The compensation for risk in credit markets
Jan Ericsson
McGill




                                              1
Plan of the talk

• Primer on credit derivatives and structured credit.


• Risk premia in single-name credit markets.


•...
3
4
Basic CDO structure


                                                            tranche




                            ...
Rating CDOs

Single name DPs

                                Simulation
Recovery assumptions                             ...
Default dependence and tranche values

• Suppose that the default probability of each CDO asset is 5% over a certain
  hor...
Definition of a risk premium

• Basic tenet of finance theory: investors are rewarded by higher expected
  returns only for ...
What’s in a credit spread?


• Consider a world without taxes and with perfectly liquid markets

• Suppose that default ri...
Systematic default risk
• So a positive spread over the risk free rate does not mean there is
  a premium for default risk...
Expected loss / Risk premia (EL / RP)


 • So the total spread of 26.3% consists of

   11.67% compensation for expected l...
Why is this important?

• Asset allocation (across products / over the cycle).


   • Bonds / CDS with the same rating / d...
Systematic risk in the CDX constituent firms




                     (Equity betas and volatilities)




                 ...
How we compute risk premia

             N
  P
 Bt,T   =         di · ci · (1 − Pt (τ < si )) + dN · p · (1 − Pt (τ < T ))...
97% of the data (excluding AAA, CCC and less)

        0.14


        0.12       Model default probabilities
             ...
300                                       300
                    Market spread (bps)              Expected loss component...
What drives risk premia?

     100                                                                    40
                 ...
Our findings - summary



• Risk premia are highly time-varying

• Expected losses and risk premium spread components behav...
Implications and discussion

• Current single-name credit ratings:


     • do not give information about the amount of sy...
Implications and discussion II

• Structured credit ratings: mostly based on static Gaussian Copula models
  + historical ...
Rating sensitivity
                                                        Associated returns
                      (VIX)
...
CDO implied vs CDS implied correlations




                                          22
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National Forum, Montreal 2009

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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).

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  • National Forum, Montreal 2009

    1. 1. The compensation for risk in credit markets Jan Ericsson McGill 1
    2. 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. 3
    4. 4. 4
    5. 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. 6. Rating CDOs Single name DPs Simulation Recovery assumptions attachment point Engine (Monte Carlo) Correlation measure default probability / tranche rating Tranche loss distribution 6
    7. 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. 7
    8. 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. 8
    9. 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% 9
    10. 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% 10
    11. 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). 11
    12. 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. 12
    13. 13. Systematic risk in the CDX constituent firms (Equity betas and volatilities) 13
    14. 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 14
    15. 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) 15
    16. 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 16
    17. 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 17
    18. 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. 18
    19. 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. 19
    20. 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. 20
    21. 21. Rating sensitivity Associated returns (VIX) )!"# Volatility (e.g. VIX) &$% )*$% ("$% (*$% '"$% '*$% ""$% "*$% #"$% !#$% (!"# !)&$% '!"# !)#$% &!"# *+# !(&$% ,,,# !(#$% ,# %!"# ---# !'&$% -# $!"# ...# !'#$% !"&$% !"# $("# %!"# %("# &!"# &("# '!"# '("# (!"# !"#$% Volatility (e.g. VIX) Based on Merton (1974) with 35% leverage - think of this as a naive model of the CDX 21
    22. 22. CDO implied vs CDS implied correlations 22

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