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
 In the future . . .

Intelligent management of risk

will be the foundation of a
successful financial institution
 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(, ) =EL(, (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.
 Types of Financial Risks
Risk is multidimensional

Market Risk
Financial
Credit Risk
Risks
Operational Risk
 Hierarchy of Financial Risks

Specific
Risk
Equity Risk Trading Risk
Market Risk General
Interest Rate Risk
Market
Gap Risk Risk
Financial Currency Risk
Credit Risk
Risks Commodity Risk
Counterparty
Operational Risk
Risk
Transaction Risk
Issuer Risk
Portfolio
Concentration
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
 The New Basel Capital Accord

Three Basic Pillars

Minimum Market
Supervisory
Capital Discipline
Review Process
Requirement Requirements
 Minimum Capital Requirement
Pillar One
Standardized

Internal Ratings
Credit Risk Credit Risk Models

Credit Mitigation

Trading Book
Risks Market Risk Banking Book

Operational
Other Risks Other
 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*2G/2x2*b2) dt +G/x*b*dz
Credit Risk
1. Minimum Capital Requirements- Credit
Risk (Pillar One)

Standardized approach
(External Ratings)
Minimum
Internal ratings-based approach Capital
Requirement
Foundation approach
Advanced approach

Credit risk modeling

(Sophisticated banks in the future)
 Evolutionary Structure of the Accord

Credit Risk Modeling ?

Advanced IRB Approach

Foundation IRB Approach

Standardized Approach

Increased level of sophistication

 The New Basel Capital Accord
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
 Standardized Approach
Based on assessment of external credit assessment
institutions
External Credit
Assessments

Sovereigns Banks/Securities Corporates Public-Sector Asset

Firms Entities Securitization
Programs
 Standardized Approach:
New Risk Weights (June 1999)
Assessment
Claim
AAA to A+ to A- BBB+ to BB+ to Below B- Unrated
AA- BBB- B-

Sovereigns 0% 20% 50% 100% 150% 100%

Option 11 20% 50% 100% 100% 150% 100%
Banks 3 3 3
Option 22 20% 50% 50% 100% 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 (January 2001)
Assessment
Claim
AAA to A+ to A- BBB+ to BB+ to Below BB- Unrated
AA- BBB- BB- (B-) (B-)

Sovereigns 0% 20% 50% 100% 150% 100%

Option 11 20% 50% 100% 100% 150% 100%
Banks 3 3 3
Option 22 20% 50% 50% 100% 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
 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

Pillar 1
 Opportunities for a
Regulatory Capital Advantage
Example: 30 year Corporate Bond
Standardized
Model Internal
Model
Capital
Market

Credit

98 Rules
 Standardized Approach
Internal rating system & Credit VaR
New standardized model
16

12

PER CENT
8

1.6
0
AAA

AA

A+

A-

BB+

BB-

B
BBB

CCC
S&P:
1 2 3 4 4.5 5 5.5 6 6.5 7
RATING
 Internal Model- Advantages

Example: Capital charge for specific risk (%)

Portfolio of Internal Standardized
100 $1 bonds model approach
diversified AAA 0.26 1.6
across AA 0.77 1.6
industries
A 1.00 1.6
BBB 2.40 1.6
BB 5.24 8
B 8.45 8
CCC 10.26 8
 Internal Ratings-Based Approach
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.]
 Expected Loss Can Be Broken Down Into Three Components

Borrower Risk Facility Risk Related

EXPECTED Probability of Loss Severity Loan Equivalent

LOSS Default x Given Default x Exposure
=
(PD) (Severity) (Exposure)
Rs. % % Rs

What is the probability If default occurs, how If default occurs, how

of the counterparty much of this do we much exposure do we
defaulting? expect to lose? expect to have?

The focus of grading tools is on modeling PD

 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)

Baa/BBB
Spread
over
Treasuries
A/A

Aa/AA

Aaa/AAA

Maturity
 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 Risk-free Corporate
(years) yield 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

e 0.051 0.951229
One-year corporate bond (principal=1) sells for
e 0.05251 0.948854
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
 Example continued

Similarly the holder of the corporate bond expects

to lose

e 0.05 2 e 0.0550 2
0.05 2
0.009950
e
or 0.9950% in the first two years
Between years one and two the expected loss is
0.7453%
 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 Cumul. Loss. Loss

(years) % 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

y* ( T )T
e e y(T )T
Q(T )
y* ( T )T
e
or
[ y( T ) y* ( T )]T
Q(T ) 1 e

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

Prob. of Def. (1 - Rec. Rate) Exp. Loss%

Exp. Loss%
Prob of Def
1 - Rec. Rate
If Rec Rate 0.5 in our example, probabilities
of default in years 1, 2, 3 , 4, and 5 are 0.004994,
0.014906, 0.021662, 0.025294, and 0.025924
 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 QA(T) as the probability that company A
will default between time zero and time T, QB(T)
as the probability that company B will default
between time zero and time T, and PAB(T) as the
probability that both A and B will default. The
default correlation measure is

PAB (T ) Q A (T )QB (T )
AB (T )
[Q A (T ) Q A (T ) 2 ][QB (T ) QB (T ) 2 ]
 Measure 2

Based on a Gaussian copula model for time to default.

Define tA and tB as the times to default of A and B
The correlation measure, AB , is the correlation between
uA(tA)=N-1[QA(tA)]
and
uB(tB)=N-1[QB(tB)]
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

Measure 1 can be calculated from Measure 2 and vice versa :

PAB (T ) M [u A (T ), u B (T ); AB ]
and
M [u A (T ), u B (T ); AB ] QA (T )QB (T )
AB (T )
[QA (T ) QA (T ) 2 ][QB (T ) QB (T ) 2 ]
where M is the cumulative bivariate normal probability
distribution function.
Measure 2 is usually significantly higher than Measure 1.
It is much easier to use when many companies are considered because
transforme d survival times can be assumed to be multivaria te normal
 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.

Value-at-Risk
X 95%
5%

(Profit/Loss Distribution)
Standard Value-at-Risk Levels:

Two standard VaR levels are 95% and 99%.

When dealing with Gaussians, we have:

95% is 1.645 standard deviations from the mean
99% is 2.33 standard deviations from the mean

99% 95%

2.33 1.645 mean

Standard Value at Risk Assumptions:

1) The percentage change (return) of assets is Gaussian:

This comes from:

dS
dS Sdt Sdz or dt dz
S

So approximately:

S
t z
S
which is normal
Standard Value at Risk Assumptions:

2) The mean return is zero:

S
This comes from an order argument on: t z
S
The mean is of order t.
t ~ O(t )
The standard deviation is of order square root of t.
z ~ O(t 1/ 2 )

Time is measured in years, so the change in time is

usually very small. Hence the mean is negligible.
S Sz
 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
day 0.063 year 6% year
252
 Daily Volatility continued

Strictly speaking we should define 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 $632,456
 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 $1,473,621
 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

50,000 10 $158,144
The VaR is
158,114 2.33 $368,405
The change in the value of a portfolio:

Let xi be the dollar amount invested in asset i, and let ri

be the return on asset i over the given period of time.
Then the change in the value of a portfolio is:
P xi ri
i
But, each ri is Gaussian by assumption:
Si
ri zi
Si
Hence, P is Gaussian. P x T r ~ N (0, x T x)
x1 r1
where x r
E rr T
xn rn
Example:
Consider a portfolio of:
$10 million of IBM
$5 million of AT&T

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.

Then P x T r 10rIBM 5rAT &T has daily variance:

T
10 0.02 2 0.7(0.01)(0.02) 10
5 2 0.0565
0.7(0.01)(0.02) 0.01 5
Example:

Then P x T r 10rIBM 5rAT &T has daily variance:

T
10 0.02 2 0.7(0.01)(0.02) 10
5 2 0.0565
0.7(0.01)(0.02) 0.01 5

Now, compute the 10 day 95% and 99% VaR:

The variance for 10 days is 10 times the variance for a day:

102 days 10(0.0565) 0.565 10 days 0.7516

Since P is Gaussian,
95% VaR = (1.645)0.7516= 1.24 million
99% VaR = (2.33)0.7516 = 1.75 million
 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

C re d it R is k M itig a n ts

C o lla te ra l G u a ra n te e s C re d it D e riv a tiv e s O n -b a la n c e S h e e t N e ttin g

 Collateral

T w o A p p ro a c h e s

S im p le A p p r o a c h C o m p r e h e n s iv e A p p r o a c h
( S t a n d a r d iz e d o n ly )
 Collateral
Comprehensive Approach

C o v e r a g e o f r e s id u a l r is k s t h r o u g h

H a ir c u t s W e ig h ts
(H ) (W )
 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 Rs800
CA Rs.770
1 H E H C 1 .04 .06
C = Current value of the collateral received (e.g.
Rs.800)
HE = Haircut appropriate to the exposure (e.g.= 6%)
HC = Haircut appropriate for the collateral received
(e.g.= 4%)
CA = Adjusted value of the collateral (e.g. Rs.770)
 Collateral Example Comprehensive
Approach
Calculation of risk weighted assets based on following
formula:
r* x E = r x [E-(1-w) x CA]
 Collateral Example Comprehensive
Approach
r* = Risk weight of the position taking into
account the risk reduction (e.g. 34.5%)
w1 = 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
Rs.800
C A Rs.770
1 0.04 0.06
Risk Weighted Assets
34.5% x Rs.1,000 = 100% x [Rs.1,000 - (1-0.15) x Rs.770] =
Rs.345

Note: comprehensive Approach saves

 Collateral Example
Simple and Comprehensive Approaches

Approach Risk Weighted Capital

Assets Charge
No Collateral 1000 80.0
Simple 360 28.8
Comprehensive 345 27.6
 IX.
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
 The Regulatory Approach:Four
Increasingly Risk Sensitive Approaches

Risk Based/ less Regulatory Capital:

Basic Indicator Standardized Internal Measurement Approach Loss Distribution

Standardized Loss Distribution

Internal Measurement Approach
Approach Approach

Bank Bank Risk Type 1 Risk Type 6

Rate
Bank 1
LOB1 Rate 1 Rate1

Base LOB1
EI1 EI1 Base Expected
Loss

LOB2 2 Rate 2 Rate2

LOB2

Probability
Severe Catastrophic
Unexpected Unexpected
EI2 EI2 Base Loss Loss

LOB3 LOB3
Base Base Loss

N RateN RateN
LOBn LOBn
EIN EIN Base

Rate of progression between stages based on necessity and capability

 Operational Risk -
Basic Indicator Approach

Capital requirement = % of gross income

Gross income = Net interest income

+
Net non-interest income

Note: supplied by BIS (currently = 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 chargei = i x exposure indicatori
Overall capital requirement =
sum of requirements for each business line
 Operational Risk -
Standardized Approach
Example
Business Lines Exposure Indicator (EI) Capital
Factors1
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 Annual Settlement 5
Settlement Throughput
Retail Brokerage Gross Income 6
Asset Management Total Funds under 7
Management

Note: 1 Definition of exposure indicator and Bi 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
 The Internal Measurement Approach
For a line of business and loss type
Rate
Op Risk Capital (OpVaR) = EI LOB x PELOB x LGELOB x industryx RPILOB

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 Components of OP VaR
e.g. VISA Per $100 transaction
20% 70%
Expected
Loss
16% 60% Severe
Unexpected
12% 50% Loss Catastrophic

Probability
8% + 40%

30%
= Unexpected
Loss
4%
0% Loss
1.3 9 70 100 9 52
Number of Unauthorized Transaction Loss per $1 00 Fraudulent Transaction Loss per $1 00Transaction

The Probability The Severity The Loss

Distribution Distribution Distribution

Eg; on average 1.3 Eg; on average Eg; on average 9

transaction per 70% (LGE) of the cents per $100 of
1,000 (PE) are value of the transaction (LR)
fraudulent transaction have to
be written off

Note: worst case Note: worst case Note: worst case

is 9 is 100 is 52
 Example - Basic Indicator Approach

Basic Indicator Captial Factor OpVar

Gross Income $10 b 30% $3 b

 Example - Standardized Approach
Business Lines Indicator Capital OpVar
Factors ()1

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

$6.25 b Annual Settlement

Payment and Settlement 0.002% = $116 mm
Throughput

Retail Brokerage $281 mm Gross Income 10% = $28 mm

Asset Management $196 b Total Funds under Mgmt 0.066% = $129 mm

Total = $2,200 mm2

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

Exposure Indicator
(EI)
Risk Loss Type1 Number Avg. PE LGE Gamma RPI OpVaR
Type Rate (Basis

Points)
1 Legal Liability 60 $32 mm 33 2.9% 43 1.3 $10.4 mm

2 Reg. Comp. / Tax 378 $68 mm 5 0.8% 49 1.6 $8.5 mm

Fines or Penalties

4 Client Restitution 60 $32 mm 33 0.3% 25 1.4 $0.7 mm

5 Theft/Fraud & 378 $68 mm 5 1.0% 27 1.6 $5.7 mm

Unauthorized Activity

6. Transaction Risk 378 $68 mm 5 2.7% 18 1.6 $10.5 mm

Total $35.8 mm2
Note:
1. Loss on damage to assets not applicable to this LOB
2. Assume full benefit of diversification within a LOB
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 (5th
Edition) Hull, John. Prentice Hall
Risk Management- Crouchy Michel, Galai Dan
and Mark Robert. McGraw Hill