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Credit Metrics. By: A V Vedpuriswar. November 11, 2010. 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:

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Credit metrics

Credit Metrics

By: A V Vedpuriswar

November 11, 2010


Introduction
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
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
Data requirements

  • Credit ratings for the debtor

  • Default data for the debtor

  • Loss given default

  • Exposure

  • Information about credit correlations


Methodology
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.



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

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Creditmetrics software creditmanager
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
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
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
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
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
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
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.



Multiple credit portfolios
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
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
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
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
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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