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, noncumulative 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 offbalance 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
Equit
y
Precious
Metals
except gold
Other
Commoditie
s
<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
N
M
RWA   wi Li   w C j
i 1
On-balance sheet
items: principal
times risk weight
j 1
*
j
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
N
 max(V ,0)
j 1
j
• With netting exposure is
 N

max   V j ,0 
 j 1

• Net Replacement Ratio
Exposurewith Netting
NRR 
Exposurewithout Netting
Netting Calculations continued
• Credit equivalent amount modified from
N
[max(V ,0)  a L ]
j
j 1
j
j
• To
N
N
j 1
j 1
max(V j ,0)   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 A+ to
to
AAA-
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 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, Ti, to a
new variable Ui and assume
U i  ai F  1 a Z i
2
i
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)
The Model continued
U  a F 
i

Prob (U i  U F )  N 
2
 1  ai 
Hence
 N 1 Q (T )  a F 
i
i

Prob (Ti  T F )  N 
2


1  ai
Assuming the Q' s and a' s are the same for all companies
 N 1 Q(T )   F 
Prob (Ti  T F )  N 

1 


w here is the copula correlation
The Model continued
• The worst case default rate for portfolio for a
time horizon of T and a confidence limit of X is
 N 1[Q(T )]   N 1 ( X ) 

WCDR(T,X) N 

1




• 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
 N -1 ( PD)    N -1 (0.999) 
WCDR  N 

1 


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)  EADi  LGDi  WCDR
i
– 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
The Expected Loss and Capital
Requirements
• The expected loss from default is:
EL   EADi  LGDi  PD
i
• The capital requirement is worst case loss
minus the expected loss:
 EAD  LGD  (WCDR PD)
i
i
i
The Model Used by Regulators:
The loss probability density function and the
capital required by a financial institution
X% Worst
Case Loss
Expected
Loss
Required
Capital
Loss over time
horizon
0
1
2
3
4
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
 1  e 50PD 
1  e 50PD
50PD
ρ  0.12

0.24

1


0
.
12
[1

e
]

50
50 
1 e
1 e


PD
0.1%
0.5%
1.0%
1.5%
WCDR
3.4%
9.8%
14.0%
16.9% 19.0%
(For small firms  is reduced)
2.0%
Capital Requirements
Capital EAD LGD (WCDR P D) MA
where MA - - maturityadjustment
1  (M 2.5) b
MA 
1  1.5 b
where M is theeffectivematurityand
b  [0.11852 0.05478 ln(P D)]2
T herisk - weighted assets are12.5 timestheCapital
so thatCapital 8% of RWA
Retail Exposures
Capital EAD LGD  (WCDR  PD)
For residential mort gages  0.15
For revolvingretailexposures  0.04
For otherretailexposures
 1  e 35PD 
1  e 35PD
  0.03
 0.16 1 
35
35 
1 e
1

e


 0.03 0.13e -35PD
T hereis no distinction between Foundationand AdvancedIRB approaches.
BanksestimatePD, 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 subadditive.
• “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 (AIRB): 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:
σ  w' Σw
2
• 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 Valueat-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.)