1. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 1 A Study of Sellers of Senior Tranched Credit Protection Jon Gregory Quant Congress USA July 8 th 2008

2. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 2 Related Papers “Credit Tails”, Risk article, January 2008 “A Trick of the Credit Tail”, Risk technical paper, March 2008 “A Free Lunch and the Credit Crunch”, to be published August 2008 “Two Faced Over Counterparty Credit Risk?”, working paper Please email me at jon-gregory@supanet.com for copies of these articlesjon-gregory@supanet.com

3. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 3 The Failure of the Gaussian Copula Model Market Gaussian Copula Model 24.00% 19.3% 82.5234.7 26.582.0 14.032.9 8.756.99 3.530.05 Dependency is defined by a single correlation parameter – No concept of idiosyncratic default – No concept of systemic default Super Senior 22-100% Equity 0-3% 3-6% 6-9% 12-22% 9-12%

4. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 4 CDO Investor Landscape [0-3%] [3-7%] [7-10%] [10-15%] [15-30%] And [30-100%] Rating of counterparty Risk of underlying Hedge funds Aaa rated Monolines and CDPCs no CSA Real money investors under CSA NR Baa Aa Aaa Super Aaa

5. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 5 The Correlation Skew in Credit Super Senior 22-100% Equity 0-3% 3-6% 6-9% Index [0-100%} 12-22% 9-12% 5Y iTraxx Europe (Investment Grade Corporate Index) 110 bps [0-3%]35% [3-6%]465 bps [6-9%]335 bps [9-12%}250 bps [12-22%]110 bps [22-100%]40 bps

6. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 6 Into the Super Senior Space Super Senior 22-100% Equity 0-3% 3-6% 6-9% 12-22% 9-12% Each default causes loss of (1-  )/125 = 0.48% (40% rec) 22% of losses requires 22% / 0.48% = 46 defaults 5Y [22-100%] pays around 50 bp pa ! Long protection on 7Y [22-100%] (Delta hedged)

7. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 7 The Toothpaste Tube Analogy (I) Super Senior 22-100% Equity 0-3% 3-6% 6-9% Index [0-100%] 12-22% 9-12% Index = Sum of tranches [22-100%] = [0-100%] – [0-3%] – [3-6%] – [6-9%] – [9-12%] – [12-22%] Typically method for extracting super senior premium implicitly assumes flat correlation curve up to 5Y 2Y5Y [0-3%]13.52%25.75% [3-6%]3.3 bps60.5 bps [6-9%]-1.0 bps19.5 bps [9-12%]-0.9 bps11.0 bps [12-22%]-0.5 bps6.0 bps

8. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 8 Summary of Super Senior Pricing We can’t price [22-60%] We can’t price tranchelets in the [22-60%] region We can’t price bespoke super senior

9. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 9 The Toothpaste Tube Analogy (II) Small changes in equity duration assumptions can change the size of the tube Upper bound where [22-100%] is equal to [12-22%] / Lower bound where [22-100%] is worth zero Change in 3Y equity premium (or IO/PO prices) moves super senior significantly Upper bound

10. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 10 Extrapolation of Base Correlation Curve Even if we can price the [22-100%] – Pricing of 1% wide tranchelets in the [22-60%] region – Clearly not arbitrage-free – No value put in the [1- , 100%] part of the capital structure (  is 40% in this case)

11. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 11 Pricing of Bespoke Super Senior Forced index tranchlets to be arbitrage-free (value distributed equally within [22-60%]) On a portfolio which is 14% more risky, common scaling techniques introduce arbitrage On a more risky portfolio this potentially becomes worse index bespoke

12. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 12 Packaging Super Senior Risk Leveraged super senior (LSS) trades – A leveraged transaction with a defined trigger event Credit derivative product companies (CDPC) – Like a more complex LSS – Trigger is not so well defined – CDPC has multiple counterparties Monoline insurer – Similar to CDPC but will insurer other financial risks also – Should benefit from diversification

13. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 13 Leveraged Super Senior Illustration × Leverage Super senior tranche pays small premium Leverage this (typically around 10 times) Create a structure paying a ‘good’ premium referenced to a default remote tranche Investor loss will come when structure deleverages –Investor may have option to post more collateral –Alternatively an unwind will occur Collateral Uncollateralized Portion

14. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 14 Rating Super Senior Risk Packaging super senior tranches can always be made to look like triple-A counterparty risk Super senior tranche (Triple-A) Packaged Super senior tranche (at least Triple-A) Capital (share) of monoline / CDPC etc (  )

15. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 15 LSS Unwind Triggers Loss only trigger –Simple to rate (default risk only, like a CDO tranche) –Issuer retains spread and implied correlation risk Spread (+ loss) triggers –More complex to rate (includes spread dynamics in rating model) –Issuer retains implied correlation risk Market value triggers –Very hard to rate (only one rating agency DBRS have ever done so) –Issuer retains only gap risk

16. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 16 Leveraged Super Senior Pricing Argument There is around $200+ billion of leveraged super senior protection out there Issuers seem to price via the equivalence argument Advantage is that we simple argue that gap risk is very small –Example : at 10 times leverage, a market value trigger of 5% is ‘safe’ This is a standard argument applied to lots of leveraged products (CPPI etc, ….) This argument is wrong for LSS LSS Protection value = SS Protection value  Leverage – Gap Risk

17. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 17 LSS Protection Valuation Bounds Perfect trigger No trigger “Gap Risk” [A, B] Upper Bound LSS Value?? × L [A, A+  ] Lower Bound

18. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 18 LSS Pricing Denote –trigger time by –initial collateral by Trigger ? No Yes Standard tranche protection Settle contract with cap at collateral value

19. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 19 LSS Pricing (II) Collateralised Protection De-leverage value Unwind value Gap option = 0 Even if client has option to deleverage then it is suboptimal

20. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 20 Formal Valuation Setting de-leverage term to zero Lower Bound Trigger Option

21. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 21 Leveraged Super Senior Overview [A, B] Upper Bound [A, A+  ] Lower Bound Perfect trigger No trigger “Gap Risk” “Trigger Option” Actual LSS Value

22. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 22 Pricing the Trigger Option Pricing (and hedging!) the trigger option is not easy –Out of the money tranche option payoff But we can get some insight in the loss only trigger case –Here we can overhedge with a contract paying  at the loss trigger K –This is simply a digital CDO tranche This effectively sets a maximum leverage independent of gap risk

23. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 23 Example For the (5Y) tranche markets as shown We calculation the maximum leverage for –A [22-100%] LSS structure –5-year maturity –With a loss trigger as a function of loss trigger level 4 th May 200519 th March 20074 th December 2007 Index442553 [0-3%]29.00%11.87%25.05% [3-6%]16854.5156.3 [6-9%]4914.885 [9-12%]256.860 [12-22%]162.834 [22-100%]5.52.415.0

24. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 24 Maximum Leverage Leverage Super Senior Pricing is not a gap risk problem!

25. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 25 Monolines and CDPCs Capital model –(Tranche) Ratings driven run on a daily basis –Capital (less any losses) must be above capital required by model to support Aaa rating Operating modes (CDPC / monoline) –Normal operating mode / Triple-A rating –Suspension mode / downgrade –Wind-down mode / Run-off Required capital Aaa attachment Ratings driven loss distribution

26. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 26 Monoline / CDPC Comparison with LSS Normal State Restricted State Wind-down State Trigger Not Hit < 6 months Losses to tranches Trigger Hit Full Deleverage (unwind) Losses to tranches Monoline / CDPC Leverage Super Senior De-leverage

27. A Study of Sellers of Senior Tranched Credit Protection, Jon Gregory, London 8 th July 2008 27 CDPC / Monoline Purchased Protection [A, B] Upper Bound [A, A+  ] Lower Bound for LSS “Counterparty Risk” No value Impact of effective leverage