 50% 100% 100% 150% 50% Corporates 20% 50% 100% 100% 150% 150% 100%
•
New Capital Requirements
IRB 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, T
i
, to a new variable U
i
and assume
U i
a i F
1
a i
2
Z i
• •
where F and the Z
i
have independent standard normal distributions Define Q
i
of T
i
as the cumulative probability distribution Prob(U
i
i
i
(T)
The Model
continued
Prob (
U i
U F
)
N
U
1
a i F a i
2 Hence Prob (
T i
T F
)
N
N
1
Q i
(
T
)
a i F
1
a i
2 Assuming the
Q
' s and
a
' s are the same for all companies Prob (
T i
T F
)
N
N
1 where is the copula correlatio n
Q
(
T
1 )
F
The Model
continued
•
The worst case default rate for portfolio for a time horizon of T and a confidence limit of X is
WCDR(T,X)
N N
1 [
Q
(
T
)] 1
N
1 (
X
) •
The VaR for this time horizon and confidence limit is
VaR
(
T
,
X
)
L
( 1
R
)
WCDR
(
T
,
X
)
where L is loan principal and R is recovery rate
Key Model in Basel II IRB (Gaussian Copula)
•
The 99.9% worst case default rate is
WCDR
N
N -
1 (
PD
) 1
N -
1 ( 0
.
999 )
PD – probability of default
•
We are 99.9% certain not to exceed WCRD next year
The Loss on the Portfolio
•
There is 99.9% chance that the loss on the portfolio will be less than
VaR
( 99 .
99 %, 1 year) – i EAD i LGD i WCDR
EAD i – 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
The Expected Loss and Capital Requirements
•
The expected loss from default is:
EL i EAD i LGD i PD •
The capital requirement is worst case loss minus the expected loss:
i EAD i LGD i (WCDR PD)
The Model Used by Regulators
: The loss probability density function and the capital required by a financial institution
X
% Worst
Numerical Results for WCDR
=0.0
=0.2
=0.4
=0.6
=0.8
PD
=0.1%
PD
=0.5%
PD
=1%
PD
=1.5%
PD
=2% 0.1% 0.5% 2.8% 9.1% 7.1% 13.5% 23.3% 21.1% 38.7% 66.3% 1.0% 14.6% 31.6% 54.2% 83.6% 1.5% 18.9% 39.0% 63.8% 90.8% 2.0% 22.6% 44.9% 70.5% 94.4%
Dependence of
on PD
•
For corporate, sovereign and bank exposure
ρ 0.12
1 1 e 50 PD e 50 0.24
1 1 e 50 PD 1 e 50 0 .
12 [1 e 50 PD ]
PD WCDR
0.1% 3.4% 0.5% 9.8% 1.0% 14.0% 1.5% 2.0% 16.9% 19.0% (For small firms
is reduced)
Capital Requirements
Capital EAD LGD (WCDR PD) MA where MA maturity MA 1 (M 2.5) 1 1.5
b b adjustment where
M
is the effective maturity and b [0.11852
0.05478
ln(PD)] 2 The risk so that weighted assets are 12.5
times the Capital Capital 8% of RWA
Retail Exposures
Capital
EAD
LGD
(
WCDR
PD
) For residentia For revolving l mortgages 0.15
retail exposures 0.04
For other retail exposures 0 .
03 1 1
e
35
PD e
35 0.16
1 1
e
35
PD
1
e
35 0.03
0
.
13
e -
35
PD
There is no distinctio n between Foundation and Advanced IRB approaches .
Banks estimate PD, LGD, and EAD in both cases
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=2 10 = 1024 normalized assets Portfolio P: w = 1/n, mean 0, variance =
σ 2
Expected loss:
w' Σw •
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).
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
×
PD g where PD g probability of default of guarantor is
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.