drake drake university universite d’auvergne creditmetrics
TRANSCRIPT
UNIVERSITED’AUVERGNE
DrakeDrake 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 valueNeed a method to evaluate the changes in value related to changes in credit quality of the issuer in a portfolio context.
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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 derivativesNew products based upon migration.
UNIVERSITED’AUVERGNE
DrakeDrake 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 rightCredit 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Credit Metrics
User Portfolio
Ratings & Equities Series
Credit SpreadsSeniority
Credit Rating
Rat Migration
Likelihoods
PV Bond Revaluatio
n
Market Volatilities
Recov Rate in Default
Models (Correlatio
n)
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
UNIVERSITED’AUVERGNE
DrakeDrake University
Step 1 VaR due to Credit
Credit SpreadsSeniority
Credit Rating
Rat Migration
Likelihoods
PV Bond Revaluatio
n
Recov Rate in Default
Standard Deviation of value due to credit quality changes for 1 exposure
Value at Risk due to Credit
UNIVERSITED’AUVERGNE
DrakeDrake 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 Revaluatio
n
Recov Rate in Default
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
Year end rating
Probability
AAA 0.02
AA 0.33
A 5.95
BBB 86.93
BB 5.30
B 1.17
CCC 0.12
Default 0.18
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Rating at Year End (% )InitialRating AAA AA A BBB BB B CCC Defaul
t
AAA 90.81 8.33 0.68 0.06 0.12 0 0 0
AA 0.70 90.65 7.79 0.64 0.06 0.14 0.02 0
A 0.09 2.27 91.05 5.52 0.74 0.26 0.01 0.06
BBB 0.02 0.33 5.95 86.93 .30 1.17 0.12 0.18
BB 0.03 0.14 0.67 7.73 80.53 8.84 1.00 1.06
B 0 0.11 0.24 0.43 6.48 83.46 4.07 5.20
CCC 0.22 0 0.22 1.30 2.38 11.24 64.86 19.79
UNIVERSITED’AUVERGNE
DrakeDrake 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 Revaluatio
n
Recov Rate in Default
UNIVERSITED’AUVERGNE
DrakeDrake University
Recovery Rates
Senority Class Mean (% ) Stnd Dev (% )
Senior Secured 53.80 26.86
Senior Unsecured 51.13 25.45
Sen Subordinated 38.52 23.81
Subordinated 32.74 20.18
Junior Sub 17.09 10.90
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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 Revaluatio
n
Recov Rate in Default
UNIVERSITED’AUVERGNE
DrakeDrake 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 horizonAssume for the example that the horizon is one year.
UNIVERSITED’AUVERGNE
DrakeDrake 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:
44
33
221 )1(
106
1
6
)1(
6
1
66
rrrrV
UNIVERSITED’AUVERGNE
DrakeDrake 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)
UNIVERSITED’AUVERGNE
DrakeDrake University
One year forward zero rate curves
Category Year 1 Year 2 Year 3 Year 4AAA 3.60 4.17 4.73 5.12AA 3.65 4.22 4.78 5.17A 3.72 4.32 4.93 5.32
BBB 4.10 4.67 5.25 5.63BB 5.55 6.02 6.78 7.27B 6.05 7.02 8.03 8.52
CCC 15.5 15.02 14.03 13.52
UNIVERSITED’AUVERGNE
DrakeDrake 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
66.108)0532.1(
106
0493.1
6
)0432.1(
6
0372.1
66
432
V
UNIVERSITED’AUVERGNE
DrakeDrake University
One year forward values plus coupon
Year End Rating ValueAAA $109.37AA 109.19A 108.66
BBB 107.55BB 102.02B 98.10
CCC 83.64Default 51.13
UNIVERSITED’AUVERGNE
DrakeDrake University
Expected value of Bond
The expected value of the bond is then simply the sum of the values multiplied by the probabilities
UNIVERSITED’AUVERGNE
DrakeDrake University
Year End Rating Value Prob(% ) VxProb
AAA $109.37 .02 .02
AA 109.19 .33 .36
A 108.66 5.95 6.47
BBB 107.55 86.93 93.49
BB 102.02 5.30 5.41
B 98.10 1.17 1.15
CCC 83.64 .12 1.10
Default 51.13 .18 0.09
Sum = 107.09
UNIVERSITED’AUVERGNE
DrakeDrake 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.
99.2
09.107))13.51%(18.0)64.83%(12.0
)10.98%(17.1)02.102%(3.5)55.107%(93.86
)66.108%(95.5)19.109%(33.0)37.109%(02.0(
)(
222
222
222
1
22
S
iiitotal valueaverageValueprob
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
New calculation of Standard Dev
18.3
09.107)45.2513.51%(18.0)064.83%(12.0
)010.98%(17.1)002.102%(3.5)055.107%(93.86
)066.108%(95.5)019.109%(33.0)037.109%(02.0(
)()(
2222
222
222
1
222
S
iiiitotal valueaverageValueprob
UNIVERSITED’AUVERGNE
DrakeDrake University
Credit Metrics
User Portfolio
Ratings & Equities Series
Credit SpreadsSeniority
Credit Rating
Rat Migration
Likelihoods
PV Bond Revaluatio
n
Market Volatilities
Recov Rate in Default
Models (Correlatio
n)
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
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Portfolio Values
AAA AA A BBB BB B CCC D
106.59 106.49 106.3 105.64 103.15 101.39 88.71 51.13
AAA 109.37 215.96 215.86 215.67 215.01 212.52 210.76 198.08 160.50
AA 109.19 215.78 215.68 215.49 214.83 212.34 201.58 197.90 160.32
A 108.66 215.25 215.15 214.96 214.30 211.81 210.05 197.37 159.79
BBB 107.55 214.14 214.04 13.85 218.19 210.70 08.94 196.37 158.79
BB 02.02 208.61 208.51 208.33 07.66 205.17 203.41 190.73 153.15
B 98.10 204.69 204.59 204.40 203.74 201.25 199.49 186.81 149.23
CCC 83.64 190.23 190.13 189.94 189.28 186.79 185.03 172.35 134.77
D 51.13 157.72 157.62 157.43 156.77 154.28 152.52 39.84 102.26
.
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake University
Rating Migration
Year End Rating Probability (% )AAA .09AA 2.27A 91.05
BBB 5.52BB 0.74B 0.60
CCC 0.01Default 0.06
UNIVERSITED’AUVERGNE
DrakeDrake 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%
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Joint Probabilities
AAA AA A BBB BB B CCC D
.09 2.27 91.05 5.52 0.74 0.26 0.01 0.06
AAA .02 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00
AA 0.33 0.00 0.04 0.29 0.00 0.00 0.00 0.00 0.00
A 5.95 0.02 0.39 5.44 0.08 0.01 0.00 0.00 0.00
BBB 86.93 0.07 1.81 79.69 4.55 0.57 0.19 0.01 0.04
BB 5.30 0.00 0.02 4.47 0.64 0.11 0.04 0.00 0.01
B 1.17 0.00 0.00 0.92 0.18 0.04 0.02 0.00 0.00
CCC 0.12 0.00 0.00 0.09 0.02 0.00 0.00 0.00 0.00
D 0.18 0.00 0.00 0.13 0.04 0.01 0.00 0.00 0.00.
UNIVERSITED’AUVERGNE
DrakeDrake University
Credit Risk Measures
Given the portfolio values and probabilities it is easy to calculate an expected value of the portfolio and standard deviation.
iStateinValueV
istateofyprobabilitpwhere
EVVp
VpEVValueExpected
i
i
S
iii
S
iii
35.3)(
63.213$
1
2
1
UNIVERSITED’AUVERGNE
DrakeDrake 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 33.25 standard deviations below the average.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Alternative approach
For the distribution in the example, the 1st percentile would result in a return of 204.40 9there 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 204.40.This implies a credit risk of 213.63–204.40= 9.23
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Credit Metrics
User Portfolio
Ratings & Equities Series
Credit SpreadsSeniority
Credit Rating
Rat Migration
Likelihoods
PV Bond Revaluatio
n
Market Volatilities
Recov Rate in Default
Models (Correlatio
n)
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
UNIVERSITED’AUVERGNE
DrakeDrake University
Exposures
So far we have only presented the case of credit risks in bondsOther types of exposures can be addressed using similar techniques.
UNIVERSITED’AUVERGNE
DrakeDrake University
Exposures
Non interest bearing receivables (trade credit)Bonds and LoansCommitments to lendFinancial letters of credit Market driven instrument (Swaps, forwards, etc)
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake University
Year end ratingFee: Un drawn Portion (Basis
Points)
AAA 3
AA 4
A 6
BBB 9
BB 18
B 40
C 120
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake University
Usage of Loan Commitment
Credit Rating Usage Usage of unused in Defualt
AAA 0.1% 69%
AA 1.6% 73%
A 4.6% 71%
BBB 20.0% 65%
BB 46.8% 52%
B 63.7% 48%
CCC 75% 44%
UNIVERSITED’AUVERGNE
DrakeDrake 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% reductionGiven that we start at 80% undrawn, we would have a 16.1%(80%) =12.9% increase in borrowing.
UNIVERSITED’AUVERGNE
DrakeDrake University
Year End Rating
Current Drawdown
Change in Drawdown
Est od New Drawdown
AAA 20 -19.6 .4
AA 20 -13 7
A 20 0 20
BBB 20 12.9 32.9
BB 20 35.4 55.4
B 20 49.6 69.6
CCC 20 59 79
Default 20 56.8 76.8
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake University
Observations
Some things are observed in the calculationsThe expected percentage drawn down is the most important factorFees have a relatively small impact on the revaluationsIt is possible to have negative revaluations greater than the current draw downCovenants that reset the spread on up and down grades would help in offsetting the risk
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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
UNIVERSITED’AUVERGNE
DrakeDrake 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 = 67,284,888Standard deviation = 1,136,077
UNIVERSITED’AUVERGNE
DrakeDrake University
Chart 11.4 to 11.8
As sample size increase confidence bands are tighter.
UNIVERSITED’AUVERGNE
DrakeDrake University
Chart 11.10
Combines risk measure (marginal standard deviation with credit exposure).Provides information about risk reduction possabilities.
UNIVERSITED’AUVERGNE
DrakeDrake 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.
UNIVERSITED’AUVERGNE
DrakeDrake 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.