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).

Published on: **Mar 3, 2016**

- 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 6
- 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. 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. 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. 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. 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. 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. Systematic risk in the CDX constituent ﬁrms (Equity betas and volatilities) 13
- 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. 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. 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. 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. 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. 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. 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. 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. CDO implied vs CDS implied correlations 22