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MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

Lecture 13 Collateralized Debt Obligations (CDO) Thursday, July 26, 2007 Readings: Duffie and Singleton Chapter 11 Longstaff and Rajan (2006). MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang. Review. Credit risk modeling:

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MFIN 7011: Credit Risk Management Summer, 2007 Dragon Tang

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  1. Lecture 13 Collateralized Debt Obligations (CDO) Thursday, July 26, 2007 Readings: Duffie and Singleton Chapter 11 Longstaff and Rajan (2006) MFIN 7011: Credit Risk ManagementSummer, 2007Dragon Tang Collateralized Debt Obligations (CDO)

  2. Review • Credit risk modeling: • Structural models: start from firm fundamentals such as asset value, leverage, volatility etc. • Reduced-form models: directly model default intensity • Recovery risk • Credit derivatives: tools for trading credit risk • CDS and CDS options • Default correlation • Today: Collateralized Debt Obligations (CDO) Collateralized Debt Obligations (CDO)

  3. Collateralized Debt Obligation (CDO) • Objectives: • Basic structure of CDO • CDO credit enhancement • Pricing of CDO Collateralized Debt Obligations (CDO)

  4. Institutions often hold credit portfolio with large number of individual credit exposures CDS will be inefficient for portfolio credit risk management Portfolio Credit Risk Collateralized Debt Obligations (CDO)

  5. A CDO is an asset backed security (ABS) whose underlying collateral is typically a portfolio of bonds (corporate or sovereign) or bank loans.CDO can be classified according to debt type: Collateralized loan obligation (CLO); Collateralized bond obligations (CBO); Collateralized mortgage obligations (CMO) The first CDO was created in 1987 by the famous Drexel Burnham Lambert, for a $100 million loan. Collateralized Debt Obligation (CDO) Collateralized Debt Obligations (CDO)

  6. A CDO cashflow structure allocates interest income and principal repayments from a collateral pool of different debt instruments to a prioritized collection (tranches) of CDO securities. First tranche covers x% of notional and absorbs first x% of default losses Second tranche covers y% of notional and absorbs next y% of default losses Etc. A tranche earns a promised yield on remaining principal in the tranche Collateralized Debt Obligation (CDO) Collateralized Debt Obligations (CDO)

  7. Cash CDO Structure Illustration Tranche 1 1st 5% of loss Yield = 35% Bond 1 Bond 2 Bond 3  Bond n Average Yield 8.5% Tranche 2 2nd 10% of loss Yield = 15% Trust Tranche 3 3rd 10% of loss Yield = 7.5% Tranche 4 Residual loss Yield = 6% Collateralized Debt Obligations (CDO)

  8. CDO Life Cycle • Ramp-up period: Collateral portfolio is gathered and formed • CDO manager representing the SPV purchases the collateral from loan originator (bank) • Tranches are sold to investors • Cash-flow period: cash flow is distributed • CDO manager can actively manage the portfolio • Or the portfolio can be passively left unmanaged to generate cash flow • Unwind period: principal is repaid Collateralized Debt Obligations (CDO)

  9. Typical CDO Contractual Relationships Ongoing Communication Collateral Manager Trustee CDO Special Purpose Vehicle (SPV) Underlying Securities (Collateral) Hedge Provider (If Needed) Senior Fixed/ Floating Rate Notes Mezzanine Fixed/Floating Rate Notes Subordinated Notes/Equity Collateralized Debt Obligations (CDO)

  10. Why CDO? • In perfect capital markets, CDOs would serve no purpose; the costs of constructing and marketing a CDO would inhibit its creation • In practice, CDOs address important market imperfections: • Banks and certain other financial institutions have regulatory capital requirements that make it valuable for them to securitize and sell some portion of their assets, reducing the amount of (expensive) regulatory capital that they must hold. • Individual bonds or loans my be illiquid, leading to a reduction in their market values. Securitization may improve liquidity, and thereby raise the total valuation to the issuer of the CDO structure. • Demand for corporate debt is barbell-shaped: more demand for AAA and B bonds; but supply concentrates on A/BBB. CDOs can mitigate this supply/demand imbalance by creating more AAA bonds from A/BBB bonds Collateralized Debt Obligations (CDO)

  11. Economics of CDO • Two main use of CDO: • Balance-sheet CDO: remove loans from bank balance sheet in the form of CLO • Arbitrage CDO: capture the difference between the total cost of acquiring collateral assets and the value of management fees and sale of CDO structure • Limitations: • Adverse selection: bank may know more about the quality of loans, investors may be “picked off” • Trading costs: Search for buyers can be expensive, winner’s curse • Moral hazard: CDO managers may shirk, or cherry picking, or front-running • Solution: • Smaller tranche of lower quality portion • Issuer/manager keeps the subordinated tranche Collateralized Debt Obligations (CDO)

  12. CDO Example NationsBank 1997-1 CLO tranches Obligors $2.164 billion Interest Rate Swaps Issuer • $2 billion • (AAA) B. $43 million (A) C. $54 million (BBB) D. $64 million (NR) Collateralized Debt Obligations (CDO)

  13. More CDO Types • Synthetic CDO: SPV selling CDS contracts instead of buying loans from the bank • No principal, no cash exchange at origination • CDS as collateral (similarly, credit linked notes and total return swaps can be used as collateral) • Loans remains on bank’s balance-sheet • “Pure credit” trade; spread is higher than cash CDOs • CDOs of EDS • Equity Default Swaps (EDS): a contract in which protection buyer receives a payment from seller should a predefined equity event takes place (price falling below a level) • EDS can be used similar to CDS in synthetic CDO • Single-tranche (“bespoke”) CDO, CDO Squared, … Collateralized Debt Obligations (CDO)

  14. Single-Tranche CDO Senior Tranche Bond 1 Bond 2 Bond 3  Bond n Selected Tranche Trust investors Equity Tranche Collateralized Debt Obligations (CDO)

  15. CDO Squared Senior Tranche SelectedTranche Equity Tranche Senior Tranche Senior Tranche SelectedTranche MezzanineTranche Equity Tranche Equity Tranche Senior Tranche SelectedTranche Equity Tranche Collateralized Debt Obligations (CDO)

  16. CDO Credit Structures How to shield the tranches of the CDO from credit losses in case of default events, especially the more senior tranche • Cash-Flow CDO: Pays a fixed amount in the event of default • No active trading; cash flow from the collateral is used to pay investors • Payments are made according to seniority • Market-Value CDO: manager can trade the collateral, market value is used as total collateral portfolio value • Mark-to-market return determined by CDO manager’s trading performance • Make sure market value is above certain level • Credit protection is assured through coverage tests such as overcollateralization (O/C) and interest coverage (I/C) Collateralized Debt Obligations (CDO)

  17. Tranches have different priorities Payment of trustee fees, asset manager fees Payment of interest to the most senior notes. If OC and IC tests are satisfied If they are not satisfied, redeem notes until test is met Payment of interest to the next subordinated tranche if OC and IC tests are not satisfied, redeem first most senior notes, and then, this tranche until test is met Pay down tranches according to their priority Any remaining cash goes to equity investors CDO Cashflow “Waterfalls” Collateralized Debt Obligations (CDO)

  18. CDO Cash-Flow Waterfall Payment Cash Waterfall Costs for deal structuring (underwriting, legal, rating) Asset manager fee (senior piece) Interest on A tranche If A tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Interest on B tranche If B tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Interest on C tranche If C tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Asset manager fee (subordinated piece) Interest on A tranche Collateralized Debt Obligations (CDO)

  19. Cash-Flow CDO Credit Enhancement Further reduce the credit risk of an obligation through coverage tests such as O/C and I/C. • Overcollateralization (O/C) • Monitor the general robustness of the CDO’s tranches and ensures the principal value is above certain level O/C= (collateral principal)/(tranche principal+more senior tranche principal) • Interest coverage (I/C) • Monitor the robustness of interest proceeds I/C=(collateral interest)/(tranche interest+more senior tranche interest) • O/C and I/C need to be above some target level. Example: total collateral $100 million at 10%, manager takes 5%. • A tranche $60 million with spread 50 bps; O/C target 1.35; I/C target 1.6; • B tranche $10 million with spread 200 bps; O/C target 1.25; I/C target 1.4 • C tranche $10 million with spread 500 bps; O/C target 1.13; I/C target 1.2 • Equity tranche $20 million Collateralized Debt Obligations (CDO)

  20. O/C and I/C Test Example Let interest rate = 6% Initially, there is no default, then A: O/C=100/60=1.67, I/C=5.0/(0.11+0.2+1.95)=2.21 B: O/C=100/(60+10)=1.43; I/C=5.0/(0.11+0.2+1.95+0.4)=1.88 C: O/C=100/(60+10+10)=1.25; I/C=5.0/(0.11+0.2+1.95+0.4+0.55)=1.56 All above target! If there is default, 10%is lost, remaining collateral is $90 million A: O/C=90/60=1.5, I/C=4.5/(0.11+0.18+1.95)=2.01 B: O/C=90/(60+10)=1.29; I/C=4.5/(0.11+0.18+1.95+0.4)=1.7 C: O/C=90/(60+10+10)=1.125; I/C=4.5/(0.11+0.18+1.95+0.4+0.55)=1.41 O/C for C fails (1.125<1.13), then $0.354 million of interest payment is Diverted to principal [90/(60+10+10-0.354)=1.13] paying off A tranche Principal (now A’s principal becomes $59.646 million) Collateralized Debt Obligations (CDO)

  21. CDO Cash-Flow Waterfall: No Default Payment Cash Waterfall Costs for deal structuring (underwriting, legal, rating) (USD million) $0.11 Asset manager fee (senior piece) $0.20 Interest on A tranche $1.95 If A tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Interest on B tranche $0.40 If B tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Interest on C tranche $0.55 If C tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Asset manager fee (subordinated piece) $0.10 Interest on A tranche $1.69 Collateralized Debt Obligations (CDO) $5.00

  22. CDO Cash-Flow Waterfall: After Default Payment Cash Waterfall Costs for deal structuring (underwriting, legal, rating) (USD million) $0.11 Asset manager fee (senior piece) $0.18 Interest on A tranche $1.95 If A tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Interest on B tranche $0.40 If B tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met Interest on C tranche $0.55 If C tranche failes coverage tests, repay principal on A,B,C tranches in seniority until tests are met $0.354 Asset manager fee (subordinated piece) $0.09 Interest on A tranche $0.87 Collateralized Debt Obligations (CDO) $4.50

  23. CDO Pricing • Pricing CDO as the following steps: • Protection leg: expected total default payment • Premium fee leg: expected cumulative fees buyer pays • Fee is set such that protection equals premium • Expectation is evaluated through Monte Carlo Simulation • Joint default probabilities (or default correlations) are required for calculating the expectation. Two ways to modeling default correlation: • Cholesky decomposition: decompose correlated variables as combinations of independent variables (which drives individual defaults such as in Merton’s structural model) • Copulas: capture default timing, only requires finding the underlying asset whose default timing is shorter than each payment date Collateralized Debt Obligations (CDO)

  24. CDO Pricing and Default Correlation Senior tranche price increases as default correlation increases; Equity tranche price decreases as default correlation increases; Mezzanine tranche first increases then decreases Equity CDO Spread Mezzanine Senior Default Correlation Collateralized Debt Obligations (CDO)

  25. CDO Single Tranche Trading • This involves trading standard tranches of standard portfolios that are not funded • CDX IG (Aug 30, 2005): • iTraxx IG (Aug 30, 2005) Collateralized Debt Obligations (CDO)

  26. CDO Pricing Results from Longstaff and Rajan (2006) • Investigate CDX NA IG credit index pricing • CDX: synthetic CDO using 125 CDS names, 5 tranches (0-3; 3-7; 7-10; 10-15; 15-30 percent losses) • Those 125 constitutes are updated every half year, resulting 5 CDX indices between Oct 2003 to Oct 2005 • Main findings: CDO prices conforms well with theory • Firm-specific default explains 65%; industry explains 28%; economy catastrophe explains 7% • CDO prices imply that losses of 0.4%, 6%, 35% occurs at frequencies of 1.2, 41.5, and 763 years Collateralized Debt Obligations (CDO)

  27. CDO Credit Rating • Profit center for rating agencies • CDO performance is driven by three factors; • the behaviour of the underlying assets, • the CDO’s structural features • and asset manager performance. Collateralized Debt Obligations (CDO)

  28. CDO Credit Rating Rating process: • Request from a CDO arranger or sponsoring institution. • Review of the asset manager, originator or servicer to determine the motivation behind the transaction and their ability to manage and service the portfolio appropriately. [CDO Asset Manager Rating: CAM1-CAM5 (+/-)] • Determine the portfolio’s quality and the probability of defaults. • Review the proposed structure and its impact on the transaction cash flows. • Typically rated with multiple tranhes (AAA to D) of liabilities of varying credit quality and seniority (with Stability Score) Collateralized Debt Obligations (CDO)

  29. Summary • Introduction to CDO: • Basic structure and variants • Credit enhancement and valuation • Next: Credit Derivatives Strategies Collateralized Debt Obligations (CDO)

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