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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®

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 of a given rating being upgraded or downgraded within a given time horizon.
- Transition matrices are published by ratings agencies such as Standard and Poor's and Moody's.

Data requirements

- Credit ratings for the debtor
- Default data for the debtor
- Loss given default
- Exposure
- Information about credit correlations

Methodology

- CreditMetrics™ measures changes inportfolio value by predicting movements in a debtor's credit ratings.
- After the values of the individual portfolio investments are determined, CreditMetrics™ can calculate the credit risk.

Average cumulative default rates (%), 1970-2003 (Source: Moody’s)

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Recovery rates on corporate bonds as a percent of face value, 1982-2004. (Source: Moody’s).

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CreditMetrics™ Software – CreditManager® value, 1982-2004. (

- 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

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.

Steps for calculating credit risk for a two-credit portfolio 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.

Steps for calculating credit risk for a multiple-credit portfolio

- Calculate the distribution of values using a Monte Carlo simulation.
- Use the standard deviation for this distribution to calculate the credit risk for the portfolio.
- Alternatively use percentile levels.

Single credit portfolios portfolio

- 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.

Bond values for different ratings portfolio

- 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.

Discounting the cashflows portfolio

- 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.

- Given a distribution of final values for Bond X, we can then calculate two risk measurements for the portfolio:
- Standard deviation
- Percentile

Multiple-Credit Portfolios calculate two risk measurements for the portfolio

- 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 to calculate credit risk for the portfolio.
- Alternatively, we can use percentile levels.

Portfolio Value Estimates at Risk Horizon calculate two risk measurements for the portfolio

- 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

Correlations calculate two risk measurements for the portfolio

- 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 calculate two risk measurements for the portfolio

- 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.

Implementing Credit Metrics calculate two risk measurements for the portfolio

- The first step is to estimate the rating class for a debt claim.
- The rating may remain the same, improve or deteriorate, depending on the firm’s performance.
- Ratings transition matrix gives us the probability of the credit migrating from one rating to another during one year.
- Next, we construct the distribution of the value of the debt claim.
- We compute the value we expect the claim to have for each rating in one year.

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- Based on the term structure of bond yields for each rating category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.
- If the migration probabilities are independent, we can compute the probabilities for transition of each bond independently and multiply them to obtain the joint probability.
- By computing the value of the portfolio for each possible outcome and the probability of each outcome, we can construct the distribution for the portfolio value.
- We can then find out the VAR at a given level of confidence.

Transforming distributions with Gaussian copula category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

Bivariate distribution with 0.3 correlation

Transforming distributions with Gaussian copula category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

Joint probability distribution using Gaussian Copula, category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year. ρ=0.5

Credit Metrics Illustration category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

The Credit migration of a BBB Bond category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

Gupton, Finger, Bhatia, Credit Metrics technical document

Using the forward curve to compute bond values category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

Consider an A Bond. The present value of cash flows can be calculated as follows:

V = 6 + 6/1.0372 + 6/1.04322+ 6/1.04933+ 106/1.05324= 108.66

Consider a BBB Bond. The present value of cash flows can be calculated as follows:

V = 6 + 6/1.041 + 6/1.04672 + 6/1.05253 + 106/1.05634 = 107.55

The credit migration of an A Bond category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

Gupton, Finger, Bhatia, Credit Metrics technical document

Gupton category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year. , Finger, Bhatia, Credit Metrics technical document

Gupton category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year. , Finger, Bhatia, Credit Metrics technical document

Gupton category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year. , Finger, Bhatia, Credit Metrics technical document

Distribution of portfolio returns category, we can get today’s price of a zero coupon bond for a forward contract to mature in one year.

Gupton, Finger, Bhatia, Credit Metrics technical document

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