Transcript Credit Risk Plus and Credit Metrics

Credit Risk Plus and Credit Metrics
By: A V Vedpuriswar
October 4, 2009
Credit Risk Plus
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Introduction
CreditRisk+ is a statistical credit risk model launched by
Credit Suisse First Boston (CSFB) in 1997.
CreditRisk+ can be applied to any type of credit product,
including loans, bonds, financial letters of credit and
derivatives.
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Credit Risk Plus
Credit Risk + allows only two outcomes – default and no
default.
In case of default, the loss is of a fixed size.
The probability of default depends on credit rating, risk factors
and the sensitivity of the obligor to the risk factors.
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Analytical techniques
CreditRisk+ uses analytical techniques, as opposed to
simulations, to estimate credit risk.
The techniques used are similar to those applied in the
insurance industry.
CreditRisk+ makes no assumptions about the cause of
default.
It models credit risk based on sudden events by treating
default rates as continuous random variables.
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Data requirements
Exposure
Default rates
Default rate volatilities
Recovery rates
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Methodology
Model the frequency of default events
Model the severity of default losses
Model the distribution of default losses
Sector analysis
Stress testing
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Factors for Estimating Credit Risk
When estimating credit risk, CreditRisk+ considers :
– credit quality and systematic risk of the debtor
– size and maturity of each exposure
– concentrations of exposures within a portfolio
CreditRisk+ accounts for the correlation between different
default events by analyzing default volatilities across different
sectors, such as different industries or countries.
This method works because defaults are often related to the
same background factors, such as an economic downturn.
To estimate credit risk due to extreme events such as
earthquakes, CreditRisk+ uses stress testing.
For low probability events that can't be covered under the
statistical model, it uses a scenario-based approach.
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Frequency of default events
The timing of default events cannot be predicted.
The probability of default by any debtor is relatively small.
CreditRisk+ concerns itself with sudden default – as
opposed to continuous change – when estimating credit risk.
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Poisson Distribution
CreditRisk+ uses the Poisson distribution to model the
frequency of default events.
The Poisson distribution is used to calculate the probability
that a given number of events will take place during a specific
period of time.
The Poisson distribution is useful when the probability of an
event occurring is low and there are a large number of
debtors.
For this reason, it is more appropriate than the normal
distribution for estimating the frequency of default events.
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Using the Poisson distribution
Suppose there are N counterparties of a type and the probability
of default by each counterparty is p.
The expected number of defaults, , for the whole portfolio is Np.
If p is small, the probability of n defaults is given by the Poisson
distribution, i.e, the following equation:
 p (n) =
e   n
n!
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Modeling the Severity of Default Losses
After calculating the frequency of default events, we need to
look at the exposures in the portfolio and model the recovery
rate for each exposure.
 From this, we can conclude the severity of default losses.
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Modeling the Distribution of Default Losses
After estimating the number of default events and the severity
of losses, CreditRisk+ calculates the distribution of losses for
the items in a portfolio.
In order to calculate the distributed losses, CreditRisk+ first
groups the loss given default into bands of exposures.
The exposure level for each band is approximated by a
common average.
.
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Sector analysis
Each sector is driven by a single underlying factor, which
explains the volatility of the mean default rate over time.
Through sector analysis, CreditRisk+ can measure the impact
of concentration risk and the benefits of portfolio diversification.
As the number of sectors is increased, the level of
concentration risk is reduced.
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Stress Testing
Stress tests can be carried out in CreditRisk+ and outside
CreditRisk+.
CreditRisk+ can be stress tested by increasing default rates
and the default rate volatilities and by stressing different
sectors to different degrees.
Some stress tests, such as those that model the effect of
political risk, can be difficult to carry out in CreditRisk+.
 In this case, the effect should be measured without reference
to the outputs of the model.
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Applications of CreditRisk+
Calculating credit risk provisions
Enforcing credit limits
 Managing credit portfolios
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Calculating Credit Risk Provisions
When credit losses are modelled, the most frequent loss
tends to be much lower than the estimated average loss.
 This is because the estimated average takes into account
the risk of occasional extreme losses.
Credit provisions, also known as economic capital,
need to be set aside to protect against such losses.
CreditRisk+ can be used to set provisions for credit losses
in a portfolio.
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Enforcing Credit Limits
High concentrations of a small number of exposures can
significantly increase portfolio risk.
Credit limits are an effective way of avoiding concentrations.
They provide a means of limiting exposure to different
debtors, maturities, credit ratings and sectors.
An individual credit limit should be set at a level that is
inversely proportional to the default rating associated with a
particular debtor's credit rating.
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Managing Portfolios
CreditRisk+ incorporates all the factors that determine credit risk
into a single measure.
This is known as a portfolio-based approach.
The four factors that determine default risk are:
– size
– maturity
– probability of default
– concentration risk
CreditRisk+ provides a means of measuring diversification and
concentration by sector.
More diverse portfolios with fewer concentrations require less
economic capital.
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Credit Metrics
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Introduction
CreditMetrics™ was launched by JP Morgan in 1997
It evaluates credit risk by predicting movements in the credit
ratings of the individual investments in a portfolio.
CreditMetrics consists of three main components:
– Historical data sets
– A methodology for measuring portfolio Value at Risk (VAR)
– A software package known as CreditManager®
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Transition Matrices and Probability of Default
CreditMetrics uses transition matrices to generate a
distribution of final values for a portfolio.
A transition matrix reflects the probability that a bond with a
given rating will be upgraded or downgraded within a given
time horizon.
Transition matrices are published by ratings agencies such as
Standard and Poor's and Moody's.
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Data requirements
Credit ratings for the debtor
Default data for the debtor
Loss given default
Exposure
Information about credit correlations
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Methodology
CreditMetrics™ measures changes in portfolio value by
predicting movements in a debtor's credit ratings and
accordingly the values of individual portfolio investments.
 After the values of the individual portfolio investments have
been determined, CreditMetrics™ can then calculate the
credit risk.
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CreditMetrics™ Software – CreditManager®
The software used by Credit Metrics is called CreditManager.
CreditManager® enables a financial institution to consolidate
credit risk across its entire organization.
CreditManager® automatically maps each credit that the user
loads into the system to its appropriate debtor and market data
It computes correlations and changes in asset value over the
risk horizon due to upgrades, downgrades and defaults.
 In this way, it arrives at a final figure for portfolio credit risk.
The software uses two types of data :
– Position
– Market
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Steps for calculating credit risk for a single-credit
portfolio
Determine the probability of credit rating migration.
Calculate the current value of the bond's remaining cashflows
for each possible credit rating.
Calculate the range of possible bond values for each rating.
Calculate the credit risk.
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Steps for calculating credit risk for a two-credit
portfolio
Examine credit migration.
Calculate the range of possible bond values for each rating
using independent or correlated credit migration probabilities.
Calculate the credit risk.
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Steps for calculating credit risk for a multiplecredit portfolio
Calculate the distribution of values using a Monte Carlo
simulation.
Use the standard deviation and percentile levels for this
distribution to calculate credit risk for the portfolio.
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Single credit portfolios
The steps to calculate distributed values for single-credit
portfolios are:
Determine the probability of change in credit ratings.
Calculate the value of remaining cash flows for each possible
credit rating.
Calculate the range of possible credit values for each rating.
The first step is to examine the probability of the bond moving
from an one credit rating to another say within of one year.
The movement from one credit rating to another is known as
credit migration.
Credit rating agencies publish credit migration probabilities
based on historic data.
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Bond values for different ratings
Having examined the different probabilities for credit rating
migration, the next step is to calculate the range of possible
bond values for each rating.
That means calculating the value of Bond X for a credit rating
of Aaa, Aa, A, Baa, Ba, B, Caa, Ca, C.
To do this, we first need to calculate the value of the bond's
remaining cash flows for each possible rating.
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Discounting the cashflows
We use discount rates to calculate the current value of the
bond's remaining cashflows for each credit rating.
These discount rates are taken from the forward zero coupon
curve for each rating.
The forward zero coupon curve ranges from the end of the
risk horizon – one year from now – to maturity.
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Given a distribution of final values for Bond X, we can then
calculate two risk measurements for the portfolio:
– Standard deviation
– Percentile
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Multiple-Credit Portfolios
Because of the exponential growth in complexity as the
number of bonds increases, a simulation-based approach is
used to calculate the distribution of values for large portfolios.
Using Monte Carlo simulation, CreditMetrics simulates the
quality of each debtor, which produces an overall value for the
portfolio.
This procedure is then repeated many times in order to get
the distributed portfolio values.
After we have the distributed portfolio values, we can then use
the standard deviation and percentile levels for this
distribution to calculate credit risk for the portfolio.
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Portfolio Value Estimates at Risk Horizon
CreditMetrics requires three types of data to estimate portfolio
value at risk horizon:
– coupon rates and maturities for loans and bonds
– drawn and undrawn amounts of a loan, including spreads or fees
– market rates for market driven instruments, such as swaps and forwards
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Correlations
One key issue in using Credit Metrics is handling correlations
between bonds.
While determining credit losses, credit rating changes for
different counterparties cannot be assumed to be independent.
How do we determine correlations?
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Gausian Copula
A Gaussian Copula Model comes in useful here.
Gaussian Copula allows us to construct a joint probability
distribution of rating changes.
The Copula correlation between the ratings transitions for two
companies is typically set equal to the correlation between
their equity returns using a factor model.
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