Stress testing and sensitivity analysis are important risk management tools required by regulators. Stress testing assesses the financial health of institutions under hypothetical stressful scenarios to determine if they remain solvent and liquid. It can test solvency by examining capital ratios or test liquidity by analyzing net cash flows. Sensitivity analysis varies inputs to risk models to determine the models' responses. This document discusses stress testing methods like scenario analysis and sensitivity analysis techniques and provides a case study applying these methods to a probability of default model.

1. Stress Testing and Sensitivity Analysis:
Requirements and Methods
Name: Ananya Bhattacharyya
Designation: Business Analyst, Genpact Analytics & Research
Business Vertical: Financial Services Analytics
E-Mail: ananya.bhattachryya@genpact.com
Date: 31st December 2015
Genpact Analytics & Research

2. 2
Table of Contents
StressTesting 4
Why Stress testing is required:Regulatory guidelines 4
Howstress testing helps to assessthe financialhealth of an Institution 4
Solvency Test 4
Liquidity Test 5
Methodsof StressTesting 5
Scenario Analysis 5
MacroeconomicStressTesting 6
Approachesof MacroeconomicStressTesting 6
PPNRasa stress testing tool 7
SensitivityAnalysis 7
Regulatory Guidelines 8
VariousMethodsforSensitivityAnalysis 9-11
Differentmethodsfortheinput variation 11
CaseStudy 11-16
Result Interpretation & Conclusion 16
References

3. 3
Abstract
The global financial crisis has brought the spotlight on stress testing both as a regulatory requirement and as an internal
risk management tool. This paper depicts the evolution of stress testing as a regulatory requirement and finds out why it
is being considered very important as a supervisory tool. The first part of the paper attempts to discuss different types of
stress testing based on the ultimate objective it serves and the various approaches followed by the regulators for
carrying out this exercise. It also throws light on the regulators’ changing focus towards making the entire exercise
dynamic by including pre-provision net revenue (PPNR) for capturing the variability in projected loss. It has made an
attempt to discuss a few mostly used quantitative methods for sensitivity analysis and their major advantages and
disadvantages. The second part applies a logistic regression based model for estimating default probabilities on
consumer loan portfolio. A few approaches of sensitivity analysis and stress testing have been applied on this model to
check how the model is performing under stress scenarios and the results have been interpreted.
Key Words
Stress Testing, Sensitivity Analysis, Probability of Default model, Risk, Regulations
Paper Type
Technical

4. 4
1. Stress Testing:
Stress testing has been conceived as a key component of the Financial Sector Assessment Program (FSAP) and
presently it is being used as an analytical tool in Global Financial Stability Reports (GFSRs). Stress testing measures
the vulnerability of a financial institution or an entire system under different hypothetical scenarios and helps to chalk out
proactive measures that can act as a future shock absorber.
1.2. Why Stress testing is required: Regulatory guidelines
Stress testing has become a regulatory requirement only after passing of the Dodd-Frank Wall Street Reform and
Consumer Protection Act (Dodd-Frank Act or DFA) of 2010, motivated by the widely perceived success of the Federal
Reserve's Supervisory Capital Assessment Program (SCAP) of 2009. Practical implementation of banks' stress testing
(Dodd-Frank Act stress testing or DFAST) began in early 2011 with the release of the Comprehensive Capital Analysis
and Review (CCAR) stress scenarios by the Federal Reserve. As defined in Fed’s website “CCAR is an annual exercise
by the Federal Reserve to assess whether the largest bank holding companies(BHCs) operating in the United States
have sufficient capital to continue operations throughout times of economic and financial stress and that they have
robust, forward-looking capital-planning processes that account for their unique risks.” The 2011 CCAR contained only
one stress scenario with nine domestic variables and was more limited in scope than its successors. The 2012 CCAR
expanded the number of domestic variables, added international variables and provided the series for both baseline and
stressed scenarios. Now the standard format includes baseline, adverse and severely adverse scenarios. DFAST is a
complementary exercise to CCAR conducted by the Fed to assess whether institutions have sufficient capital to absorb
losses and support operations during adverse economic conditions.
Table1.2.1: Evolution of stress testing as a regulatory requirement
To validate the capital calculation Basel Committee on Banking Supervision, 2005 states that stress testing will be
employed to verify that the minimum capital computed under Basel II is sufficient to protect against macroeconomic
downturns. In the Basel II framework (BCBS 2006), stress testing is part of Pillar I and Pillar II whereby banks are asked
to analyze possible future scenarios that may threaten their solvency.
Based on the regulatory guidelines provided in section 1.2, stress testing evaluates an institution’s performance along
two lines- solvency and liquidity.
Timeline: Regulatory guidelines
2009 2010 2011 2012 2013
CCAR: $10
BILLION &
ABOVE
CCAR:
$50
BILLION
&
ABOVE
CCAR:
TOP 19
BHCS
DODD
FRANK
REFORM
SCAP

5. 5
1.3. How stress testing helps to assess the financial health of an Institution
1.3.1. Solvency Test:
A solvency test assesses whether a financial institution will be sufficiently solvent (value of its asset is larger than debt
ensuring a positive equity capital) when put into a hypothetically challenging situation by studying changes in its balance
sheet variables. Solvency is measured by the capital adequacy ratio, debt to equity ratio or capital shortfall (i.e, the
amount of capital needed to maintain a certain capital ratio) defined by regulatory requirement. A financial institute will
pass the solvency test if its capital ratio is above the “hurdle rate” (set on minimum regulatory requirement).
1.3.2 Liquidity Test:
Liquidity tests examine the resilience of the financial institution or system under shocks. If under adverse economic
scenario huge amount of deposits is withdrawn suddenly and the banks do not have enough cash inflows or liquid
assets then they face liquidity crisis. The bank can withstand this crisis if it starts selling its liquid assets or by using
repos but it can also happen that the value of the collaterals fall during an adverse economic situation. In this case the
liquidity crisis may actually turn into a solvency crisis. Hurdle rate in case of a liquidity stress test can be fixed by tak ing
into consideration the net cash flow position of the bank or the stressed liquidity ratio.
1.4. Methods of Stress Testing
Stress tests can be divided into two categories: scenario analysis and sensitivity tests.
1.4.1. Scenario analysis:
The scenarios are based either on
1. Portfolio-driven approach
Or
2. Event-driven approach
Table 1.4.1: Approaches towards scenario analysis
Portfolio driven Event driven
Risk drivers of a given portfolio are identified and then
plausible scenarios are designed under which those
factors are stressed.
This approach is based on plausible events and how
these events might affect the relevant risk factors for a
bank or a given portfolio.
Under each approach scenarios can be developed either based on historical events (past crisis) or hypothetically (that
have not yet happened).
Based on the ultimate objective stress tests can be of four types-
Table 1.4.1.1: Types of Stress Testing depending on the objective
Type Internal Risk Management Crisis Management Macro prudential Micro prudential
Objective Financial institutions use
stress testing to measure and
manage risk with their
investment. It serves as an
input for business planning
After the financial
crisis supervisory
authorities use stress
testing to check
whether the key
institutions need to be
recapitalized
Ensures system wide
monitoring and
analyze the system
wide risk
This entails
supervisory
assessment of the
financial health of
individual institutions

6. 6
1.4.1.2. Macroeconomic Stress Testing:
A stress test can look into the impact of one source of risk or multiple sources of risks. Risk factors can be combined or
can be generated using a macroeconomic framework. Allen and Saunders (2004) provided a detailed study on the
impact of cyclical effects on major credit risk parameters (e.g., probability of default (PD), loss given default (LGD),
exposure at default (EAD) etc.) and they were found to be highly exposed. For macro scenario stress tests empirical
relationship between key risk parameters (probability of default (PD), loss given default (LGD) etc.) and relevant
macroeconomic variables (GDP, unemployment rate etc.) are checked. Macro scenario stress tests should take into
consideration at least one economic cycle. This implies for net interest income models it should cover an interest rate
cycle and for non-interest income models it should cover one business cycle. Macro stress tests are carried out taking
non-performing loans (NLPs) as dependent variable and various macroeconomic variables like GDP growth, interest
rates, inflation, real wages, oil price etc. as main drivers for corporate credit risk (Virolainen,2004).For household sector
these factors can be unemployment rate, interest rate etc.
Suppose there are k macroeconomic risk drivers that are expected to have an impact on a bank’s portfolio and a vector
of stressed macroeconomic drivers is Xstress= (X1,…, Xk). The model for measuring the PD of obligor j looks like
PDj =1/1+exp (-β0 -∑ β𝑛
𝑖=1 i .K j,I - ∑ 𝛾𝑘
𝑙=1 l.Xl)
where Ki are obligor specific risk drivers. To compute the stressed PD we can simply put Xstress into the above
formula.These PDs are then used in the calculation of expected losses and regulatory capital under stress.
Table 1.4.1.2: Approaches for translating macro scenarios into balance sheets
Approach Description Advantage Disadvantage
Bottom Up Granular borrower
level analysis
 Granular risk
factor driven
approach leads
to more precise
results
 Uses advanced
internal model
 Provides detailed
risk analysis and
risk management
capacity of an
institution
 The result it provides is
institution specific. Hence,
comparison across similar
institutions can be difficult.
 Implementing this approach is
resource intensive
Top down The impact is
estimated using
aggregated data
 Ensures
uniformity in
methodology and
consistency of
assumptions
across all the
institutions
 An effective tool
for validating
bottom up
approaches
 Applying the tests only to
aggregate data can disguise
concentration of exposures to
risk at the level of individual
institutions
 Risk estimates may not be
precise due to limited data
coverage

7. 7
Both of these approaches are used as complements rather than as substitutes by the regulators to extract the
advantages of both the approaches and minimize their challenges. Liquidity tests are mostly conducted as bottom- up
exercise because they require granular individual level analysis.
1.4.1.3. PPNR as a Stress Testing Tool:
During the initial years of evolution of stress testing as a regulatory measure major thrust was given on ensuring that
banks should understand the potential impact of credit losses on capital. Gradually, when the banks achieved an
improved state in their credit risk modeling competency regulators found PPNR estimation more meaningful because it
covers more variations on credit losses. Traditionally stress testing methods mainly focused on loss calculation only but
for a complete assessment of capital adequacy under stressed scenarios both the balance sheet and the income
statement must be taken into consideration. SCAP changed the traditional method of stress testing and included
profitability (pre- provision net revenue) to make the exercise dynamic. Historical relationship between the
macroeconomic variables and the revenue components is estimated and projected into the future for BHCs.
Pre-provision net revenue (PPNR) = net interest income+ non-interest income- non-interest expense
Table 1.4.1.3: An overview of PPNR Modeling
Data Requirement Advantages Challenges
 10 years of monthly
balance and fee data
 Portfolio level balance
histories
 Records of management
actions(e. g, marketing or
pricing strategies)
 It helps to understand the
variability in projected loss –
thus helping in a more
transparent capital
management and allocation
 PPNR modeling enhances
firm’s ability to foresee and
identify extreme but possible
risk at various levels.
 It serves as an important tool
for liquidity management by
looking at enterprise wide
stress tests results.
 Model granularity: If the
institution models on each
balance sheet or P&L item it
would become cumbersome and
the model would reflect little
macro sensitivity.
 Data availability: Most BHCs do
not have detailed revenue
related time series data of at
least 8-10 years required for
PPNR modeling due to changes
in internal strategy, business
structure or unavailability of a
robust data management
system. Back testing of model is
quite hard due to limited data.
So it is difficult to check the
consistency of the results.
1.4.2. Sensitivity Analysis:
One of the very important requirements for a model is that the modeler provides an evaluation of the confidence in the
model. Hence along with the quantification of uncertainty in any model, an evaluation of how much each input is
contributing in the uncertainty of the output is equally important and that is where sensitivity comes into play. Generally,
sensitivity analyses are conducted by: (a) defining the model and its independent and dependent variables (b) assigning
probability density functions to each input parameter, (c) generating an input matrix through an appropriate random

8. 8
sampling method,(d) calculating an output vector, and (e) assessing the influences and. It helps reducing model
uncertainty and therefore improves model robustness with regard to:
 Magnitude of sensitivity
 Output uncertainty reduction
 Model simplification (by removing unnecessary parameters)
 Enhancing model transparency
 Evaluation of model confidence
Excerpt from Regulatory guidelines:
According to SR Letter 11-7 guidelines, “Banks should employ sensitivity analysis in model development and validation
to check the impact of small changes in inputs and parameter values on model outputs to make sure they fall within an
expected range. Unexpectedly large changes in outputs in response to small changes in inputs can indicate an unstable
model. Varying several inputs simultaneously as part of sensitivity analysis can provide evidence of unexpected
interactions, particularly if the interactions are complex and not intuitively clear.” To be specific, sensitivity analysis i s a
technique used to determine how change in the values of an independent variable can impact a particular dependent
variable under a given set of assumptions. It is a way to predict the outcome of a decision if the situation turns out to be
different from the one used for key prediction(s).
In sensitivity tests, risk factors are moved instantaneously by a unit amount and the source of the shock is not identified.
Moreover, the time horizon for sensitivity tests is generally shorter in comparison with scenarios.
Fig. 1.4.2.: Sensitivity analysis: A diagrammatic representation
Portfolio disaggregation PD/LGD/EAD shock calibration Result interpretation
Loan
Portfolio
Asset
type A
Asset
type B
Asset
type C
PD/LGD/EAD
shock
Stressed
portfolio
Sensitivity Analysis Diagram
Profit
effect
Solvency
effect

9. 9
1.4.2.1. Various methods for Sensitivity Analysis:
Table 1.4.2.1: Different types of sensitivity analysis and their advantages and disadvantages
Method Procedure Advantage Disadvantage
One factor at a
time (OFAT)
sensitivity
measure /
partial
sensitivity
analysis
Repeatedly varying one parameter at a
time while holding the other inputs fixed
and then monitoring changes in the
output
It is the most simple
and common
approach best
suited for linear
model.
They examine only
small perturbations
and do not explore
full input space. It
does not work well
with non-linear
models since it
ignores interaction
with other inputs.
Multiple factor
at a time
sensitivity
measure
Examine the relationship between two
or more simultaneously changing inputs
and the model output. The variation
could be
1. Percentage change
2. Standard deviation
3. Best or worst “possible” values
(extreme values) of inputs etc.
The outputs can be
presented as
scatterplots, tornado
diagrams etc. Such
presentations help
assess the rank
order of key inputs
or key drivers. It
considers aggregate
impact of multiple
inputs, hence more
accurate.
It is typically limited
to two inputs since it
is difficult to assess
the impact for three
or more inputs
Regression
Analysis
It typically involves fitting a relationship
between inputs and an output. The
effect of inputs on the output can be
studied using regression coefficients,
standard error of regression coefficients
and the level of significance of the
regression coefficients.
It allows evaluation
of sensitivity of
individual model
inputs taking into
account the
simultaneous impact
of other model
inputs on the result.
Possible lack of
robustness if key
assumptions of
regression are not
met
Difference in
Log-Odds
Ratio (DLOR)
The odds ratio of an event is a ratio of
the probability that the event occurs to
the probability that the event does not
occur. DLOR is used to examine the
difference between the outputs when
the input changes and when it is at its
baseline value.
It can be used when
the output is a
probability
It cannot be used for
non-linear models
Response
Surface
It is used to represent the relation
between a response variable (output)
and one or more explanatory inputs
It helps to reduce
the model in such a
Most RS studies are
based on fewer
inputs compared to

10. 10
Method (RSM) using a sequence of designed
experiments to obtain optimal response.
It can be thought of as “model of a
model” (Frey et al., 2005).To develop a
response surface least squares
regression is used to fit a first or second
order equation to the original data. After
developing, the sensitivity of the model
output to the inputs can be determined
by either employing regression analysis
or other sensitivity analysis to the
response surface (Frey et al., 2005).
form so that
computation can be
much faster. It can
also be used when
the output is a
probability.
original model.
Therefore the effect
of all original inputs
on the sensitivities
cannot be evaluated.
Fourier
Amplitude
Sensitivity
Test (FAST)
It is used to estimate the expected
value and variance of the output and
the contribution of individual inputs to
the variance of the output. For example,
a relatively large conditional variance of
expected value of model output Y given
a set of parameters xi (i.e, V (E(y| xi))
will indicate that a relatively large
proportion of model output variance is
contributed by parameter xi. The ratio of
the contribution of each input to the
output variance and the total variance of
the output gives the first order
sensitivity index.
It is better than
OFAT as it can
apportion the output
variance to the
variance in the
inputs. First order
sensitivity indices
are used to rank the
inputs (Saltelli et al.,
2000).
First order indices
cannot capture the
interaction among
the inputs. Saltelli et
al (1999) developed
the extended FAST
method which can
address this
limitation but it is a
complex procedure
to carry.
Mutual
Information
Index
It is a conditional probability analysis. It
provides a measure of the information
about the output that is provided by a
particular input. The magnitude of the
measure can be compared for different
inputs to determine which input
provides useful information about the
output. It involves three general steps:
(1) generating an overall confidence
measure of the output value which is
estimated from the CDF of the output;
(2) obtaining a conditional confidence
measure for a given value of an input by
holding an input constant at some value
and varying all other inputs; and (3)
calculating sensitivity indices (Critchfield
and Willard, 1986):
IaXY = ∑x ∑y PX PY|Xlogn (PY | X / PY)
where,PY|X = conditional confidence;
PY = overall confidence;
PX = probability distribution for the input;
and n = 2, to indicate binary output.IaXY
is always positive. If IaXY is large, then
X provides a great deal of information
about Y. If X and Y are statistically
independent, then it is zero.
MII includes the joint
effects of all the
inputs when
evaluating
sensitivities of an
input. Correlation
coefficient of two
random variables
examines the
degree of linear
relatedness of the
variables. MII is a
more informative
method.
Calculation of the
MII by Monte Carlo
techniques suffers
from computational
complexity

11. 11
Scatter Plot
It is used for visual
assessment of the influence of
individual inputs on an output
It is the first step in
sensitivity analysis
to identify the nature
of association
among variables.
It is tedious to
generate if there are
large number of
inputs and outputs.
1.4.2.2 Different methods for the input variation considering the type of model and the data
available:
1. Choosing a percentage range:
It is possible to select the variation range as a percentage and then change the input consequently. For
example, the input variable may be varied by -20% and +20% and then the impact on the model performance is
observed.
2. Choosing a standard deviation factor:
The main limitation with the previous method is that it only addresses sensitivity relative to a chosen point and
not for the entire parameter distribution. Here each parameter is individually increased by a factor of its
standard deviation.
3. Choosing the extremes:
An alternative method is to calculate the sensitivity index (SI) by checking the change in the output level under
ceteris paribus condition by taking the minimum and maximum values of each input.
The process is in 3 steps:
 First, the corresponding outputs coming from the calculation with the minimum and maximum of the selected
input are computed
 Second, the corresponding 𝑂𝑢𝑡 𝑚𝑖𝑛 and 𝑂𝑢𝑡 𝑚𝑎𝑥 values resulting of the previous step are figured out
 Third, the %change is calculated:
%𝑐ℎ𝑎𝑛𝑔𝑒 =
𝑂𝑢𝑡 𝑚𝑎𝑥−𝑂𝑢𝑡 𝑚𝑖𝑛
𝑂𝑢𝑡 𝑚𝑎𝑥
2. Case Study:
Let us look at a probability of default (PD) model used on commercial loan portfolio. The model is a logistic regression
based model using separate dummy variables for companies belonging to different industries. An initial model is
defined, based on which different scenarios were considered for the purpose of quantifying their impact on probability of
default. We studied operating revenue for the year 2010, company age, number of employees, dummies for different
industries and their impact on default rate. The dependent variable (default rate) is restricted to the values of zero or
one, where one indicates bad loan and zero indicates good loan. After performing regression analysis, we consider only
those independent variables that are significantly related to the dependent variable. Once the model is developed, the
signs of the parameter estimates associated with each variable are analyzed. Each sign suggests the relationship
(positive/negative) of an independent variable with the dependent variable.

12. 12
Table 2.1: Final variables and their relation with default rate
Variable Sign
Operating revenue(2010) Negative
Number of employees(WOE) Negative
Company age Positive
Dummy for companies belonging to consumer industries Positive
Dummy for companies belonging to hotel industries Positive
A convincing negative relation with the default rate and operating revenue was found. The relation with number of
employees is also significant. Positive relation with the company age for the sector Consumer industries and hotel
industries were found. It can be concluded that if any economic downturn affects the companies and operating revenue
falls, it will significantly impact default rate.
Fig 2.1: Portfolio distribution industry wise
0
5
10
15
20
25
Distribution(%)
Portfoliodistributionby industry
Samplesize

13. 13
Fig 2.2: Industry wise Default rate
After model development sensitivity analysis has been conducted to see how the model is performing based on
Kolmogorov-Smirnov Statistic (KS statistic), a model discriminatory measure and Somers’ D to check the accuracy in
the prediction.
• KS is the measure of maximum separation between good and bad distribution. Higher value of the KS statistic
reflects the higher quality of the scorecard.
• Somers′ D =
Number of pairs that are concordant – Number of pairs that are discordant
Total Number of pairs.
• The % of pairs for which the predicted probability of the event given the occurrence of the event is greater than
predicted probability of the event given the non-occurrence of the event is called percentage concordant and
vice-versa. Theoretically Somers’ D ranges from -1 to +1. For an accurate model, higher value of Somers’ D is
preferred.
For our original model KS was reported as 32.3 and Somers’ D as 0.387.Now let us check after adopting a few
approaches of Sensitivity Analysis how the model is performing in terms of KS and Somers’ D.
2.1. Sensitivity Analysis:
2.1.1. One factor at a time:
Mean, Standard Deviation, maximum and minimum values for all the variables were noted. To check how the default
rate is sensitive to each parameter we replaced the variables with their mean values and checked the movement of KS
and Somers’ D. Table 2.1.1.1 displays the results.
0%
5%
10%
15%
20%
25%
30%
35%
Distribution(%)
Industry wise Default rate
Default rate

14. 14
Table 2.1.1.1: Impact of changing one factor at a time on KS and Somers’ D
The model was rebuilt taking into consideration only consumer industry and OFAT was applied and how the model
discriminatory power was varying was noted. Table 2.1.1.2. shows the result.
Table 2.1.1.2: Impact of changing one factor at a time on KS and Somers’ D considering Consumer industry
Again, the model was redeveloped taking into consideration only hotel services industry and same procedure was
applied.
Table 2.1.1.3: Impact of changing one factor at a time on KS and Somers’ D considering Hotel industry
Parameter KS Somers’ D
Company age replaced with mean 32 0.384
Operating revenue replaced with
mean
17.7 0.243
WOE value of number of employees
replaced with minimum WOE
30.2 0.383
Parameter KS Somers’ D
Original model taking only consumer
industry
35.9 0.389
Company age replaced with mean 34.7 0.388
Operating revenue replaced with
mean
13.9 0.202
WOE value of number of employees
replaced with minimum WOE
33.8 0.385
Parameter KS Somers’ D
Original model taking only hotel
industry
34 0.382
Company age replaced with mean 33.3 0.381
Operating revenue replaced with
mean
15.5 0.225
WOE value of number of employees
replaced with minimum WOE
30 0.381

15. 15
2.1.2 Multiple factor at a time:
Two inputs were simultaneously changed and the model performance was checked.
Table 2.1.1.4: Impact of changing two factors simultaneously on KS and Somers’ D
It can be concluded from the above methods of Sensitivity Analysis that the variable operating revenue is highly
impacting model’s discriminatory power and accuracy level of prediction. So it is the key parameter to check the
institution’s financial health.
2.2 Stress Testing:
Since we do not have any macroeconomic variable in our dataset and data is available for only one year (2010) it was
neither possible to do macroeconomic stress testing nor to check the performance period. So, we simply increased the
default rate of the population creating hypothetical stressed scenarios and checked the model performance in terms of
KS and Somers’ D.
Default rate of the original data was 2.1% and average estimated probability of default for the model was 0.021. KS for
our original model was reported as 32.3 and Somers’ D as 0.387.This represents the base scenario. For stress testing
the default rate of the model was gradually increased and consequently stressed PDs were calculated. Table 2.2 and
figure 2.2 show the behaviour of KS and Somers’ D of the respective models resulting from the following stress
scenarios.
Table 2.2.: Model’s performance against various stress scenarios
Stress scenario Stressed PD KS Somers’ D
Default rate=2.9% 0.029 32.2 0.395
Default rate=3.5% 0.035 31.5 0.376
Default rate=4.4% 0.044 31.3 0.376
Default rate=5.3% 0.053 31.4 0.373
Parameter KS Somers’
D
Company age replaced with mean + Operating revenue replaced with mean 18.2 0.223
Company age replaced with mean + WOE value of number of employees
replaced with maximum WOE
30.2 0.373
Operating rev. replaced with mean + WOE value of number of employees
replaced with maximum WOE
11.3 0.171

16. 16
Default rate=7.7% 0.1 31.7 0.368
Fig 2.2.: Somers’ D against various stress scenarios
2.2.1. Result Interpretation & Conclusion:
From table2.2 and figure 2.2, it can be concluded that model’s accuracy level to predict the probability of default slightly
falls as we increased the default rate. So, under stressed scenarios the model is performing moderately well, implying
that the model is robust and with sufficient accuracy it predicts the probability of default even during stress periods.
From the above analysis it can be concluded that arbitrarily varying a model variable will reveal how sensitive the
portfolio is to that parameter but cannot infer anything about the likelihood of such a stress or how the portfolio might
perform in an economic downturn.
From this case study it can be concluded that no one method is clearly best for risk assessment models. In general,
combining two or more methods may be needed to increase confidence in the model and for ranking the key inputs.
Through this paper due to data limitation exploring all the techniques discussed in the first part of the paper was not
possible. If it was possible to incorporate some macroeconomic variables into the model it would have been possible to
check how the model’s stressed PD is varying against the macroeconomic stressed scenarios and calculate the
associated risk. This paper recommends a future study for exploring all the techniques empirically.
0.395
0.376 0.376
0.373
0.368
0.35
0.36
0.37
0.38
0.39
0.4
Default rate=2.9%Default rate=3.5%Default rate=4.4%Default rate=5.3%Default rate=7.7%
Somers’ D
Somers’ D

17. 17
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8. Dodd Frank Act Stress Test 2015:Supervisory Stress TEST Methodology and Results March 2015 (Board of
Governors of the Federal Reserve System)
9. BIS (2005), An Explanatory Note on the Basel II IRB Risk weight Functions
10. CCAR submissions- GENPACT internal training material
11. DFAST – GENPACT internal training material
12. PD Modelling – GENPACT internal training material
13. PPNR Modelling - GENPACT internal training material