Risk Management & Banks Analytics &

Information Requirement
By
A.K.Nag
To-days Agenda
Risk Management and Basel II- an overview
Analytics of Risk Management
Information Requirement and the need for
building a Risk Warehouse
Roadmap for Building a Risk Warehouse

Intelligent management of risk
will be the foundation of a
successful financial institution
In the future . . .
Concept of Risk
Statistical Concept
Financial concept
Statistical Concept
We have data x from a sample space .
Model- set of all possible pdf of indexed by .
Observe x then decide about . So have a decision
rule.
Loss function L(,a): for each action a in A.
A decision rule-for each x what action a.
A decision rule (x)- the risk function is defined
as R(, ) =E

L(, (x)).
For a given , what is the average loss that will be
incurred if the decision rule (x) is used
Statistical Concept- contd.
We want a decision rule that has a small expected
loss
If we have a prior defined over the parameter
space of , say () then Bayes risk is defined as
B(, )=E

(R(, ))
Financial Concept
We are concerned with L(,a). For a given
financial asset /portfolio what is the amount we
are likely to loose over a time horizon with what
probability.
Financial
Risks
Operational Risk
Market Risk
Credit Risk

Types of Financial Risks
Risk is multidimensional
Hierarchy of Financial Risks
Portfolio
Concentration
Risk
Transaction Risk
Counterparty
Risk
Issuer Risk
Trading Risk
Gap Risk
Equity Risk
Interest Rate Risk
Currency Risk
Commodity Risk
Financial
Risks
Operational
Risk
Market Risk
Credit Risk
Specific
Risk
General
Market
Risk
Issue Risk
* From Chapter-1, Risk Management by Crouhy, Galai and Mark
Response to Financial Risk
Market response-introduce new products
Equity futures
Foreign currency futures
Currency swaps
Options
Regulatory response
Prudential norms
Stringent Provisioning norms
Corporate governance norms
Evolution of Regulatory environment
G-3- recommendation in 1993
20 best practice price risk management
recommendations for dealers and end-users of
derivatives
Four recommendations for legislators, regulators and
supervisors
1988 BIS Accord
1996 ammendment
BASELII
BASEL-I
Two minimum standards
Asset to capital multiple
Risk based capital ratio (Cooke ratio)
Scope is limited
Portfolio effects missing- a well diversified portfolio is
much less likely to suffer massive credit losses
Netting is absent
No market or operational risk


BASEL-I contd..
Calculate risk weighted assets for on-balance sheet
items
Assets are classified into categories
Risk-capital weights are given for each category
of assets
Asset value is multiplied by weights
Off-balance sheet items are expressed as credit
equivalents
Minimum
Capital
Requirement
Three Basic Pillars
Supervisory
Review Process
Market
Discipline
Requirements
The New Basel Capital Accord
Standardized
Internal Ratings
Credit Risk Models
Credit Mitigation
Market Risk
Credit Risk
Other Risks
Risks
Trading Book
Banking Book
Operational
Other
Minimum Capital Requirement
Pillar One
Workhorse of Stochastic Process
Markov Process
Weiner process (dz)
Change z during a small time period(t) is z=(t)
z for two different short intervals are independent
Generalized Wiener process
dx=adt+bdz
Ito process
dx=a(x,t)+b(x,t)dz
Itos lemma
dG=(G/x*a+G/t+1/2*
2
G/
2
x
2
*b
2)
dt
+
G/x*b*dz
Credit Risk
1. Minimum Capital Requirements- Credit
Risk (Pillar One)
Standardized approach
(External Ratings)
Internal ratings-based approach
Foundation approach
Advanced approach
Credit risk modeling
(Sophisticated banks in the future)
Minimum
Capital
Requirement
Evolutionary Structure of the Accord
Credit Risk Modeling ?
Standardized Approach
Foundation IRB Approach
Advanced IRB Approach
Standardized Approach

Provides Greater Risk Differentiation than 1988
Risk Weights based on external ratings
Five categories [0%, 20%, 50%, 100%, 150%]
Certain Reductions
e.g. short term bank obligations
Certain Increases
e.g.150% category for lowest rated obligors
The New Basel Capital Accord
Standardized Approach
External Credit
Assessments
Sovereigns Corporates
Public-Sector
Entities
Banks/Securities
Firms
Asset
Securitization
Programs
Based on assessment of external credit assessment
institutions
Option 2
2

Assessment
Claim
AAA to
AA-
A+ to A- BBB+ to
BBB-
BB+ to
B-
Below B- Unrated
Sovereigns 0% 20% 50% 100% 150% 100%
20% 50% 50% 100% 150%
100%
Banks
Option 1
1
20% 50%
3
100%
3
100%
3
150%
50%
3
Corporates 20% 100% 100% 100% 150% 100%
1
Risk weighting based on risk weighting of sovereign in which the bank is incorporated.
2
Risk weighting based on the assessment of the individual bank.
3
Claims on banks of a short original maturity, for example less than six months,
would receive a weighting that is one category more favourable than the usual risk
weight on the banks claims
.
Standardized Approach:
New Risk Weights (June 1999)
Option 2
2

Assessment
Claim
AAA to
AA-
A+ to A- BBB+ to
BBB-
BB+ to
BB- (B-)
Below BB-
(B-)
Unrated
Sovereigns 0% 20% 50% 100% 150% 100%
20% 50%
50%
100% 150%
100%
Banks
Option 1
1
20% 50%
3
100%
3
100%
3
150%
50%
3
Corporates 20%
50%(100%)
100% 100% 150% 100%
1
Risk weighting based on risk weighting of sovereign in which the bank is incorporated.
2
Risk weighting based on the assessment of the individual bank.
3
Claims on banks of a short original maturity, for example less than six months,
would receive a weighting that is one category more favourable than the usual risk
weight on the banks claims
.
Standardized Approach:
New Risk Weights (January 2001)
Pillar 1
Internal Ratings-Based Approach
Two-tier ratings system:
Obligor rating
represents probability of default by a borrower
Facility rating
represents expected loss of principal and/or interest

98 Rules
Internal
Model
Standardized
Model
Capital
Market
Credit
Opportunities for a
Regulatory Capital Advantage
Example: 30 year Corporate Bond
Standardized Approach
0
1.6
8
16
PER CENT
A
A
A

A
A

A
+

A
-

B
B
B

B
B
+

B
B
-

B

C
C
C

RATING
New standardized model
Internal rating system & Credit VaR
12
1 2 3 4 4.5 5 5.5 6 7 6.5
S & P :

Internal Model- Advantages
Example:
Portfolio of
100 $1 bonds
diversified
across
industries
Capital charge for specific risk (%)

Internal
model

Standardized
approach

AAA

0.26

1.6

AA

0.77

1.6

A

1.00

1.6

BBB

2.40

1.6

BB

5.24

8

B

8.45

8

CCC

10.26

8

Three elements:
Risk Components [PD, LGD, EAD]
Risk Weight conversion function
Minimum requirements for the management of policy
and processes
Emphasis on full compliance

Definitions;
PD = Probability of default [conservative view of long run average (pooled) for borrowers assigned to a RR grade.]
LGD = Loss given default
EAD = Exposure at default
Note: BIS is Proposing 75% for unused commitments
EL = Expected Loss
Internal Ratings-Based Approach
Risk Components

Foundation Approach
PD set by Bank
LGD, EAD set by Regulator
50% LGD for Senior Unsecured
Will be reduced by collateral (Financial or Physical)

Advanced Approach
PD, LGD, EAD all set by Bank
Between 2004 and 2006: floor for advanced
approach @ 90% of foundation approach

Notes
Consideration is being given to incorporate maturity explicitly into the Advancedapproach
Granularity adjustment will be made. [not correlation, not models]
Will not recognize industry, geography.
Based on distribution of exposures by RR.
Adjustment will increase or reduce capital based on comparison to a reference portfolio
[different for foundation vs. advanced.]

Internal Ratings-Based Approach
Expected Loss Can Be Broken Down Into Three Components

EXPECTED
LOSS

Rs.
=

Probability of
Default
(PD)
%
x

Loss Severity
Given Default
(Severity)
%

Loan Equivalent
Exposure
(Exposure)
Rs
x
The focus of grading tools is on modeling PD
What is the probability
of the counterparty
defaulting?
If default occurs, how
much of this do we
expect to lose?
If default occurs, how
much exposure do we
expect to have?
Borrower Risk Facility Risk Related
Credit or Counter-party Risk
Credit risk arises when the counter-party to a financial
contract is unable or unwilling to honour its obligation. It
may take following forms
Lending risk- borrower fails to repay interest/principal. But more
generally it may arise when the credit quality of a borrower
deteriorates leading to a reduction in the market value of the loan.
Issuer credit risk- arises when issuer of a debt or equity security
defaults or become insolvent. Market value of a security may
decline with the deterioration of credit quality of issuers.
Counter party risk- in trading scenario
Settlement risk- when there is a one-sided-trade
Credit Risk Measures
Credit risk is derived from the probability distribution of
economic loss due to credit events, measured over some
time horizon, for some large set of borrowers. Two
properties of the probability distribution of economic loss
are important; the expected credit loss and the unexpected
credit loss. The latter is the difference between the
potential loss at some high confidence level and expected
credit loss. A firm should earn enough from customer
spreads to cover the cost of credit. The cost of credit is
defined as the sum of the expected loss plus the cost of
economic capital defined as equal to unexpected loss.
Contingent claim approach
Default occurs when the value of a companys
asset falls below the value of outstanding debt
Probability of default is determined by the
dynamics of assets.
Position of the shareholders can be described as
having call option on the firms asset with a strike
price equal to the value of the outstanding debt.
The economic value of default is presented as a
put option on the value of the firms assets.
Assumptions in contingent claim
approach
The risk-free interest rate is constant
The firm is in default if the value of its assets falls
below the value of debt.
The default can occur only at the maturity time of
the bond
The payouts in case of bankruptcy follow strict
absolute priority
Shortcoming of Contingent claim
approach
A risk-neutral world is assumed
Prior default experience suggests that a firm
defaults long before its assets fall below the value
of debt. This is one reason why the analytically
calculated credit spreads are much smaller than
actual spreads from observed market prices.
KMV Approach
KMV derives the actual individual probability of
default for each obligor , which in KMV
terminology is then called expected default
frequency or EDF.
Three steps
Estimation of the market value and the volatility of the
firms assets
Calculation of the distance-to-default (DD) which is an
index measure of default risk
Translation of the DD into actual probability of default
using a default database.
An Actuarial Model: CreditRisk+
The derivation of the default loss distribution in
this model comprises the following steps
Modeling the frequencies of default for the portfolio
Modeling the severities in the case of default
Linking these distributions together to obtain the
default loss distribution
The CreditMetrics Model
Step1 Specify the transition matrix
Step2-Specify the credit risk horizon
Step3-Specify the forward pricing model
Step4 Derive the forward distribution of the
changes in portfolio value

IVaR and DVaR
IVaR-incremental vaR -it measures the
incremental impact on the overall VaR of the
portfolio of adding or eliminating an asset
I is positive when the asset is positively correlated with
the rest of the portfolio and thus add to the overall risk
It can be negative if the asset is used as a hedge against
existing risks in the portfolio
DeltaVaR(DVaR) - it decomposes the overall risk
to its constituent assetss contribution to overall
risk
Information from Bond Prices
Traders regularly estimate the zero curves for
bonds with different credit ratings
This allows them to estimate probabilities of
default in a risk-neutral world
Typical Pattern
(See Figure 26.1, page 611)
Spread
over
Treasuries
Maturity
Baa/BBB
A/A
Aa/AA
Aaa/AAA
The Risk-Free Rate
Most analysts use the LIBOR rate as the risk-free
rate
The excess of the value of a risk-free bond over a
similar corporate bond equals the present value of
the cost of defaults

Example (Zero coupon rates; continuously
compounded)

Maturity
(years)
Risk-free
yield
Corporate
bond yield
1 5% 5.25%
2 5% 5.50%
3 5% 5.70%
4 5% 5.85%
5 5% 5.95%
Example continued
One-year risk-free bond (principal=1) sells for

One-year corporate bond (principal=1) sells for

or at a 0.2497% discount
This indicates that the holder of the corporate bond expects
to lose 0.2497% from defaults in the first year

e

=
0 05 1
0951229
.
.
e

=
0 0525 1
0948854
.
.
Example continued
Similarly the holder of the corporate bond expects
to lose


or 0.9950% in the first two years
Between years one and two the expected loss is
0.7453%

e e
e

=
0 05 2 0 0550 2
0 05 2
0009950
. .
.
.
Example continued
Similarly the bond holder expects to lose 2.0781%
in the first three years; 3.3428% in the first four
years; 4.6390% in the first five years
The expected losses per year in successive years
are 0.2497%, 0.7453%, 1.0831%, 1.2647%, and
1.2962%
Summary of Results
(Table 26.1, page 612)
Maturity
(years)
Cumul. Loss.
%
Loss
During Yr (%)
1 0.2497 0.2497
2 0.9950 0.7453
3 2.0781 1.0831
4 3.3428 1.2647
5 4.6390 1.2962


Recovery Rates
(Table 26.3, page 614. Source: Moodys Investors Service, 2000)
Class Mean(%) SD (%)
Senior Secured 52.31 25.15
Senior Unsecured 48.84 25.01
Senior Subordinated 39.46 24.59
Subordinated 33.71 20.78
Junior Subordinated 19.69 13.85


Probability of Default Assuming No
Recovery
T T y T y
T T y
T T y T T y
e T Q
or
e
e e
T Q
)] ( ) ( [
) (
) ( ) (
*
*
*
1 ) (
) (

=
Where y(T): yield on a T-year corporate zero-coupon bond
Y
*
(T): Yield on a T-year risk free zero coupon bond
Q(T): Probability that a corporation would default between time zero and T
Probability of Default

0.025924 and 0.025294, 0.021662, 0.014906,
0.004994, are 5 and 4, , 3 2, 1, years in default of
ies probabilit example, our in 0.5 Rate Rec If
Rate Rec. - 1
Loss% Exp.
Def of Prob
Loss% Exp. Rate) Rec. - (1 Def. of Prob.
=
=
=
Large corporates and specialised lending
Characteristics of these sectors
Relatively large exposures to individual obligors
Qualitative factors can account for more than 50% of the risk of obligors
Scarce number of defaulting companies
Limited historical track record from many banks in some sectors

Statistical models are NOT applicable in these sectors:
Models can severely underestimate the credit risk profile of obligors given the low
proportion of historical defaults in the sectors.
Statistical models fail to include and ponder qualitative factors.
Models results can be highly volatile and with low predictive power.

To build an internal rating system for Basel II you need:
1. Consistent rating methodology across asset classes
2. Use an expected loss framework
3. Data to calibrate Pd and LGD inputs
4. Logical and transparent workflow desk-top application
5. Appropriate back-testing and validation.

Six Organizational Principles for
Implementing IRB Approach
All credit exposures have to be rated.
The credit rating process needs to be segregated from the loan
approval process
The rating of the customer should be the sole determinant of all
relationship management and administration related activities.
The rating system must be properly calibrated and validated
Allowance for loan losses and capital adequacy should be
linked with the respective credit rating
The rating should recognize the effect of credit risk mitigation
techniques
Credit Default Correlation
The credit default correlation between two
companies is a measure of their tendency to
default at about the same time
Default correlation is important in risk
management when analyzing the benefits of credit
risk diversification
It is also important in the valuation of some credit
derivatives
Measure 1
One commonly used default correlation measure
is the correlation between
1. A variable that equals 1 if company A defaults
between time 0 and time T and zero otherwise
2. A variable that equals 1 if company B defaults
between time 0 and time T and zero otherwise
The value of this measure depends on T. Usually
it increases at T increases.
Measure 1 continued
Denote Q
A
(T) as the probability that company A
will default between time zero and time T, Q
B
(T)
as the probability that company B will default
between time zero and time T, and P
AB
(T) as the
probability that both A and B will default. The
default correlation measure is

] ) ( ) ( ][ ) ( ) ( [
) ( ) ( ) (
) (
2 2
T Q T Q T Q T Q
T Q T Q T P
T
B B A A
B A AB
AB


= |
Measure 2
Based on a Gaussian copula model for time to default.
Define t
A
and t
B
as the times to default of A and B
The correlation measure,
AB
, is the correlation between
u
A
(t
A
)=N
-1
[Q
A
(t
A
)]
and
u
B
(t
B
)=N
-1
[Q
B
(t
B
)]
where N is the cumulative normal distribution function


Use of Gaussian Copula
The Gaussian copula measure is often used in
practice because it focuses on the things we are
most interested in (Whether a default happens and
when it happens)

Suppose that we wish to simulate the defaults for
n companies . For each company the cumulative
probabilities of default during the next 1, 2, 3, 4,
and 5 years are 1%, 3%, 6%, 10%, and 15%,
respectively
Use of Gaussian Copula continued
We sample from a multivariate normal distribution
for each company incorporating appropriate
correlations
N
-1
(0.01) = -2.33, N
-1
(0.03) = -1.88,
N
-1
(0.06) = -1.55, N
-1
(0.10) = -1.28,
N
-1
(0.15) = -1.04
Use of Gaussian Copula continued
When sample for a company is less than
-2.33, the company defaults in the first year
When sample is between -2.33 and -1.88, the company defaults in the
second year
When sample is between -1.88 and -1.55, the company defaults in the
third year
When sample is between -1,55 and -1.28, the company defaults in the
fourth year
When sample is between -1.28 and -1.04, the company defaults during
the fifth year
When sample is greater than -1.04, there is no default during the first
five years
Measure 1 vs Measure 2



normal te multivaria be to assumed be can times survival d transforme
because considered are companies many when use to easier much is It
1. Measure than higher tly significan usually is 2 Measure
function. on distributi
y probabilit normal bivariate cumulative the is where
and
: versa vice and 2 Measure from calculated be can 1 Measure
M
T Q T Q T Q T Q
T Q T Q T u T u M
T
T u T u M T P
B B A A
B A AB B A
AB
AB B A AB
] ) ( ) ( ][ ) ( ) ( [
) ( ) ( ] ); ( ), ( [
) (
] ); ( ), ( [ ) (
2 2


= |
=
Modeling Default Correlations

Two alternatives models of default correlation are:
Structural model approach
Reduced form approach

Market Risk
Market Risk
Two broad types- directional risk and relative
value risk. It can be differentiated into two related
risks- Price risk and liquidity risk.
Two broad type of measurements
scenario analysis
statistical analysis
Scenario Analysis
A scenario analysis measures the change in market
value that would result if market factors were
changed from their current levels, in a particular
specified way. No assumption about probability of
changes is made.
A Stress Test is a measurement of the change in
the market value of a portfolio that would occur
for a specified unusually large change in a set of
market factors.
Value at Risk
A single number that summarizes the likely loss in
value of a portfolio over a given time horizon with
specified probability
C-VaR- Expected loss conditional on that the
change in value is in the left tail of the distribution
of the change.
Three approaches
Historical simulation
Model-building approach
Monte-Carlo simulation

Historical Simulation
Identify market variables that determine the
portfolio value
Collect data on movements in these variables for a
reasonable number of past days.
Build scenarios that mimic changes over the past
period
For each scenario calculate the change in value of
the portfolio over the specified time horizon
From this empirical distribution of value changes
calculate VaR.
Model Building Approach
Consider a portfolio of n-assets
Calculate mean and standard deviation of change
in the value of portfolio for one day.
Assume normality
Calculate VaR.
Monte Carlo simulation
Calculate the value the portfolio today
Draw samples from the probability distribution of
changes of the market variables
Using the sampled changes calculate the new
portfolio value and its change
From the simulated probability distribution of
changes in portfolio value calculate VaR.

Pitfalls- Normal distribution based VaR
Normality assumption may not be valid for tail
part of the distribution
VaR of a portfolio is not less than weighted sum
of VaR of individual assets ( not sub-additive). It
is not a coherent measure of Risk.
Expected shortfall conditional on the fact that loss
is more than VaR is a sub-additive measure of
risk.
VaR
VaR is a statistical measurement of price risk.
VaR assumes a static portfolio. It does not take
into account
The structural change in the portfolio that would
contractually occur during the period.
Dynamic hedging of the portfolio
VaR calculation has two basic components
simulation of changes in market rates
calculation of resultant changes in the portfolio value.
VaR (Value-at-Risk) is a measure of the risk in a portfolio
over a (usually short) period of time.
It is usually quoted in terms of a time horizon, and a
confidence level.
For example, the 10 day 95% VaR is the size of loss X that
will not happen 95% of the time over the next 10 days.
5%
95%
(Profit/Loss Distribution)
X
Value-at-Risk
Standard Value-at-Risk Levels:
Two standard VaR levels are 95% and 99%.
When dealing with Gaussians, we have:
mean
95% is 1.645 standard deviations from the mean
95%
1.645o
99% is 2.33 standard deviations from the mean
99%
2.33o
Standard Value at Risk Assumptions:
1) The percentage change (return) of assets is Gaussian:
This comes from:
Sdz Sdt dS o + =
dz dt
S
dS
o + =
or
So approximately:
z t
S
S
A + A =
A
o
which is normal
Standard Value at Risk Assumptions:
2) The mean return is zero:
This comes from an order argument on: z t
S
S
A + A =
A
o
The mean is of order At.
) ( ~ t O t A A
The standard deviation is of order square root of Dt.
) ( ~
2 / 1
t O z A A o
Time is measured in years, so the change in time is
usually very small. Hence the mean is negligible.
z S S A = A o
VaR and Regulatory Capital
Regulators require banks to keep capital for market
risk equal to the average of VaR estimates for past 60
trading days using X=99 and N=10, times a
multiplication factor.
(Usually the multiplication factor equals 3)

Advantages of VaR
It captures an important aspect of risk
in a single number
It is easy to understand
It asks the simple question: How bad can things
get?
Daily Volatilities
In option pricing we express volatility as volatility
per year
In VaR calculations we express volatility as
volatility per day

year year
year
day
o o
o
o ~ = = % 6 063 . 0
252
Daily Volatility continued
Strictly speaking we should define o
day
as the
standard deviation of the continuously compounded
return in one day
In practice we assume that it is the standard deviation
of the proportional change in one day
IBM Example
We have a position worth $10 million in IBM
shares
The volatility of IBM is 2% per day (about 32%
per year)
We use N=10 and X=99
IBM Example continued
The standard deviation of the change in the
portfolio in 1 day is $200,000
The standard deviation of the change in 10 days is

200 000 10 456 , $632, =
IBM Example continued
We assume that the expected change in the value of
the portfolio is zero (This is OK for short time
periods)
We assume that the change in the value of the
portfolio is normally distributed
Since N(0.01)=-2.33, (i.e. Pr{Z<-2.33}=0.01)
the VaR is
2 33 632 456 473621 . , $1, , =
AT&T Example
Consider a position of $5 million in AT&T
The daily volatility of AT&T is 1% (approx 16%
per year)
The S.D per 10 days is

The VaR is


50 000 10 144 , $158, =
158114 233 405 , . $368, =
The change in the value of a portfolio:
Let x
i
be the dollar amount invested in asset i, and let r
i

be the return on asset i over the given period of time.

= A
i
i i
r x P
Then the change in the value of a portfolio is:
But, each r
i
is Gaussian by assumption:
i
i
i
i
z
S
S
r A =
A
= o
Hence, AP is Gaussian.
) , 0 ( ~ x x N r x P
T T
E = A
where
(
(
(

=
n
x
x
x
1
| |
T
rr E = E
(
(
(

=
n
r
r
r
1
Example:
Returns of IBM and AT&T have bivariate normal distribution
with correlation of 0.7.
Volatilities of daily returns are 2% for IBM and 1% for AT&T.
$10 million of IBM
$5 million of AT&T
Consider a portfolio of:
T AT IBM
T
r r r x P
&
5 10 + = = A
has daily variance:
0565 . 0
5
10
01 . 0 ) 02 . 0 )( 01 . 0 ( 7 . 0
) 02 . 0 )( 01 . 0 ( 7 . 0 02 . 0
5
10
2
2
=
(

T
Then
Example:
T AT IBM
T
r r r x P
&
5 10 + = = A
has daily variance:
0565 . 0
5
10
01 . 0 ) 02 . 0 )( 01 . 0 ( 7 . 0
) 02 . 0 )( 01 . 0 ( 7 . 0 02 . 0
5
10
2
2
=
(

T
Then
Now, compute the 10 day 95% and 99% VaR:
Since AP is Gaussian,
95% VaR = (1.645)0.7516= 1.24 million
99% VaR = (2.33)0.7516 = 1.75 million
The variance for 10 days is 10 times the variance for a day:
565 . 0 ) 0565 . 0 ( 10
2
10
= =
days
o 7516 . 0
10
=
days
o
VaR Measurement Steps based on EVT
Divide total time period into m blocks of equal
size
Compute n daily losses for each block
Calculate maximum losses for each block
Estimate parameters of the Asymptotic
distribution of Maximal loss
Choose the value of the probability of a maximal
loss exceeding VaR
Compute the VaR
Credit Risk Mitigation
Credit Risk Mitigation
Recognition of wider range of mitigants
Subject to meeting minimum requirements
Applies to both Standardized and IRB Approaches

Collateral Guarantees Credit Derivatives On-balance Sheet Netting
Credit Risk Mitigants
Collateral
Simple Approach
(Standardized only)
Comprehensive Approach
Two Approaches
Collateral
Comprehensive Approach
Haircuts
(H)
Weights
(W)
Coverage of residual risks through
Collateral
Comprehensive Approach
H - should reflect the volatility of the collateral

w - should reflect legal uncertainty and other residual
risks.
Represents a floor for capital requirements
Collateral Example
Rs1,000 loan to BBB rated corporate
Rs. 800 collateralised by bond
issued by AAA rated bank
Residual maturity of both: 2 years



Collateral Example
Simple Approach

Collateralized claims receive the risk weight
applicable to the collateral instrument, subject to a
floor of 20%
Example: Rs1,000 Rs.800 = Rs.200
Rs.200 x 100% = Rs.200
Rs.800 x 20% = Rs.160
Risk Weighted Assets: Rs.200+Rs.160 = Rs.360
Collateral Example Comprehensive
Approach
C = Current value of the collateral received (e.g.
Rs.800)
H
E
= Haircut appropriate to the exposure (e.g.= 6%)
H
C
= Haircut appropriate for the collateral received
(e.g.= 4%)
C
A
= Adjusted value of the collateral (e.g. Rs.770)



770 .
06 . 04 . 1
800
1
Rs
Rs
H H
C
C
C E
A
=
+ +
=
+ +
=
Collateral Example Comprehensive
Approach
Calculation of risk weighted assets based on following
formula:
r* x E = r x [E-(1-w) x C
A
]

Collateral Example Comprehensive
Approach
r* = Risk weight of the position taking into
account the risk reduction (e.g. 34.5%)
w
1
= 0.15
r = Risk weight of uncollateralized exposure
(e.g. 100%)
E = Value of the uncollateralized exposure
(e.g. Rs1000)
Risk Weighted Assets
34.5% x Rs.1,000 = 100% x [Rs1,000 - (1-0.15) x Rs.770]
= Rs.345

Note: 1 Discussions ongoing with BIS re double counting of w factor with Operational Risk
Collateral Example Comprehensive
Approach
Risk Weighted Assets
34.5% x Rs.1,000 = 100% x [Rs.1,000 - (1-0.15) x Rs.770] =
Rs.345

06 . 0 04 . 0 1
800 .
770 .
+ +
= =
Rs
Rs C
A
Note: comprehensive Approach saves
Collateral Example
Simple and Comprehensive Approaches
Approach Risk Weighted
Assets
Capital
Charge
No Collateral 1000 80.0
Simple 360 28.8
Comprehensive 345 27.6

Operational Risk

Operational Risk
Definition:
Risk of direct or indirect loss resulting from inadequate or
failed internal processes, people and systems of external events
Excludes Business Risk and Strategic Risk
Spectrum of approaches
Basic indicator - based on a single indicator
Standardized approach - divides banks activities into a number
of standardized industry business lines
Internal measurement approach
Approximately 20% current capital charge
CIBC Operational Risk Losses Types
1. Legal Liability:
inludes client, employee and other third party law suits

2 . Regulatory, Compliance and Taxation Penalties:
fines, or the cost of any other penalties, such as license revocations and associated costs - excludes lost /
forgone revenue.

3 . Loss of or Damage to Assets:
reduction in value of the firms non-financial asset and property

4 . Client Restitution:
includes restitution payments (principal and/or interest) or other compensation to clients.

5 . Theft, Fraud and Unauthorized Activities:
includes rogue trading

6. Transaction Processing Risk:
includes failed or late settlement, wrong amount or wrong counterparty

Operational Risk- Measurement
Step1- Input- assessment of all significant operational risks
Audit reports
Regulatory reports
Management reports
Step2-Risk assessment framework
Risk categories- internal dependencies-people, process and
technology- and external dependencies
Connectivity and interdependence
Change,complexity,complacency
Net likelihood assessment
Severity assessment
Combining likelihood and severity into an overall risk assessment
Defining cause and effect
Sample risk assessment report
Operational Risk- Measurement
Step3-Review and validation
Step4-output
Basic Indicator Loss Distribution
Rate
Base
Bank
|
1

EI
1

LOB1
|
2

EI
2

LOB2
LOB3
|
N

EI
N

LOBn
Bank
Expected
Loss
Loss
Catastrophic
Unexpected
Loss

Severe
Unexpected
Loss
Standardized
Standardized
Approach
Loss Distribution
Approach
The Regulatory Approach:Four
Increasingly Risk Sensitive Approaches



Bank
Internal Measurement Approach
Rate
1

Base
Rate
2

Base
Base
Rate
N

Base
Risk Type 6
Rate 1
EI
1

LOB1
Rate 2
EI
2

LOB2
Base
LOB3
Rate
N

EI
N

LOBn
Risk Type 1
Internal Measurement Approach

Rate of progression between stages based on necessity and capability
Risk Based/ less Regulatory Capital:
Operational Risk -
Basic Indicator Approach

Capital requirement = % of gross income

Gross income = Net interest income
+
Net non-interest income
Note: o supplied by BIS (currently o = 30%)

Proposed Operational Risk Capital Requirements
Reduced from 20% to 12% of a Banks Total Regulatory Capital
Requirement (November, 2001)

Based on a Banks Choice of the:

(a) Basic Indicator Approach which levies a single operational risk charge
for the entire bank

or

(b) Standardized Approach which divides a banks eight lines of business,
each with its own operational risk charge

or

(c) Advanced Management Approach which uses the banks own internal
models of operational risk measurement to assess a capital requirement

Operational Risk -
Standardized Approach
Banks activities are divided into standardized business
lines.
Within each business line:
specific indicator reflecting size of activity in that area
Capital charge
i
=
i
x exposure indicator
i

Overall capital requirement =
sum of requirements for each business line

Operational Risk -
Standardized Approach
Business Lines Exposure Indicator (EI) Capital
Factors
1
Corporate Finance Gross Income |
1
Trading and Sales Gross Income (or VaR) |
2
Retail Banking Annual Average Assets |
3
Commercial Banking Annual Average Assets |
4
Payment and
Settlement
Annual Settlement
Throughput
|
5
Retail Brokerage Gross Income |
6
Asset Management Total Funds under
Management
|
7
Example
Note:
1
Definition of exposure indicator and B
i
will be supplied by BIS
Operational Risk -
Internal Measurement Approach
Based on the same business lines as standardized
approach
Supervisor specifies an exposure indicator (EI)
Bank measures, based on internal loss data,
Parameter representing probability of loss event (PE)
Parameter representing loss given that event (LGE)
Supervisor supplies a factor (gamma) for each business
line


Op Risk Capital (OpVaR) = EI
LOB
x PE
LOB
x LGE
LOB
x
industry
x RPI
LOB


LR
firm


EI = Exposure Index - e.g. no of transactions * average value of transaction

PE = Expected Probability of an operational risk event
(number of loss events / number of transactions)

LGE = Average Loss Rate per event - average loss/ average value of transaction

LR = Loss Rate ( PE x LGE)

= Factor to convert the expected loss to unexpected loss

RPI = Adjusts for the non-linear relationship between EI and OpVar
(RPI = Risk Profile Index)

The Internal Measurement Approach
For a line of business and loss type
Rate
The Components of OP VaR
e.g. VISA Per $100 transaction
20%
4%
8%
12%
16%
1.3 9








Loss per $1 00Transaction
0%
30%
40%
50%
60%
70%
+ =
The Probability
Distribution
The Severity
Distribution
The Loss
Distribution
Expected
Loss
Loss
Catastrophic
Unexpected
Loss

Severe
Unexpected
Loss
Eg; on average 1.3
transaction per
1,000 (PE) are
fraudulent


Note: worst case
is 9
Eg; on average
70% (LGE) of the
value of the
transaction have to
be written off

Note: worst case
is 100
Eg; on average 9
cents per $100 of
transaction (LR)



Note: worst case
is 52
Loss per $1 00 Fraudulent Transaction Number of Unauthorized Transaction
Example - Basic Indicator Approach
OpVar
Gross Income $3 b
Basic Indicator Captial Factor o
$10 b 30%
Example - Standardized Approach
Business Lines Indicator Capital
Factors (|)
1
OpVar
Corporate Finance $2.7 b Gross Income 7% = $184 mm
Trading and Sales $1.5 mm Gross Income 33% = $503 mm
Retail Banking $105 b Annual Average Assets 1% = $1,185 mm
Commercial Banking $13 b Annual Average Assets 0.4 % = $55 mm
Payment and Settlement
$6.25 b Annual Settlement
Throughput
0.002% = $116 mm
Retail Brokerage $281 mm Gross Income 10% = $28 mm
Asset Management $196 b Total Funds under Mgmt 0.066% = $129 mm
Total = $2,200 mm
2
Note:
1. |s not yet established by BIS
2. Total across businesses does not allow for diversification effect
Example - Internal Measurement Approach
Business Line (LOB): Credit Derivatives
Note:
1. Loss on damage to assets not applicable to this LOB
2. Assume full benefit of diversification within a LOB
Exposure Indicator
(EI)
Risk
Type
Loss Type
1
Number Avg.
Rate
PE
(Basis
Points)
LGE Gamma

RPI OpVaR
1 Legal Liability 60 $32 mm 33 2.9% 43 1.3 $10.4 mm
2 Reg. Comp. / Tax
Fines or Penalties
378 $68 mm 5 0.8% 49 1.6 $8.5 mm
4 Client Restitution 60 $32 mm 33 0.3% 25 1.4 $0.7 mm
5 Theft/Fraud &
Unauthorized Activity
378 $68 mm 5 1.0% 27 1.6 $5.7 mm
6. Transaction Risk 378 $68 mm 5 2.7% 18 1.6 $10.5 mm
Total $35.8 mm
2
Implementation Roadmap
Seven Steps
Gap Analysis
Detailed project plan
Information Management Infrastructure- creation
of Risk Warehouse
Build the calculation engine and related analytics
Build the Internal Rating System
Test and Validate the Model
Get Regulators Approval


References
Options,Futures, and Other Derivatives (5
th

Edition) Hull, John. Prentice Hall
Risk Management- Crouchy Michel, Galai Dan
and Mark Robert. McGraw Hill