1 Northwestern University Did Market Structure Contribute to the Recent Financial Crisis? P RESENTATION TO Ravi Mattu

2 (CDS – Bond) Basis Post the Lehman Bankruptcy:  What happened to the basis? –Historical behavior of the basis and volatility during the crisis  Plausible explanations –Issues with LIBOR –Risky counterparties and impact of default correlations –Market structure? Was the deleveraging in corporate bonds triggered by the basis? –Flows in the derivative market  A look at other Forward/Futures Markets –FX, Equities, Mortgages, Treasury Futures Role of Market Structure

3 OAS (bp) DateCorp IG Corp HY 9/12/ /16/ /8/ U.S. Investment Grade and High Yield Corporate Bond Spreads: Option Adjusted Spreads Over Treasuries a Source: Barclays Capital, Moody’s for default rates in the period, we assume recovery rates of 20% and that losses were equally distributed over this time period. ª Average for the Barclays Capital Indices. Breakeven Spreads Implied by default rates from

4 Definition of the (CDS – Bond) Basis Basis = CDS Spread – Par Priced Asset Swap Spread (over the Swap curve) of bond Adjustments Calculate CDS spread for a default swap with maturity matched to the cash bond by interpolating the par CDS curve. The Par Priced-Asset Swap Spread represents the Spread over LIBOR that would equal the risk-free present value of the coupon stream of a cash bond plus the current difference between par and the price of the bond: Where DF i is the risk free discount factor for time i, L i is the LIBOR rate for time i, c is the risky bond coupon and s is the par priced asset swap spread.

5 Average Daily Asset Swap Spread and (Bond–CDS) Basis: for A-rated Bonds Date Par asset Swap Spread (Bond-CDS) Basis 9/12/ bp 54bp 12/16/ /8/ Source: J.P.Morgan

6 Average Daily (Bond–CDS) Basis: by Rating (Bond-CDS) Basis DateABBBBB 9/12/ bp 105bp 126bp 12/16/ /8/ Source: J.P.Morgan

7 Libor As Well As Swap Spreads Were Contaminated  Libor is not a true transaction rate. Banks are asked at what rate they “perceive” they can raise rates.  Swap spreads have become extremely low in the 10-year sector and have been negative in the 30-year sector due to demand to receive fixed. On-the-run and Off-the-run 10-year Treasuries Par Asset Swap Spreads Spreads over LIBOR DateOn-the-runOff-the-run 9/12/08 -61bp -38bp 12/16/ /08/ Source: J.P.Morgan

8 Impact of Counterparty Credit Risk on CDS Spreads  Both parties in a CDS are exposed to counterparty risk.  However, the exposure is “asymmetric” with the buyer of protection having more exposure to the counterparty than the seller. Bond spread = CDS spread + Counterparty credit adjustment + Liquidity To estimate the adjustment required calculate the implied default probability of both the reference entity (on which the CDS is based) and the financial counterparty (the seller of protection) from the cash bond spreads. For an assumed default correlation calculate the joint probability of both the reference entity and the counterparty defaulting. Calculate counterparty credit adjustment from (see Appendix) and back out “liquidity” compensation. Subtract it from bond spread and iterate again using Bond Spread less liquidity premium to calculate default probability in step

9 Calculating Counterparty Credit Cost Adjustment – Numerical Example Reference Entity: A-rated Industrial CDS protection seller: A-rated financial Assumed recovery rates: Counterparty = 25%, Reference entity = 35% Assume, default correlation = 0.2 (3 to 5 year maturity) Date: November 3, 2008 Financials spread = 446 bp/treasuries A-rated Industrial spread = 602 bp/treasuries A-rated CDS – Bond basis = -279 bp Probability of default (4yr) for Financials = 15% Probability of default (4yr) for Industrial = 31% Joint probability of default = 8% Counterparty credit costs = 35 bp16 The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

10 Sensitivity of Counterparty Credit Costs to Spread Levels ¹ Par Asset Swap Spread is assumed to be 200bp above CDS spread. ² If reference entity bond spread is 400 bp and the spread on the seller of protection is 500bp, then the Counterparty credit adjustment is 33bp and the liquidity premium is 167bp. Default Correlation = 0.2 Source: Citadel Investment Group The analysis shown above is performed using Citadel proprietary models. The estimates and projections used in this presentation rely on numerous assumptions that forecast market conditions. These assumptions can be materially inaccurate. Further, regulatory changes can cause the models used to be materially inaccurate. The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

11 Sensitivity of Counterparty Credit Costs to Spread Levels Default Correlation = 0.4 Source: Citadel Investment Group The analysis shown above is performed using Citadel proprietary models. The estimates and projections used in this presentation rely on numerous assumptions that forecast market conditions. These assumptions can be materially inaccurate. Further, regulatory changes can cause the models used to be materially inaccurate. The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

12 Does Counterparty Risk Explain Movements in the (Bond-CDS) Basis? Counterparty Credit Adjustment Versus Average Basis in A-Rated Industrials Default Correlation between Reference Entity and Protection seller = 0.2 Source: Citadel Investment Group and J.P. Morgan The analysis shown above is performed using Citadel proprietary models. The estimates and projections used in this presentation rely on numerous assumptions that forecast market conditions. These assumptions can be materially inaccurate. Further, regulatory changes can cause the models used to be materially inaccurate. The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

13 Sensitivity of Counterparty Credit Cost Adjustment to Default Correlation Source: Citadel Investment Group and JP Morgan The analysis shown above is performed using Citadel proprietary models. The estimates and projections used in this presentation rely on numerous assumptions that forecast market conditions. These assumptions can be materially inaccurate. Further, regulatory changes can cause the models used to be materially inaccurate. The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

14 Maximum Possible Counterparty Credit Cost Adjustment Versus Average (Bond-CDS) basis on A-Rated Industrials Source: Citadel Investment Group and J.P. Morgan The analysis shown above is performed using Citadel proprietary models. The estimates and projections used in this presentation rely on numerous assumptions that forecast market conditions. These assumptions can be materially inaccurate. Further, regulatory changes can cause the models used to be materially inaccurate. The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

15 Historical Default Correlations Five and Ten Year Default Correlation by Initial Moody’s Ratings (1970 to 1993) Source: “Default Correlation and Credit Analysis”, Douglas J. Lucas, The Journal of Fixed Income, March Five Year Ten Year ABaaBaB ABaaBaB A Baa Baa B

16 Scale of Dealer Deleveraging in Corporate Bonds over 2007 and 2008 Source: Primary Dealer Survey, Federal Reserve Bank of New York

17 Scale of Deleveraging Relative to Peak Levels Source: Federal Reserve Bank of New York

18 Why did Dealers Have Large Positions in Corporate Bonds? Many Clients took credit risk exposure through single name CDS or structured credit tranches. Dealers could not offset the hedges by buying protection in the CDS market and, therefore, were buying corporate bonds (cash). These cash positions became extremely hard to finance during the crisis.

19 Change in “Haircut” or Initial Margin, April 2007 versus August 2008 April 2007August 2008 U.S. Treasuries Investment-grade Bonds High-yield Bonds Equities1520 Investment grade CDS15 Senior leveraged loans Mezzanine leveraged loans Prime MBS ABS Source: “Financial Stress and Deleveraging”, IMF Global Financial Stability Report, October 2008, Page 42

20 Market Structure and Dislocation in other Forward/Futures Markets ProductExchange/OTCClearing Mechanism  Credit DerivativesOTCBilateral till recently  U.S. Agency MortgagesOTCMultilateral, MBSCC  Foreign ExchangeLargely OTCMultilateral  Equities FuturesExchange (CME)Multilateral

21 Implied Financing of Forwards/Futures during the Crisis: Agency Mortgage Current Production Coupon (Implied spread over LIBOR for financing between front month delivery and back month delivery) Source: JP Morgan

22 Implied Spread in Financing Deposits in Various Currencies (Euros, Sterling, Yen) through 6 month U.S. Dollars Source: Citadel Investment Group and JP Morgan The analysis shown above is performed using Citadel proprietary models. The estimates and projections used in this presentation rely on numerous assumptions that forecast market conditions. These assumptions can be materially inaccurate. Further, regulatory changes can cause the models used to be materially inaccurate. The example shown should not be relied upon as representative of an actual investment. No representation is being made that any account will or is likely to achieve profits or losses similar to those being shown.

23 Implied Financing Rate in S&P 500 Futures (90 days Constant Maturity) Versus 3 months LIBOR Source: JP Morgan

24 Appendix

25 Citadel Methodology for Calculating Counterparty Credit - Derivations Step1: Calculating the marginal 4 year default probability 1

26  Let A be the event that the counterparty defaults, and B be the event that the reference entity defaults. Also, define I A and I B as the indicator functions of A and B respectively.  Following these definitions, we have: 2 (Joint Probability) Citadel Methodology for Calculating Counterparty Credit - Derivations Step2: Calculating the 4 year Joint default probability

27 3 Citadel Methodology for Calculating Counterparty Credit - Derivations  Step3: Backing-out the counterparty credit from the 4yr joint default probability

28 This presentation reflects the analysis and views of certain members of Citadel Investment Group, LLC’s Fixed Income Team. No recipient should interpret this presentation to represent the general views of Citadel Investment Group, LLC or its affiliates (together “Citadel”) or its personnel. Facts, analysis and views presented in this presentation have not been reviewed by, and may not reflect information known to, other Citadel professionals. This presentation is based upon information that Citadel considers to be reliable, but Citadel does not warrant to its completeness, accuracy or adequacy and it should not be relied upon as such. Assumptions, opinions, views and estimates constitute the Fixed Income Team’s judgment as of the date of this presentation and are subject to change without notice and without any duty to update. Citadel is not responsible for any errors or omissions contained in this presentation and accepts no liability whatsoever for any direct or consequential loss arising from your use of this presentation or its contents. The analysis in this presentation was based on a number of quantitative and qualitative estimations and assumptions. These assumptions and estimations were subjectively determined and may not be accurate. Different estimations and assumptions would have produced materially different results. As a result, the analysis in this presentation has many inherent limitations and no representation is being made that the analysis will translate into actual outcomes. This material is not intended as an offer or solicitation for the purchase or sale of any security or other financial instrument. Nothing in this presentation constitutes investment, legal, accounting or tax advice or a representation that any investment or strategy is suitable or appropriate to your individual circumstances or otherwise constitutes a personal recommendation to you. This presentation is not directed to, or intended for distribution to or use by, any person or entity who is a citizen or resident of or located in any locality, state, country or other jurisdiction where such distribution, publication, availability or use would be contrary to law or regulation or which would subject Citadel to any registration or licensing requirement within such jurisdiction. None of the material, nor its content, nor any copy of it, may be altered in any way, transmitted to, copied or distributed to any other party, without the prior express written permission of Citadel. Citadel may issue other presentations or materials that are inconsistent with, or reach different conclusions from, the information presented in this presentation. Those presentations and materials may reflect the different assumptions, views and analytical methods of the individuals who prepared them and Citadel is under no obligation to ensure that such other presentations or materials are brought to the attention of any recipient of this presentation. Citadel is involved in many strategies that relate to the asset classes mentioned in this presentation. Citadel’s businesses may make investment decisions that are inconsistent with the views, opinions or conclusions expressed in this presentation. All trademarks, service marks and logos used in this presentation are trademarks or service marks or registered trademarks or service marks of Citadel. Copyright All rights reserved.