This is a talk on the compensation for bearing risk in markets for single-name credit as well as structured credit. Presented at the National Forum on Management, organized by HEC, SSHRC and the Canadian Federation of Business School Deans (CFBSD).

1. The compensation for risk in credit markets
Jan Ericsson
McGill
1

2. Plan of the talk
• Primer on credit derivatives and structured credit.
• Risk premia in single-name credit markets.
• Risk premia and credit ratings.
• Implications for structured credit ratings.
2

3. 3

4. 4

5. Basic CDO structure
tranche
Tranches
average rating rated AAA
might be BBB or above
would by
far the
largest
part
(80-90%)
Individual CDS ... are pooled ... ... and tranched
Contracts / credits
5

6. Rating CDOs
Single name DPs
Simulation
Recovery assumptions attachment point
Engine
(Monte Carlo)
Correlation measure
default probability / tranche rating Tranche loss distribution
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7. Default dependence and tranche values
• Suppose that the default probability of each CDO asset is 5% over a certain
horizon.
• Maximum positive correlation would mean that 5% of the time, the
entire portfolio defaults and 95% of time no credit defaults.
• Maximum negative correlation would mean that 5% of the portfolio
always defaults over the given horizon.
• In the first scenario both equity and debt tranches are at risk of massive
losses that occur infrequently.
• In the second scenario the equity tranche is sure to sustain losses but
debt tranches are completely insulated from it.
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8. Definition of a risk premium
• Basic tenet of finance theory: investors are rewarded by higher expected
returns only for bearing non-diversifiable risk.
• In credit markets this will impact the price of default protection in CDS and
multi-name markets.
• But yields / spreads must not be confused with expected returns: spreads
will be positive even if there is no systematic default risk.
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9. What’s in a credit spread?
• Consider a world without taxes and with perfectly liquid markets
• Suppose that default risk is completely diversifiable: objective (P)=
risk neutral (Q) survival rates
• Assume P= 90%, zero recovery and r=5%. What is the bond yield
(and spread)?
0.9 · 100 100
B= = 85.71 = 85.71 → y = 0.1667
1.05 1+y
s = 11.67%
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10. Systematic default risk
• So a positive spread over the risk free rate does not mean there is
a premium for default risk - just compensation for expected losses.
• Suppose now that default risk is systematic and as a result there is
a default risk premium
• This will translate into a lower risk-adjusted survival probability than the
objective (Q<P) 0.9, say 0.8. So the bond price would be
0.8 · 100 100
B= = 76.16 = 76.16 → y = 0.3130
1.05 1+y
s = 26.3%
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11. Expected loss / Risk premia (EL / RP)
• So the total spread of 26.3% consists of
11.67% compensation for expected losses (EL spread)
14.63% default risk premium (RP spread).
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12. Why is this important?
• Asset allocation (across products / over the cycle).
• Bonds / CDS with the same rating / default rate can have very different
spreads depending on the systematic nature of their default risk.
• Bonds / CDS across rating categories appear to have different mixes of
expected losses / risk premia.
• The same is true for multi-name tranched products. Equity tranches
may have more risk in an absolute sense but super senior tranches
should compensate more for systematic risk than expected losses.
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13. Systematic risk in the CDX constituent firms
(Equity betas and volatilities)
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14. How we compute risk premia
N
P
Bt,T = di · ci · (1 − Pt (τ < si )) + dN · p · (1 − Pt (τ < T ))
i=1
T
P
+R · p · ds · dPt (s) →y
t
N
Q
Bt,T = di · ci · (1 − Qt (τ < si )) + dN · p · (1 − Qt (τ < T ))
i=1
T
+R · p · ds · dQt (s) → y Q,model , y Q,market
t
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15. 97% of the data (excluding AAA, CCC and less)
0.14
0.12 Model default probabilities
Moody’s default experience 1970−2004
0.1
0.08
0.06
0.04
0.02
0
0 2 4 6 8 10 12 14 16 18 20
Horizon (years)
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16. 300 300
Market spread (bps) Expected loss component (bps)
250 250
200 200
150 150
100 100
50 50
0 0
95 97 00 02 95 97 00 02
300 1
risk premium component (bps) EL ratio
250 RPratio
0.8
200
0.6
150
0.4
100
0.2
50
0 0
95 97 00 02 95 97 00 02
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17. What drives risk premia?
100 40
RP swap curve (bps)
S&P 500 volatility in percentage
50 20
0 0
95 96 97 98 99 00 01 02 03 04
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18. Our findings - summary
• Risk premia are highly time-varying
• Expected losses and risk premium spread components behave
differently.
• RP tends to be higher in a relative sense for higher grade credits and in
times of relatively low default rates.
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19. Implications and discussion
• Current single-name credit ratings:
• do not give information about the amount of systematic risk an
investment is exposed to. Not all AAAs created equal
• If high spread exposures are favoured within a rating category, then
the portfolio may be biased towards higher systematic risk /
correlation - which will hurt the most in turbulent markets.
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20. Implications and discussion II
• Structured credit ratings: mostly based on static Gaussian Copula models
+ historical default rates.
• Difficult to check scenarios on e.g. volatility (see example)
• Ignore risk premia - you can see significant degradation in MTM
without defaults - increased discount rates suffice.
• If firms in a CDO are selected on the basis of spread for a given
rating (cheapest to supply) then the actual correlation in pool greater
than industry averages.
• Correlation assumptions.
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21. Rating sensitivity
Associated returns
(VIX)
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Volatility (e.g. VIX)
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Volatility (e.g. VIX)
Based on Merton (1974) with 35% leverage - think of this as a naive model of the CDX
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22. CDO implied vs CDS implied correlations
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