Credit Risk Plus and Credit Metrics

October 4, 2009

By: A V Vedpuriswar

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.

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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1111

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

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

IntroductionCreditMetrics™ 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 25

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 multiple-credit 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.