## 1.  U.S. Cash CDO Issuance

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### Introduction: systemic risk and credit derivatives
- Systemic risk is a major policy concern because increased financial integration raises the probability that single defaults could trigger second-round defaults (example cited: 1998 collapse of Long Term Capital Management).
- The rapid growth of the credit derivatives market provides market-implied information on systemic risk:
  - "notional amount in the global credit derivatives market amounted to about $5 trillion in 2005, up from less than $1 trillion five years ago."
- Portfolio credit derivatives (payoffs tied to default loss distribution of a pool) reflect market views on the probability of multiple defaults; the most popular portfolio product is the collateralized debt obligation (CDO).
- Objective: construct idiosyncratic and systemic risk indicators for Europe using prices of different tranches of standardized CDOs referencing regional credit derivatives indices.

### A brief primer on CDOs: structure, motives, and types
- CDO definition and market growth:
  - A Collateralized Debt Obligation (CDO) issues notes to investors to raise funds invested in a portfolio of risky financial assets.
  - U.S. cash CDO issuance: "increased to $137 billion in 2005 from $91 billion in 2004."
  - Single-tranche CDOs: "outstanding notional amount of single-tranche CDOs almost doubled" between 2004 and 2005.
- Cash CDOs (structure and incentives):
  - SPV buys assets from arranger; SPV must be bankruptcy-remote from originator.
  - Typical tranche hierarchy: Equity (first loss, zero percent attachment point), Mezzanine (typically rated A/BBB), Senior (AAA), Super-senior (above AAA).
  - Investor incentives: diversified exposure; investment-grade tranches often generate higher returns compared with alternative investments with same ratings due to diversification and leverage.
  - Arranger incentives: reduce required regulatory capital by removing assets from balance sheet.
- Synthetic CDOs (funded and unfunded):
  - Synthetic CDOs reference credit derivatives (usually credit default swaps, CDSs).
  - Funded synthetic CDO: SPV sells a portfolio of CDSs, buys collateral, issues notes to investors who pay principal upfront and receive CDS premiums; investors lose principal if defaults occur.
  - Unfunded synthetic CDO: works as a swap; arranger buys a CDS portfolio from investors by issuing CDO notes; no SPV; arranger manages counterparty credit risk.
- Single-Tranche CDOs (STCDOs):
  - STCDOs sell only one tranche to investors, defined by attachment and exhaustion points (example: a 3-7 percent mezzanine tranche).
  - Arranger hedges exposure by delta-hedging via single-name CDSs or by selling/buying protection on unsold tranches.
  - Standardized STCDOs emerged with major CDS indices:
    - CDX IG attachment points: 0-3%, 3-7%, 7-10%, 10-15%, and 15-30%.
    - iTraxx Europe attachment points: 0-3%, 3-6%, 6-9%, 9-12%, and 12-22%.
  - Market roles blur: arrangers and investors can be protection buyers or sellers; market makers provide liquidity; prices are market-clearing equilibrium prices.

### Default probability, default correlation, and tranche pricing
- Two risk drivers for STCDO tranche values:
  - Changes in default probability of single issuers (idiosyncratic risk) affect CDS spreads and tranche sensitivities (deltas).
  - Changes in default correlation (systemic risk) alter the portfolio loss distribution and the probability that losses reach tranche subordination levels.
- Qualitative effects of correlation on tranche prices:
  - As default correlation increases, the portfolio loss distribution spreads out; probabilities of very low or very high losses increase.
  - Equity tranche: higher correlation increases probability of very low losses (potentially zero losses), reducing the spread (price of equity protection falls). Selling protection on equity tranche ≈ "long" correlation.
  - Super-senior tranche: higher correlation raises probability of very high losses that can breach exhaustion points, increasing price of protection. Selling protection on super-senior tranche ≈ "short" correlation.
- Illustrative example (100 homogeneous names portfolio):
  - As correlation (ρ) increases (examples shown for ρ = 0.0, 0.3, 0.6, 0.9), probability mass shifts to extremes:
    - Probability of zero portfolio loss increases with ρ.
    - Probability that losses exceed high thresholds (e.g., 12% or exhaustion points like 22%) increases with ρ.

### Identification: idiosyncratic vs. systemic risk in STCDO tranches
- Mapping tranche price responses to risk components:
  - Idiosyncratic risk: company-specific default probability changes; equity and super-senior tranche prices react similarly to idiosyncratic shocks.
  - Systemic risk: captured by default correlation; equity and super-senior tranche prices move in opposite directions to changes in systemic risk.
- Identification strategy:
  - Use comovements of equity and super-senior tranche prices to extract idiosyncratic vs. systemic drivers in the underlying market.

### Data and empirical framework
- Data used to identify risk components for Europe:
  - Price data for traded tranches referencing the iTraxx Europe credit derivatives index.
  - Index construction:
    - IIC-administered dealer liquidity poll selects companies incorporated in Europe with highest CDS trading volume over previous six months; removes companies rated BBB- by Standard and Poor’s or on negative outlook.
    - Final portfolio: 125 companies, equally weighted, sector composition:
      - 10 autos
      - 30 consumers (15 cyclicals and 15 non-cyclicals)
      - 20 energy
      - 20 industrials
      - 20 telecoms, medias, and technologies (TMT)
      - 25 financials
    - Index rolled every six months by adding next most liquid entity to replace defaulted, merged, or downgraded entities.
  - Sample and quotation conventions:
    - Summary statistics correspond to quotes for five-year STCDO tranches referencing iTraxx Europe for the period "August 28, 2003 – May 16, 2005."
    - Equity tranche (0-3%) is quoted as an upfront fee (percent of notional) plus an annualized spread of "500 basis points (bps)" paid quarterly if no default occurs.
    - Other tranches are quoted as quarterly spreads in basis points.
- Empirical method:
  - Principal component analysis (PCA) is proposed to reduce correlated tranche-spread variables to a smaller set of uncorrelated factors; PCA is commonly used in financial data analyses and is applicable here because tranche spreads exhibit significant correlations.

### Descriptive statistics and correlations (iTraxx tranche data)
- Tranche attachment points (in percent) and associated statistics (as presented):
  - Equity 0 - 3: 26.312.946.5  5.4
  - Junior Mezzanine 3 -6: 182.684.6330.0  56.6
  - Senior Mezzanine 6 - 9: 70.925.3152.5  28.2
  - Super-senior 12 - 22: 18.08.139.0  5.4
  - Note: "Equity tranche prices quoted as an upfront percentage of the notional amount of the contract plus a 500 bps annualized spread paid quarterly."
- Tranche prices, in bps 1/ (correlation matrix presented):
  - Equity (0 - 3) correlations: with Junior Mezzanine 0.8221.000, Senior Mezzanine 0.7740.9761.000, Super-Senior 0.7550.8510.905 1.000
- Sample period for correlations: August 28, 2003 – May 16, 2005.

### Method: PCA mechanics and implementation
- Data matrix notation and PCA objective:
  - Data ordered in matrix Y n×k, where n is number of observations and k is number of variables.
  - Principal components correspond to columns of matrix P k×k such that variance of transformed data Z = P’Y is maximized subject to P’P=I.
  - Principal components correspond to eigenvectors associated to characteristic vector λ solving the eigenequation | ∑ - λI| = 0, where ∑ is variance-covariance matrix of Z.
- Background references: Timm (2002); Litterman and Scheinkman (1991).
- Correlations of tranche prices in the sample range from 0.76 to 0.98, "suggesting that it is proper to analyze the data using PCA."

### Results: principal components of iTraxx tranche spreads
- Principal Components Coefficients (Table 3 as presented):
  - Coefficients by tranche (First, Second, Third, Fourth):
    - Equity: 0.0007-0.0012-0.0069-1.0000
    - Junior Mezzanine: 0.8950-0.4391-0.07870.0017
    - Senior Mezzanine: 0.44000.83950.3189-0.0029
    - Super-Senior: 0.07400.3201-0.94450.0062
  - Percent of variation explained: 99.050.850.100.00
- Interpretation of components:
  - First principal component:
    - Explains most of the variation of the transformed data.
    - All tranche coefficients for the first principal component are positive; identified with idiosyncratic risk factor in Europe.
  - Second principal component:
    - Equity tranche coefficient has opposite sign to senior tranche coefficient; identified with systemic risk factor.
  - Third and fourth components:
    - Contribution described as negligible.

### Time-series behavior and event associations
- Idiosyncratic and systemic risk series were recovered from transformed data Z and are forward-looking risk measures reflecting market views on default risk going forward five years.
- Notable movements in the sample:
  - Second half of 2004: systemic risk reacted to rapid increases of oil and commodity prices and uncertainty about the relative pace of interest rate tightening in the United States and European region.
  - Early 2004: idiosyncratic risk surged following the bankruptcy of Parmalat.
  - May 2005: idiosyncratic and systemic risks rose together when hedge funds active in credit markets were forced to unwind positions following rating downgrades of General Motors and Ford.
  - End of sample: mounting losses among hedge funds increased counterparty risk for banks and drove credit spreads up in the banking sector, contributing to simultaneous increases in systemic and idiosyncratic risk.

### Conclusions, policy relevance, and extensions
- Method and contribution:
  - A simple method was presented to extract measures of idiosyncratic and systemic risk from CDO tranche prices, exploiting differential impacts of idiosyncratic and systemic risk on tranche prices.
  - Extracted forward-looking risk measures for the corporate sector in Europe.
- Usefulness for policymakers:
  - These forward-looking measures are useful to policymakers concerned about a buildup of risks that could potentially threaten financial stability.
- Stated limitations and future work:
  - Robustness of these indicators under different econometric methods is indicated as a current concern.
  - Planned extensions include:
    - Assessing comovements of idiosyncratic risk and systemic risk across emerging markets, Asia, Europe, and the United States.
    - Examining main economic determinants of both types of risk to predict their future evolution.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06107.pdf*

### 1.  U.S. Cash CDO Issuance .............................................................................................

### 1.  U.S. Cash CDO Issuance

### Introduction: systemic risk and credit derivatives
- Systemic risk is a major policy concern because increased financial integration raises the probability that single defaults could trigger second-round defaults (example cited: 1998 collapse of Long Term Capital Management).
- The rapid growth of the credit derivatives market provides market-implied information on systemic risk:
  - "notional amount in the global credit derivatives market amounted to about $5 trillion in 2005, up from less than $1 trillion five years ago."
- Portfolio credit derivatives (payoffs tied to default loss distribution of a pool) reflect market views on the probability of multiple defaults; the most popular portfolio product is the collateralized debt obligation (CDO).
- Objective: construct idiosyncratic and systemic risk indicators for Europe using prices of different tranches of standardized CDOs referencing regional credit derivatives indices.

### A brief primer on CDOs
- CDO definition and market growth:
  - A Collateralized Debt Obligation (CDO) issues notes to investors to raise funds invested in a portfolio of risky financial assets.
  - U.S. cash CDO issuance: "increased to $137 billion in 2005 from $91 billion in 2004."
  - Single-tranche CDOs: "outstanding notional amount of single-tranche CDOs almost doubled" between 2004 and 2005 (figure referenced).
- Cash CDOs (structure and incentives):
  - SPV buys assets from arranger; SPV must be bankruptcy-remote from originator.
  - Typical tranche hierarchy: Equity (first loss, zero percent attachment point), Mezzanine (typically rated A/BBB), Senior (AAA), Super-senior (above AAA).
  - Investor incentives: diversified exposure; investment-grade tranches often generate higher returns compared with alternative investments with same ratings due to diversification and leverage.
  - Arranger incentives: reduce required regulatory capital by removing assets from balance sheet.
- Synthetic CDOs (funded and unfunded):
  - Synthetic CDOs reference credit derivatives (usually credit default swaps, CDSs).
  - Funded synthetic CDO: SPV sells a portfolio of CDSs, buys collateral, issues notes to investors who pay principal upfront and receive CDS premiums; investors lose principal if defaults occur.
  - Unfunded synthetic CDO: works as a swap; arranger buys a CDS portfolio from investors by issuing CDO notes; no SPV; arranger manages counterparty credit risk.
- Single-Tranche CDOs (STCDOs):
  - STCDOs sell only one tranche to investors, defined by attachment and exhaustion points (example: a 3-7 percent mezzanine tranche).
  - Arranger hedges exposure by delta-hedging via single-name CDSs or by selling/buying protection on unsold tranches.
  - Standardized STCDOs emerged with major CDS indices:
    - CDX IG attachment points: 0-3%, 3-7%, 7-10%, 10-15%, and 15-30%.
    - iTraxx Europe attachment points: 0-3%, 3-6%, 6-9%, 9-12%, and 12-22%.
  - Market roles blur: arrangers and investors can be protection buyers or sellers; market makers provide liquidity; prices are market-clearing equilibrium prices.

### Default probability, default correlation, and tranche pricing
- Two risk drivers for STCDO tranche values:
  - Changes in default probability of single issuers (idiosyncratic risk) affect CDS spreads and tranche sensitivities (deltas).
  - Changes in default correlation (systemic risk) alter the portfolio loss distribution and the probability that losses reach tranche subordination levels.
- Qualitative effects of correlation on tranche prices:
  - As default correlation increases, the portfolio loss distribution spreads out; probabilities of very low or very high losses increase.
  - Equity tranche: higher correlation increases probability of very low losses (potentially zero losses), reducing the spread (price of equity protection falls). Selling protection on equity tranche ≈ "long" correlation.
  - Super-senior tranche: higher correlation raises probability of very high losses that can breach exhaustion points, increasing price of protection. Selling protection on super-senior tranche ≈ "short" correlation.
- Illustrative example (made-up 100 homogeneous names portfolio):
  - As correlation (ρ) increases (examples shown for ρ = 0.0, 0.3, 0.6, 0.9), probability mass shifts to extremes:
    - Probability of zero portfolio loss increases with ρ.
    - Probability that losses exceed high thresholds (e.g., 12% or exhaustion points like 22%) increases with ρ.

### Idiosyncratic and systemic risk in STCDO tranches
- Mapping tranche price responses to risk components:
  - Idiosyncratic risk: company-specific default probability changes; equity and super-senior tranche prices react similarly to idiosyncratic shocks.
  - Systemic risk: captured by default correlation; equity and super-senior tranche prices move in opposite directions to changes in systemic risk.
- Identification strategy:
  - Use comovements of equity and super-senior tranche prices to extract idiosyncratic vs. systemic drivers in the underlying market.

### Data and empirical framework
- Data used to identify risk components for Europe:
  - Price data for traded tranches referencing the iTraxx Europe credit derivatives index.
  - Index construction:
    - IIC-administered dealer liquidity poll selects companies incorporated in Europe with highest CDS trading volume over previous six months; removes companies rated BBB- by Standard and Poor’s or on negative outlook.
    - Final portfolio: 125 companies, equally weighted, sector composition:
      - 10 autos
      - 30 consumers (15 cyclicals and 15 non-cyclicals)
      - 20 energy
      - 20 industrials
      - 20 telecoms, medias, and technologies (TMT)
      - 25 financials
    - Index rolled every six months by adding next most liquid entity to replace defaulted, merged, or downgraded entities.
  - Sample and quotation conventions:
    - Summary statistics correspond to quotes for five-year STCDO tranches referencing iTraxx Europe for the period "August 28, 2003 – May 16, 2005."
    - Equity tranche (0-3%) is quoted as an upfront fee (percent of notional) plus an annualized spread of "500 basis points (bps)" paid quarterly if no default occurs.
    - Other tranches are quoted as quarterly spreads in basis points.
- Empirical method:
  - Principal component analysis (PCA) is proposed to reduce correlated tranche-spread variables to a smaller set of uncorrelated factors; PCA is commonly used in financial data analyses and is applicable here because tranche spreads exhibit significant correlations.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06107.pdf*

### 0.76 to 0.98, suggesting that it is proper to analyze the data using PCA.

### _wp06107 - 0.76 to 0.98, suggesting that it is proper to analyze the data using PCA.

### Data: iTraxx tranche descriptive statistics and correlations
- Tranche attachment points (in percent) and associated statistics (as presented):
  - Equity 0 - 3: 26.312.946.5  5.4
  - Junior Mezzanine 3 -6: 182.684.6330.0  56.6
  - Senior Mezzanine 6 - 9: 70.925.3152.5  28.2
  - Super-senior 12 - 22: 18.08.139.0  5.4
  - Note: "Equity tranche prices quoted as an upfront percentage of the notional amount of the contract plus a 500 bps annualized spread paid quarterly."
  - Source line in table: "Source: Authors' calculations."

- Tranche prices, in bps 1/ (correlation matrix presented):
  - Equity (0 - 3) correlations: with Junior Mezzanine 0.8221.000, Senior Mezzanine 0.7740.9761.000, Super-Senior 0.7550.8510.905 1.000
  - Table header indicates "Sources: Authors' calculations."

- Sample period for correlations: August 28, 2003 – May 16, 2005.

### Method: Principal component analysis (PCA) mechanics
- Data matrix notation and PCA objective:
  - Data ordered in matrix Y n×k, where n is number of observations and k is number of variables.
  - Principal components correspond to columns of matrix P k×k such that variance of transformed data Z = P’Y is maximized subject to P’P=I.
  - Principal components correspond to eigenvectors associated to characteristic vector λ solving the eigenequation | ∑ - λI| = 0, where ∑ is variance-covariance matrix of Z.
- References cited for PCA background and applications: Timm (2002); Litterman and Scheinkman (1991).

### Results: Principal components of iTraxx tranche spreads
- Principal Components Coefficients (Table 3 as presented):
  - First, Second, Third, Fourth coefficients by tranche:
    - Equity: 0.0007-0.0012-0.0069-1.0000
    - Junior Mezzanine: 0.8950-0.4391-0.07870.0017
    - Senior Mezzanine: 0.44000.83950.3189-0.0029
    - Super-Senior: 0.07400.3201-0.94450.0062
  - Percent of variation explained: 99.050.850.100.00
  - Source line in table: "Source: Authors' calculations."

- Interpretation of components:
  - First principal component:
    - Explains most of the variation of the transformed data.
    - All tranche coefficients for the first principal component are positive; identified with idiosyncratic risk factor in Europe.
  - Second principal component:
    - Equity tranche coefficient has opposite sign to senior tranche coefficient; identified with systemic risk factor.
  - Third and fourth components:
    - Contribution described as negligible.

### Time-series behavior and events
- Idiosyncratic and systemic risk series were recovered from transformed data Z and are forward-looking risk measures reflecting market views on default risk going forward five years.
- Notable movements in the sample:
  - Second half of 2004: systemic risk reacted to rapid increases of oil and commodity prices and uncertainty about the relative pace of interest rate tightening in the United States and European region.
  - Early 2004: idiosyncratic risk surged following the bankruptcy of Parmalat.
  - May 2005: idiosyncratic and systemic risks rose together when hedge funds active in credit markets were forced to unwind positions following rating downgrades of General Motors and Ford.
  - End of sample: mounting losses among hedge funds increased counterparty risk for banks and drove credit spreads up in the banking sector, contributing to simultaneous increases in systemic and idiosyncratic risk.

### Conclusions and policy relevance
- Method and contribution:
  - A simple method was presented to extract measures of idiosyncratic and systemic risk from CDO tranche prices, exploiting differential impacts of idiosyncratic and systemic risk on tranche prices.
  - Extracted forward-looking risk measures for the corporate sector in Europe.
- Usefulness for policymakers:
  - These forward-looking measures are useful to policymakers concerned about a buildup of risks that could potentially threaten financial stability.
- Stated limitations and future work:
  - Robustness of these indicators under different econometric methods is indicated as a current concern.
  - Planned extensions include:
    - Assessing comovements of idiosyncratic risk and systemic risk across emerging markets, Asia, Europe, and the United States.
    - Examining main economic determinants of both types of risk to predict their future evolution.

*Source: Authors' calculations.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06107.pdf_