Bank Regulation and
Basel I, II, III
Chapter 7
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.1
Why regulate bank capital
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Goal: to provide reliable banking system where
bank failures are rare and depositors are
protected
Crash of 1929/FDIC/Glass-Steagall Act
The ability of a bank to absorb unexpected
losses dependent on equity and other forms of
capital
Capital should cover the difference between
expected losses and “worst-case losses”
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.2
The Model used by Regulators
(Figure 7.1, page 166)
X% Worst
Case Loss
Expected
Loss
Required
Capital
Loss over time
horizon
0
1
2
3
4
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.3
Why regulate bank capital
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Competition: insurance/banks/securities firms –
regulatory arbitrage
CRD – EU Capital Requirements Directive
Is bank regulation unnecessary?
Sistemic risk – “ripple effect”
Deposit insurance – moral hazard?
Therefore: necessary to combine deposit
insurance with regulations on the capital banks
must hold
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.4
History of Bank Regulation
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Pre-1988
1988: BIS Accord (Basel I)
1995: netting
1996: Amendment to BIS Accord
1999: Basel II first proposed
2006: Basel II
2009: Basel 2.5
2010: Basel III
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.5
Pre-1988
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Banks were regulated using balance sheet measures
such as capital : assets (capital to total assets)
Definitions of capital and required ratios varied from
country to country (posibility for “regulatory arbitrage”)
Enforcement of regulations varied from country to
country
Bank transactions became more complicated. Bank
leverage increased in 1980s.
Off-balance sheet derivatives trading increased
Total assets was no longer a good indicator of the total
risk being taken.
Basel Committee on Bank Supervision set up
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.6
1988: BIS Accord – Basel I
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First standard: Assets/Capital must be less
than 20. Assets includes off-balance sheet
items that are direct credit substitutes such
as letters of credit and guarantees
Second standard: Cooke Ratio: Capital
must be 8% of risk weighted assets. At
least 50% of capital must be Tier 1.
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.7
Basel I: Risk Weights
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.8
Risk-Weighted Capital
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A risk weight is applied to each on-balancesheet 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.)
N
RWA   i Li
i 1

N - number of on-balance-sheet items, Li –
principal amount of the ith item, ωi – risk weight
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.9
Risk-Weighted Capital
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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
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sum of risk weight times asset amount for onbalance sheet items
Sum of risk weight times credit equivalent
amount for off-balance sheet items
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.10
Credit Equivalent Amount
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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)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.11
Add-on Factors (% of Principal)
Table 7.2, page171
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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.12
The Math
N
M
RWA   i Li    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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.13
Risk-weighted assets
N
i Li
For on-ballance-sheet items, Example 7.1
i 1
For off-balance-sheet items we use credit equivalent amount (Cj).
For an OTC derivative, (Cj) is:
max V , 0  aL
Example 7.2
Total risk-weighted assets for a bank with N on-balance-sheet and
M off-balance sheet items
N
M
 L   C
i 1
i
i
i 1

j
j
Example 7.3
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.14
Types of Capital (page 172)
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Tier 1 Capital: common equity, noncumulative perpetual preferred shares,
less goodwill
Tier 2 Capital: cumulative perpetual
preferred stock, certain types of 99-year
debentures, subordinated debt with an
original life of more than 5 years
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.15
G-30 Policy Recommendations
(page 172-3)
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Influential publication from derivatives
dealers, end users, academics,
accountants, and lawyers
20 recommendations published in 1993
Report itself is not a regulatory document
but has been very influential in the
development of risk managment practices.
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.16
Netting (page 174-5)
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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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.17
Netting Calculations
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Without netting exposure is
N
 max(V ,0)
j 1

j
With netting exposure is
 N

max   V j ,0 
 j 1

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Net replacement ratio
NRR 
Exposurewith Netting
Exposurewithout Netting
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.18
Netting Calculations continued
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Credit equivalent amount modified from
N
[max(V ,0)  a L ]
j 1

j
j
j
To
N
N
j 1
j 1
max(V j ,0)   a j L j (0.4  0.6  NRR)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.19
1996 Amendment (page 176)
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Implemented in 1998
Distinguishes between bank’s trading book
and banking book
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)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.20
The Market Risk Capital
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Standardized approach
Internal Model Based Approach – IMBA
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VaR
Benefit of diversification
Total capital = 0,08 x (Credit risk RWA + Market risk RWA)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.21
The Market Risk Capital
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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 (primarily for debt
securities held in trading book)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.22
Basel II
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Implemented in 2007
Three pillars
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New minimum capital requirements for credit
and operational risk
Supervisory review: more thorough and
uniform
Market discipline: more disclosure
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.23
New Capital Requirements
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Risk weights will be based on 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
Total capital = 0,08 x (Credit risk RWA + Market risk RWA
+ Operational risk RWA)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.24
USA vs European Implementation
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In US Basel II will apply 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 banks
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.25
Basel II Credit Risk
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Standardized Approach
Foundation IRB
Advanced IRB
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.26
New Capital Requirements
Standardized Approach, Table 7.4, page 180
Banks counterparties are treated similarly to corporations. Under Basel
I corporations are assumed to be substantially less creditworthy
Rating
AAA
A+ to A- BBB+ to BB+ to
to AABBBBB-
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%
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.27
Adjustments for Collateral
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Two approaches
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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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.28
New Capital Requirements
IRB Approach for corporate, banks and sovereign
exposures
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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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.29
Key Model (Gaussian Copula)
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The 99.9% worst case default rate is
 N -1 ( PD)    N -1 (0.999) 
WCDR  N 

1 


Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.30
Numerical Results for WCDR
Table 7.5, page 183
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%
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.31
IRB approach
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In a general portfolio of loans, there is a 99,9%
chance that the total loss will be less than the
sum of
EAD  LGD  WCDR
for the individal loans
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.32
Corporate, Sovereign and Bank
Exposures
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Capital required:
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EAD x LGD x (WCDR – PD) x MA
MA – Maturity adjustment is designed to allow
for the fact if an instrument lasts longer than one
year, there is a one-year credit exposure arising
from a possible decline in the creditworthiness of
the counterparty
RWA = 12.5 x EAD x LGD x (WCDR – PD) x MA
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.33
Retail Exposures
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Capital required:
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EAD x LGD x (WCDR – PD)
RWA = 12.5 x EAD x LGD x (WCDR – PD)
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.34
Credit Risk Mitigants
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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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.35
Guarantees
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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
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.36
Operational Risk Capital
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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.
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.37
PILLAR II: Supervisory Review
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Banks should have a process for assesing their overall
capital adequacy in relation to their risk profile
Supervisors should review and evaluate bank’s internal
capital adequacy assesments and strategies
Supervisors should have the ability to require banks to
hold capital in excess of minimum regulatory
requirement
Similar amount of thoroughness in different countries
Local regulators can adjust parameters to suit local
conditions
Importance of early intervention stressed
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.38
PILLAR II: particular attention
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Interest rate risk in the banking book
Credit risk
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stress tests used,
default definitions used,
credit risk concentration,
risks associated with the use of colateral,
guarantees, and credit derivatives
Operational risk
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.39
PILLAR III: Market Discipline
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To encourage banks to increase disclosure of
risk assessment procedures and capital
adequacy
Banks will be required to disclose
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Scope and application of Basel framework within the
banking group
Nature and components of capital (Tier 1, 2, 3)
Capital requirements for credit, market, op. risk
Nature of institution’s risk exposures
Structure of the risk management function and how it
operates
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.40
Basel III : Capital
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Quality – min 4,5% equity
Capital loss absorption at the point of nonviability
Capital conservation buffer – 2,5% equity
Countercyclical buffer – up to 2,5%
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.41
Basel III: Risk Coverage
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Securitization
Trading book
Counterparty credit risk
Bank exposure to central counterparties
(CCPs)
SIFIs: progressive Common Equity Tier 1
capital 1% - 2,5%
Leverage ratio
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.42
Basel III: Liquidity
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Liquidity coverage ratio (LCR): sufficient
high liquidity to sustain 30 day stress
scenario
Net stable funding ration (NSFR): longer
term structural ratio designed to address
liquidity mismatches.
Risk Management and Financial Institutions, Chapter 7, Copyright © John C. Hull 2006
7.43