Drake DRAKE UNIVERSITY UNIVERSITE D’AUVERGNE CreditMetrics

UNIVERSITE D’AUVERGNE Drake Drake University Credit Risk Generally Credit risk is related to the probability of default. However default does not necessarily imply that a zero recovery rate. Also changes in credit quality can cause changes in value Need a method to evaluate the changes in value related to changes in credit quality of the issuer in a portfolio context.

UNIVERSITE D’AUVERGNE Drake Drake University Credit Metrics vs. Risk Metrics RiskMetrics Large amount of Data Conditional Volatility Depends on Normality Assumptions Historical Data Produces Distributions of Returns CreditMetrics Limited Data Unconditional Volatility No dependence on Normality Historical Data using Migration Analysis Credit changes based on likelihood with outcomes related to value change

UNIVERSITE D’AUVERGNE Drake Drake University Portfolio Considerations Need to address portfolio impacts due to the possibility of concentration risk. Traditionally this is accomplished with intuitive exposure based credit limits. A more quantitative approach allows for investigation in terms of portfolio volatility.

UNIVERSITE D’AUVERGNE Drake Drake University Reasons for Quantitative Approach Complexity of Financial Products including more derivative instruments make managing exposures more difficult. Increased use of credit enhancements (3rd party guarantees, margin arrangement etc) Improved liquidty in secondary cash markets and increased use of credit derivatives New products based upon migration.

UNIVERSITE D’AUVERGNE Drake Drake University Portfolios of Credit Risk Unlike equity returns, credit returns are not symmetric. The downside loss is larger (fat tails) and the mean is skewed to the right Credit returns can be characterized as having a large likelihood of receiving a fairly small return based on NIM, combined with a small chance of a large loss.

UNIVERSITE D’AUVERGNE Drake Drake University Credit Returns vs Equity Returns 0

UNIVERSITE D’AUVERGNE Drake Drake University Credit Metrics User Portfolio Ratings & Equities Series Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Market Volatilities Recov Rate in Default Models (Correlation) Joint Credit rating changes Exposure Distributions Portfolio Value at Risk Due to Credit Standard Deviation of value due to credit quality changes for 1 exposure Exposures Value at Risk due to CreditCorrelations

UNIVERSITE D’AUVERGNE Drake Drake University Step 1 VaR due to Credit Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Recov Rate in Default Standard Deviation of value due to credit quality changes for 1 exposure Value at Risk due to Credit

UNIVERSITE D’AUVERGNE Drake Drake University Given the current credit rating, the asset may change in rating over the next year. The probability of a rating change can be calculated from historical experience Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Recov Rate in Default

UNIVERSITE D’AUVERGNE Drake Drake University Example: Distribution of Returns for a single bond Consider a single BBB rated bond that matures in five years, pays a 6% yearly coupon payments and is a senior unsecured debt. If the rating changes over the course of the next year, there will be a corresponding change in the value of the bond. The value of the bond will depend upon the change in the rating and the level of interest rates.

UNIVERSITE D’AUVERGNE Drake Drake University Rating Changes The probability of a change in ratings can be observed historically based on the migration of bonds starting with a BBB ratings to other ratings classes.

UNIVERSITE D’AUVERGNE Drake Drake University Rating Changes Similar rating change migrations can be found for any beginning rating. The next slide shows the rating migration based upon S&P data covering the 15 years prior to 1996.

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UNIVERSITE D’AUVERGNE Drake Drake University If the bond defaults, it does not imply that there will be a zero recovery rate. The recovery rate by class of bond can be represents by the mean recovery rate and standard deviation by class of security. Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Recov Rate in Default

UNIVERSITE D’AUVERGNE Drake Drake University Recovery Rates

UNIVERSITE D’AUVERGNE Drake Drake University Recovery Rate In our example the bond is a senior unsecured debt. Assuming that the average recovery rate is received in the event of default, the bond would be worth $51.13 for every $100 of par value.

UNIVERSITE D’AUVERGNE Drake Drake University If the bond experiences a change in credit rating it will experience a change in its value. This is also a component of credit risk. The change in value can be calculated based upon the new rating at the end of the year and the forward level of interest rates associated with the rating class. Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Recov Rate in Default

UNIVERSITE D’AUVERGNE Drake Drake University PV of the bond The basic bond pricing formula states that the value of the bond at a given point of time is equal to the PV of the cash flows. In this case we want to consider the value of the bond at a time in the future, therefore we need to discount the cash flows back to the time in the future that corresponds with our risk horizon Assume for the example that the horizon is one year.

UNIVERSITE D’AUVERGNE Drake Drake University Example The bond in the example makes payments of $6 at the end of each year for the next five years. At the end of the year the next coupon payment would be received, it would have a PV at the end of the year of $6. Each of the other cash flows then needs to be discounted back to the end of the first year. The value is then:

UNIVERSITE D’AUVERGNE Drake Drake University Interest rates The value of the bond will depend upon the new rating and the level of rates corresponding to the zero spot forward rate curve that corresponds to that rating category. The forward rate represent the interest rate that is implied to be received in the future given the current yield curve for the risk class. Assume that we know the forward yield curve based upon risk class(shown on next slide)

UNIVERSITE D’AUVERGNE Drake Drake University One year forward zero rate curves

UNIVERSITE D’AUVERGNE Drake Drake University Value of the bond Assume that the bond is upgraded to a rating of A over the next year. Its value is then: Similarly the value for any of the ratings changes could be calculated. The value represents the mean value of the rating class given the characteristics of the bond

UNIVERSITE D’AUVERGNE Drake Drake University One year forward values plus coupon

UNIVERSITE D’AUVERGNE Drake Drake University Expected value of Bond The expected value of the bond is then simply the sum of the values multiplied by the probabilities

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UNIVERSITE D’AUVERGNE Drake Drake University Standard Deviation The standard deviation of the value can be found based on the probabilities of rating migration, the average (or expected) value and the values of the bond for each ratings class.

UNIVERSITE D’AUVERGNE Drake Drake University Accounting for uncertainty The values for each value represent an average outcome for each state. It is possible to account for the uncertainty in each sate by including a term based on the standard deviation of returns by state. For each of the up or down grade states this will be set to zero, for the default state we will use the calculated standard deviation from before.

UNIVERSITE D’AUVERGNE Drake Drake University New calculation of Standard Dev

UNIVERSITE D’AUVERGNE Drake Drake University Credit Metrics User Portfolio Ratings & Equities Series Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Market Volatilities Recov Rate in Default Models (Correlation) Joint Credit rating changes Exposure Distributions Portfolio Value at Risk Due to Credit Standard Deviation of value due to credit quality changes for 1 exposure Exposures Value at Risk due to Credit Correlations

UNIVERSITE D’AUVERGNE Drake Drake University Portfolios The first example looked at the individual risk of an asset, however most institutions will be concerned with the risk associated with a portfolio of assets. Example 2 keeping the first bond we looked at add a 3 year 5% coupon bond that makes annual interest payments and is a senior subordinated debt that is currently rated A.

UNIVERSITE D’AUVERGNE Drake Drake University Value of the new bond The value of the bond can be calculated across various ratings changes by discounting the future cash flows just like we did in the previous case. A portfolio of one $100 par value of each bond would then have 64 possible outcomes based upon the ratings of both bonds.

UNIVERSITE D’AUVERGNE Drake Drake University Portfolio Values

UNIVERSITE D’AUVERGNE Drake Drake University Portfolio values The combined portfolio value was easy to calculate for the two portfolio case, however as the number of assets it he portfolio grows the number of combinations becomes too large to deal with effectively. For example for a 5 asset portfolio there are 32,768 portfolio values

UNIVERSITE D’AUVERGNE Drake Drake University Rating Migration

UNIVERSITE D’AUVERGNE Drake Drake University Simple Joint Probability If the rating migration of the two bonds is independent of each other then the joint probability would be the simple product of the two probabilities. For example the probability of the A staying rated A is 91.05%, the probability of the BBB staying rated BBB is 86.93%. If independent the joint probability would be (91.05%)(86.93) = 79.15%

UNIVERSITE D’AUVERGNE Drake Drake University Joint Probability In reality there needs to consideration for the correlation between the two debts. Both originators of the debt respond to the same economic conditions and it is possible that when one of the bonds decreases in rating, the other may also.

UNIVERSITE D’AUVERGNE Drake Drake University Joint Probability A positive correlation would cause the joint probability to be higher than in the simple case. The correlation can be estimated from looking at changes in the value of both firms (or cash flows, etc.) Assuming that the correlation of the two firms is 0.3 the joint probabilities are given no the next page.

UNIVERSITE D’AUVERGNE Drake Drake University Joint Probabilities

UNIVERSITE D’AUVERGNE Drake Drake University Credit Risk Measures Given the portfolio values and probabilities it is easy to calculate an expected value of the portfolio and standard deviation.

UNIVERSITE D’AUVERGNE Drake Drake University Problems Since the distribution of returns is not normally distributed it is difficult to interpret the meaning of the standard deviation. In the previous example the maximum upside (215.96) is only.70 standard deviation from the average (213.63) while the maximum downside value (102.26) is standard deviations below the average.

UNIVERSITE D’AUVERGNE Drake Drake University Alternative approach You can also simulate results then rank order the outcomes. Given the probabilities and distribution it is possible to undertake a monte carlo simulation of possible values. Remember that each value is an average for the dual set of ratings. Once 10,000 simulations are performed it is easy to find a given percentile.

UNIVERSITE D’AUVERGNE Drake Drake University Alternative approach For the distribution in the example, the 1 st percentile would result in a return of there are 100 observations less than this out of the 10,000. This implies a VaR type number, there is a 1 % chance that the value will fall below This implies a credit risk of –204.40= 9.23

UNIVERSITE D’AUVERGNE Drake Drake University Interpretations Using the standard deviation we know that one standard deviation is 3.35, but that does not tell the whole story since the distribution is not normally distributed. The simulation provides a more intuitive result, but the standard deviation is usually quicker to calculate.

UNIVERSITE D’AUVERGNE Drake Drake University Credit Metrics User Portfolio Ratings & Equities Series Credit SpreadsSeniority Credit Rating Rat Migration Likelihoods PV Bond Revaluation Market Volatilities Recov Rate in Default Models (Correlation) Joint Credit rating changes Exposure Distributions Portfolio Value at Risk Due to Credit Standard Deviation of value due to credit quality changes for 1 exposure Exposures Value at Risk due to CreditCorrelations

UNIVERSITE D’AUVERGNE Drake Drake University Exposures So far we have only presented the case of credit risks in bonds Other types of exposures can be addressed using similar techniques.

UNIVERSITE D’AUVERGNE Drake Drake University Exposures Non interest bearing receivables (trade credit) Bonds and Loans Commitments to lend Financial letters of credit Market driven instrument (Swaps, forwards, etc)

UNIVERSITE D’AUVERGNE Drake Drake University Exposures The bond model required a two step process Specifying the likelihood and joint likelihood of experiencing a credit quality change Calculating the new values given each possible rating change The first step is the same for all the other exposure types.

UNIVERSITE D’AUVERGNE Drake Drake University Receivables Often receivables will be due in a shorter time frame than the risk horizon, if this is the case a change in rating is not an issue, only default (non payment or partial payment) is an issue. Therefore the key to look at recovery rates. There is a lack of information on receivable recovery rates, but a good approximation may be that for senior unsecured bond recovery rates.

UNIVERSITE D’AUVERGNE Drake Drake University Receivables Assume that you have a $1 Million receivable outstanding. In ach non default state, it pays the entire $1 Million. If the receivable defaults, assuming a 30% recovery rate, any default state would have a value of $300,000. The key is then to estimate the probability of default

UNIVERSITE D’AUVERGNE Drake Drake University Bonds and Loans Bonds have been covered in detail, a loan is very similar. Given the likelihood that a loan will be repaid (just like the likelihood for a bond) based upon a rating the value of the loan can be found. If default occurs a recovery rate based on the principal of the loan can be used to estimate the amount recovered.

UNIVERSITE D’AUVERGNE Drake Drake University Loan Commitments Composed of two parts, the drawn portion and undrawn portion. Interest is paid on the amount already drawn, and a fee is paid on the undrawn portion The fee compensates the institution for maintaining liquidity to cover the loan if exercised. The fee is based upon the rating of the creditor

UNIVERSITE D’AUVERGNE Drake Drake University Year end rating Fee: Un drawn Portion (Basis Points) AAA3 AA4 A6 BBB9 BB18 B40 C120

UNIVERSITE D’AUVERGNE Drake Drake University Ratings and Drawdown The borrower has the ability to exercise the loan commitment at any time. This implies that there can be sudden changes in the loan portfolio. It is likely that if the borrowers credit quality deteriorates, there will be a corresponding increase in the amount they borrow.

UNIVERSITE D’AUVERGNE Drake Drake University Ratings and Drawdown To account fro this some Loan commitments have covenants that allow for a floating interest rate based upon a credit spread tied to the rating of the borrower and the level of interest rates in the economy. The worst case scenario is that the entire loan commitment is drawn down and the borrower defaults.

UNIVERSITE D’AUVERGNE Drake Drake University Example Assume that you have a three year $100 million to lend at a fixed 6% interest rate (on the drawn portion) to a borrower currently rated A. There is currently $20 M drawn down and $80M unused which is charged a fee of 6 Bp. The revaluation based on credit rating will depend upon Changes in draw down as credit quality changes Change in value of both portions

UNIVERSITE D’AUVERGNE Drake Drake University Usage of Loan Commitment

UNIVERSITE D’AUVERGNE Drake Drake University An example Assume that the credit rating decreases to BBB from the original value of A. Asarnow and Market (1996) found that the draw increased from 4.6 to 20%, or the undrawn portion changed from 95.4% to 80% This is a 100% - (80%/95.4%)=16.1% reduction Given that we start at 80% undrawn, we would have a 16.1%(80%) =12.9% increase in borrowing.

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UNIVERSITE D’AUVERGNE Drake Drake University Change in value The change in value is a combination of the lost fee income (even though a higher fee is charged, it is on a lesser amount of unused portion of the Loan commitment) and lost income due to the credit spread widening on the fixed rate portion of the bond.

UNIVERSITE D’AUVERGNE Drake Drake University Observations Some things are observed in the calculations The expected percentage drawn down is the most important factor Fees have a relatively small impact on the revaluations It is possible to have negative revaluations greater than the current draw down Covenants that reset the spread on up and down grades would help in offsetting the risk

UNIVERSITE D’AUVERGNE Drake Drake University Market Driven Instruments Usually off balance sheet items such as swaps. Market risk and credit risk are intertwined due to the option nature of many of these instruments. To fully capture the credit risk would require an integrated model of both market and credit risk. Instead Credit metrics attempts to capture the credit component of the risk

UNIVERSITE D’AUVERGNE Drake Drake University Basic Intro The swap is valued similar to the bond and loan assuming that the counter party is in an out of the money position. This implies that there is a risk of default (they owe in terms of net present value) Given the expected cash flow stream, the value of the swap can be calculated as if it was a bond including the probability of default and credit rating changes.

UNIVERSITE D’AUVERGNE Drake Drake University Example from the tech document Given a 20 asset portfolio across ratings classes, the mean return and standard deviation of the portfolio 9based on the individual rating migrations and recovery rates) was calculated. Based on the results they generated 20,000 scenarios of possible outcomes in one’s years time

UNIVERSITE D’AUVERGNE Drake Drake University Charts 11.1 to 11.3 The most common occurrence (approximate value of $67 million assumes that there were no rating changes across all securities. Default events produce more significant value changes than the other scenarios. Mean portfolio value = 67,284,888 Standard deviation = 1,136,077

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UNIVERSITE D’AUVERGNE Drake Drake University Chart 11.4 to 11.8 As sample size increase confidence bands are tighter.

UNIVERSITE D’AUVERGNE Drake Drake University Chart Combines risk measure (marginal standard deviation with credit exposure). Provides information about risk reduction possabilities.

UNIVERSITE D’AUVERGNE Drake Drake University Applications of results Chart 12.1 graphs combinations of marginal standard deviation and absolute exposure, it is easy to see which assets have the greatest impact on risk. You can set limits on exposure and risk and adjust when exceeded.

UNIVERSITE D’AUVERGNE Drake Drake University Choosing a Time Horizon The time horizon in the example has been one year. Other horizons may be used but it is likely that the horizon should be shorter than a quarter. This is due to the frequency that rating changes occur and can be quantified. If other horizons are used, the results from before should be adjusted for the new time horizon.