1. IMPERFECTIONS OF CDO’S VALUATION Petra Benešová Institute of Economic Studies, Faculty of Social Sciences Charles University in Prague, Czech Republic 24 November 2009

2. Agenda Basic Principles of CDOs 2. One Factor Gaussian Copula Model 3. Results of the Model 4. Main Flaws of the CDO Market 5. 2 Imperfections of CDO's Valuation 24 November 2009 Introduction 1. Conclusion 6.6.

3. Introduction 3 Imperfections of CDO's Valuation 24 November 2009 Defininion of a CDO (collateralized debt obligation): “A structured credit security backed by a pool of securities, loans, or credit default swaps, where securitized interests in the security are divided into tranches with differing repayment and interest earning streams.” - Source: Global Financial Stability report, IMF, 2008 Definition of CDO

4. Agenda Basic Principles of CDOs 2. One Factor Gaussian Copula Model 3. Results of the Model 4. Main Flaws of the CDO Market 5. 4 Imperfections of CDO's Valuation 24 November 2009 Introduction 1. Conclusion 6.6.

5. Basic Principles of CDOs 5 Imperfections of CDO's Valuation 24 November 2009 CDO Structure CDO Originator Tranche 4 25-100% of loss Yield: 4% Tranche 3 15-25% of loss Yield: 8% Tranche 2 5-15% of loss Yield: 15% Tranche 1 0-5% of loss Yield: 30% Asset 1 Asset 2 Asset 3 Asset 100 Average yield: 6.8% Main features: leverage and diversification

6. Basic Principles of CDOs 6 Imperfections of CDO's Valuation 24 November 2009 Motivation Motives for an originator (CDO seller): 1.Transfer of a credit risk (original purpose) 2.Capital relief and liquidity 3.Arbitrage opportunity (main purpose) Motives for an investor (CDO buyer): 1.Standardization 2.Liquidity 3.Diversification

7. Basic Principles of CDOs 7 Imperfections of CDO's Valuation 24 November 2009 CDO Indices: iTraxx, CDX iTraxx: European and Asian underlying assets CDX: North American underlying assets iTraxx Europe 5Y, Series 3, Version 1 June 2004 – February 2009 Source: Bloomberg

8. Basic Principles of CDOs 8 Imperfections of CDO's Valuation 24 November 2009 CDO Issuance (in USD millions) Source: www.abalert.com

9. Basic Principles of CDOs 9 Imperfections of CDO's Valuation 24 November 2009 TOP CDO Issuers and their writedowns Source: authors based on www.abalert.com in Millions USD

10. Agenda Basic Principles of CDOs 2. One Factor Gaussian Copula Model 3. Results of the Model 4. Main Flaws of the CDO Market 5. 10 Imperfections of CDO's Valuation 24 November 2009 Introduction 1. Conclusion 6.6.

11. One Factor Gaussian Copula Model 11 Imperfections of CDO's Valuation 24 November 2009 Present value of premium and loss payment Suppose i underlying assets, i=1,...,n. Task: Determine the premium payment V so that PV(Premium) = PV(loss) where is a discount factor denotes expected loss by time

12. One Factor Gaussian Copula Model 12 Imperfections of CDO's Valuation 24 November 2009 Expected loss and denote attachment resp. detachment point of a tranche is probability of j defaults (j=0,...,n) by time is a cummulative loss on a portfolio given j defaults by time A denotes volume of one asset in a CDO

13. One Factor Gaussian Copula Model 13 Imperfections of CDO's Valuation 24 November 2009 Probability of j defaults by time t k (1) 1.Conditional default probability -Default time of i-th asset as a random variable: τ i -One factor model: description of a random variable X i -Gaussian Copula: Connection between μ i and X i

14. One Factor Gaussian Copula Model 14 Imperfections of CDO's Valuation 24 November 2009 Probability of j defaults by time t k (2) Where from Gaussian copula approach: 1.Conditional default probability

15. One Factor Gaussian Copula Model 15 Imperfections of CDO's Valuation 24 November 2009 Probability of j defaults by time t k (3) 2. Unconditional default probability Integral of conditional default probability over all M

16. One Factor Gaussian Copula Model 16 Imperfections of CDO's Valuation 24 November 2009 Entry parameters 1.Pairwise correlation – ρ 2.Distribution of the default time τ – f(t) Aternative measure: hazard rate function After some derivations h(t) constant at λ – hazard rate → Exponencial distribution 3. Value of hazard rate - λ

17. Agenda Basic Principles of CDOs 2. One Factor Gaussian Copula Model 3. Results of the Model 4. Main Flaws of the CDO Market 5. 17 Imperfections of CDO's Valuation 24 November 2009 Introduction 1. Conclusion 6.6.

18. Results of the Model 18 Imperfections of CDO's Valuation 24 November 2009 Hypotheses testing (1) The higher the asset correlation, the lower the risk premium for a junior tranche and the higher the risk premium for a senior tranche

19. Results of the Model 19 Imperfections of CDO's Valuation 24 November 2009 Hypotheses testing (2) Base correlation is more stable measure of correlation than implied correlation

20. Results of the Model 20 Imperfections of CDO's Valuation 24 November 2009 Hypotheses testing (3) Correlation and hazard rate changed substantially between 20 September 2007 and 28 February 2009 20.9.200728.2.2009 Correlation0.320.44 Hazard rate0.010.07 Number of assets125122 Notional investedUSD 100 mil.USD 97.6 mil. AP and DP-2.4 percentage points

21. Results of the Model 21 Imperfections of CDO's Valuation 24 November 2009 Hypotheses testing (4) There has been a substantial loss even on the most senior tranche without a necessity to be hit directly by a default of this tranche Tranche 0-3%3-7%7-10%10-15%15-30% 20.9.2007Premium14.69%4.21%1.89%0.88%0.19% 28.9.2009 Premium121.1%46.94%26.52%17.76%8.37% % M-t-M loss-82.12%-71.28%-57.39%-46.13%-26.59%

22. Agenda Basic Principles of CDOs 2. One Factor Gaussian Copula Model 3. Results of the Model 4. Main Flaws of the CDO Market 5. 22 Imperfections of CDO's Valuation 24 November 2009 Introduction 1. Conclusion 6.6.

23. Main Flaws of the CDO Market 23 Imperfections of CDO's Valuation 24 November 2009 4 MAIN FLAWS 1. Insuficient analysis of underlying asset 2. Misunderstanding of the valuation model 3. Mispriced correlation 4. Use of mark-to-market valuation principle

24. Main Flaws of the CDO Market 24 Imperfections of CDO's Valuation 24 November 2009 1.Insuficient analysis of underlying assets 2.Misunderstanding of the valuation model

25. Main Flaws of the CDO Market 25 Imperfections of CDO's Valuation 24 November 2009 3. Mispriced correlation 4. Mark-to-market valuation principle

26. Agenda Basic Principles of CDOs 2. One Factor Gaussian Copula Model 3. Results of the Model 4. Main Flaws of the CDO Market 5. 26 Imperfections of CDO's Valuation 24 November 2009 Introduction 1. Conclusion 6.6.

27. 27 Imperfections of CDO's Valuation 24 November 2009 Conclusion CDO market has a chance to be regenerated. Securitization and credit market is needed, but the trades have to be done rationally and deliberately. A future CDO market would then be more conscious, driven by smarter motives and definitely less extensive.

28. Discussion 28 Imperfections of CDO's Valuation 24 November 2009 Thanks for your attention. Let´s discuss it now!

29. Contact 29 Imperfections of CDO's Valuation 24 November 2009 Petra Benešová Institute of Economic Studies Faculty of Social Sciences Charles University Opletalova str. 26 110 00 Prague Czech Republic E-mail: benesova_p@seznam.cz http://ies.fsv.cuni.cz