Javier Zapata October 25 th, 2011 Stability Analysis of Synthetic CDO Ratings Stability Analysis of Synthetic CDO Ratings

Index of Contents Introduction Basic Concepts Credit Rating Agencies Methodology Related Literature Cases of Study & Results Conclusions

The Subprime Crisis – Credit Market Meltdown: Boom and Bust in the Housing Market Case-Shiller Home Price Index and Federal Fund Reserve Rate Source: Standard & Poor’s, Federal Reserve Bank of New York Global CDO Issuance and Case Shiller Composite 10 Index Source: Standard & Poor’s, Federal Reserve Bank of New York Introduction

The Subprime Crisis – What Was the Role of the Ratings and the Synthetic CDOs?? Introduction Ratings Accuracy Ratios for CDO notes Source: Moody’s Source: Bank of International Settlements Growth of CDO Issuance by Type

Basic Concepts

Credit Risk – Credit Risk is the likelihood that a borrower will fail to meet on time his debt obligations with his counterparty, the lender. – The case in which the borrower fails to meet his debt obligation is called a default. – Credit risk is exchanged between parties with credit derivatives. Credit Default Swap (CDS) – A CDS is a type of credit derivative in which a protection buyer pays a protection fee (premium or spread) to a protection seller during a certain period of time Diagram of the Credit Default Swap Model Basic Concepts

Synthetic CDO – A Synthetic CDO transfers the credit risk in a similar way than a CDS contract, but it incorporates a sequential payment mechanism. – A Synthetic CDOs is structured using an array of many CDS agreements. Synthetic CDO Mechanics Basic Concepts

Synthetic CDO-Squared – Synthetic CDO-Squared is a Synthetic CDO where the reference portfolio consists of a pool of mezzanine tranches from previous synthetic (unfunded) CDOs. Synthetic CDO-Squared Mechanics Basic Concepts

Credit Rating Agencies (CRAs)

CRAs are private firms that publish credit risk assessments of debt instruments (ratings) issued in the fixed income market. Ratings are based on the creditworthiness of the debt issuer. In the case of a CDO, the credit risk is different for different tranches. Figure XX: Global Market Ratings Participation 2007 Source: M.C. Rom, 2009 Market Share in CDO Ratings Source: A.K. Barnett, 2009 CRAs Moody’s Expected Loss Source: Moody’s Rating Time Horizon 2 years10 years Aaa0.000%0.006% Aa10.002%0.055% Aa20.004%0.110% Aa30.011%0.220% A10.020%0.385% A20.039%0.660% A30.083%0.990% Baa10.154%1.430% Baa20.259%1.980% Baa30.578%3.355% Ba11.111%5.170% Ba21.909%7.425% Ba33.031%9.713% B14.609%12.210% B26.419%14.960% B39.136%19.195% Caa %26.235% Caa %35.750% Caa %44.385%

During the subprime crisis, the CDO rating changes were overwhelmingly downgrades. The reasons for the downgrades: conflict of interest, lack of historical data and overworked rating analysts. Average Number of Notches Upgraded and Downgraded Source: Moody’s CRAs Growth of CDO Revenue vs CDO Staff Source: M.C. Rom (2009)

This study is focused on Moody’s. – Moody’s was a big player in the CDO rating market. – Moody’s CDO rating methodology is the most well-known. CRAs Moody’s Rating Revenues & Share Price Source: Moody’s

Methodology

Moody’s Credit Rating Model Methodology Asset Parameters Synthetic CDO Structure Number of assets in the portfolio Number of tranches Size of the tranches Maturity of the CDO One-Factor Gaussian Copula Probability of Each Default Scenario Expected Loss Computation

Methodology

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Methodology

Stability Analysis of Synthetic CDO Ratings – The stability analysis is divided in two parts: Estimation of 95% confidence intervals of the expected loss. The effect of errors in the assets parameters. – The values considered for the different parameters:  Default Probability Distributed as a Normal Distribution Based on Cantor, Hamilton & Tennant (2007) o Includes U.S. corporate rating histories from 1970 through  Correlation No distribution assumption. Deterministic values between 5% and 30%. Based on Zhang, Zhu & Lee (2008) o Includes U.S. corporate defaults from from 1981 through Methodology

Recovery Rate with the Beta ModelRecovery Rate with the Log Model

Related Literature

Different studies have analyzed the credit ratings in different ways: – Cifuentes & Katsaros (2007) – Coval, Jurek & Strafford (2007) – Meng & Sengupta (2010) – Hull & White (2010) Related Literature

Cases of Study & Results

ABACUS – ABACUS synthetic CDO referencing mid-prime and subprime bonds backed by residential mortgages. – ABACUS was structured by Goldman Sachs and issued in early Cases of Study & Results Index Name Time Horizon (in Years) # of Corporate Names Total Notional Amount Tranche Structure Tranche Name Attachment/ Detachment Point Moody's Ratings ABACUS4.290 US $2 billion Super Senior45% - 100%N/A Class A21% - 45%Aaa Class B18% - 21%Aa2 Class C13% - 18%Aa3 Class D10% - 13%A2 First Loss0% - 10%N/A

Combinations of Default Correlation and Recovery Rate that Match the ABACUS Tranches Ratings ABACUS 1 st Analysis: Matching the Ratings – Calibration of Asset Parameters to Asses the Ratings

ABACUS 1 st Analysis: Matching the Ratings – 95% Confidence Intervals for the Expected Loss ABACUS Class A Tranche Confidence Intervals for the Pairwise Default Correlation and Recovery Rate. ABACUS Class D Tranche Confidence Intervals for the Pairwise Default Correlation and Recovery Rate.

ABACUS 2 nd Analysis: 95% Confidence Intervals for the Expected Loss ABACUS Class A Tranche Confidence Intervals (Beta Model) ABACUS Class A Tranche Confidence Intervals (Log Model) ABACUS Class D Tranche Confidence Intervals (Beta Model) ABACUS Class D Tranche Confidence Intervals (Log Model)

ABACUS 3 rd Analysis: Sensitivity to Errors in The Asset Parameters ABACUS Class A Tranche Parameter Sensitivity ABACUS Class D Tranche Parameter Sensitivity

CDX Indices – CDX indices are a part of the family of CDS indices released by Markit. – A CDS index is referred to the exchange of credit risk between the protection buyers of a basket of liquid CDS contracts and protection sellers. – CDX indices, give investors the opportunity to take exposure to specific segments of the CDS index default distribution. Cases of Study & Results Figure 26: CDS Indices Credit Derivative Market Participation Source: Bank for International Settlements Source: Fitch Ratings,Bank for International Settlements Figure 27: Notional Amount Outstanding of CDS Indices and Single-Name CDS

CDX Indices – The CDX indices considered for the purpose of this study are two: the CDX North America Investment Grade (CDX.NA.IG) and the CDX North America High Yield (CDX.NA.HY). Cases of Study & Results Index Name Geographic Concentration Time Horizon (Years) # of Corporate Names Average Rating of the Securities Tranche Structure Tranche Name Attachment/ Detachment Point CDX.NA.IG North American Investment Grade 1,2,3,5,7 and10125Baa Super Senior30%-100% Senior 115%-30% Senior % Mezzanine 17%-10% Mezzanine 23%-7% Equity0%-3% CDX.NA.HY North American High Yield 5100Ba Super Senior35%-100% Senior 125%-35% Senior 215%-25% Mezzanine10%-15% Equity0-10%

CDX.NA.IG 1 st Analysis: 95% Confidence Intervals for the Expected Loss CDX.NA.IG Senior 1 Tranche 5 Years Horizon (Beta Model) CDX.NA.IG Senior 1 Tranche 5 Years Horizon (Log Model) CDX.NA.IG Mezzanine 2 Tranche 5 Years Horizon (Beta Model)CDX.NA.IG Mezzanine 2 Tranche 5 Years Horizon (Log Model)

CDX.NA.IG 2 nd Analysis: Sensitivity to Errors in The Asset Parameters CDX.NA.IG Senior 1 Tranche Parameter Sensitivity CDX.NA.IG Mezzanine 2 Tranche Parameter Sensitivity

CDX.NA.HY 1 st Analysis: 95% Confidence Intervals for the Expected Loss CDX.NA.HY Senior 1 Tranche 5 Years Horizon (Beta Model) CDX.NA.HY Senior 1 Tranche 5 Years Horizon(Log Model) CDX.NA.HY Mezzanine Tranche 5 Years Horizon (Beta Model)CDX.NA.HY Mezzanine Tranche 5 Years Horizon (Log Model)

CDX.NA.HY 2 nd Analysis: Sensitivity to Errors in The Asset Parameters CDX.NA.HY Senior 1 Tranche Parameter Sensitivity CDX.NA.HY Mezzanine Tranche Parameter Sensitivity

Synthetic CDO-Squared – Two theoretical synthetic CDO-Squared are considered based on the CDX Indices. – The purpose of this structures is to understand the effect of the overlap. Cases of Study & Results Synthetic CDO-Squared CDX Index Considered # of Synthetic CDOs Mezzanine Tranches Included Synthetic CDO Tranche Structure Tranche Name Attachment/Detachment Point T-CDX.NA.IGCDX.NA.IG7 Mezzanine 2 Super Senior30%-100% Senior 115%-30% Senior % Mezzanine 17%-10% Mezzanine 23%-7% Equity0%-3% Synthetic CDO- Squared Synthetic CDO-Squared Tranche Structure Tranche Name Attachment/Detachment Point T-CDX.NA.IG Super Senior30%-100% Senior 115%-30% Senior % Mezzanine 17%-10% Mezzanine 23%-7% Equity0%-3%

T-CDX.NA.IG 1 st Analysis: 95% Confidence Intervals for the Expected Loss T-CDX.NA.IG with 0% of Overlap (Beta Model) T-CDX.NA.IG with 15% of Overlap (Beta Model) T-CDX.NA.IG with 30% of Overlap (Beta Model)

CONCLUSIONS No single-point estimators…. No no no!! Considering a deterministic recovery rate, just the uncertainty (or error) in the default probability is enough to find instability in the ratings. The overlap in a Synthetic CDO-Squared is not a relevant factor to consider. The regulatory frameworks based on credit ratings should be redesigned.

Appendix : How Much Did Banks and Insurance Companies Lose During the Subprime Crisis? Distribution of Write-Downs Source: Creditflux