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FRM Exam Part II · Credit Derivatives

CDOs and Tranche Structures for FRM Part 2

Updated 11 October 2026 · Fact-checked

A CDO pools credit assets and splits the pool's losses into tranches. Each tranche absorbs losses between its attachment and detachment points, starting with equity, then mezzanine, then senior. To solve questions, compute pool loss, subtract the attachment point, cap at tranche width, and apply correlation logic.

Understand CDOs and Tranche Structures

A collateralized debt obligation (CDO) pools credit exposures such as loans, bonds or credit default swaps. It sells claims on the pool's cash flows in slices called tranches. Each tranche has a different priority for absorbing losses.

A cash CDO owns the actual assets. It funds them by issuing tranches to investors. A synthetic CDO owns no assets. It sells credit protection through CDS on a reference portfolio and passes the credit risk to tranche investors. Collateral, if any, is posted separately. Synthetic deals are faster to build and avoid funding the assets.

Each tranche has an attachment point (where its losses start) and a detachment point (where it is wiped out). Tranche width = detachment − attachment. The equity tranche sits at the bottom, say 0% to 3%. The mezzanine sits in the middle, say 3% to 10%. The senior and super senior tranches sit at the top. Losses hit equity first. Interest and principal follow the waterfall: senior is paid first, equity last. Equity gets the residual.

Correlation changes how losses are distributed, not the expected pool loss. With low correlation, defaults are spread out, so the pool loss is near its mean. Equity is then likely to take some loss, and senior is very safe. With high correlation, defaults cluster. Either few defaults or many occur. Equity becomes less risky and its value rises. Senior becomes riskier because a large joint loss is more likely. Mezzanine is mixed and can move either way.

In the Gaussian copula model, a single correlation parameter links default times. Market quotes use implied (compound) correlation, which is the one correlation that matches a tranche's price. Because it differs across tranches, it shows a correlation smile. Base correlation uses equity-style tranches from 0 to each detachment point and gives a smoother, more usable curve.

Key formulas to remember

Tranche width
Width = Detachment point − Attachment point
Expressed as a percentage of total pool notional.
Tranche loss
Tranche loss = min(max(L − A, 0), D − A)
L is pool loss, A attachment, D detachment, all in the same units. Divide by (D − A) for percentage of tranche lost.
Pool loss from defaults
L = number of defaults × exposure × (1 − recovery rate)
Assumes equal exposures. Divide by pool notional for a percentage.
Expected pool loss
E[L] = PD × LGD × notional (equal exposures)
Does not depend on correlation. The sum of tranche expected losses equals this.
Correlation effect (rule of thumb)
Higher correlation: equity value ↑, senior value ↓
Mezzanine is ambiguous and depends on position and spread. Do not say it always falls.

How to solve CDOs and Tranche Structures questions

Use this sequence for any CDO structure or correlation question.

  1. 1Identify the structure: cash (owns assets) or synthetic (CDS-based, no asset purchase).
  2. 2List each tranche with its attachment and detachment points and compute its width.
  3. 3Compute the pool loss in rupee or dollar terms: defaults × exposure × (1 − recovery).
  4. 4Allocate the loss from the bottom up: subtract A, floor at zero, cap at width.
  5. 5Convert to a percentage of tranche notional if the question asks for tranche loss rate.
  6. 6If correlation changes, ask whether defaults cluster more. Reassess which tranche gains or loses.
  7. 7State the interpretation, and name the concept: waterfall, subordination, implied or base correlation.

Quickest way: Bottom-up loss fill

When to use it: Use for any numerical tranche loss question with a given pool loss.

  1. Convert pool loss to percent of pool notional.
  2. Fill the equity tranche first, then mezzanine, then senior, until the loss is used up.
  3. For correlation direction, remember: more correlation helps equity, hurts senior.
  4. For expected-loss totals, tranche expected losses weighted by width must add up to the pool expected loss.

Common mistakes in CDOs and Tranche Structures

  • Saying higher correlation increases the expected pool loss.

    Students link correlation with more risk in general.

    Fix: Expected pool loss depends on PD and LGD only. Correlation changes the shape of the loss distribution and shifts risk between tranches.

  • Saying equity always loses value when correlation rises.

    Confusing portfolio diversification with tranche payoffs.

    Fix: Equity is long a call-like payoff on defaults being few. Higher correlation makes zero or few defaults more likely, so equity value rises.

  • Calculating tranche loss as pool loss minus detachment point.

    Mixing up attachment and detachment.

    Fix: Subtract the attachment point, floor at zero, then cap at the tranche width.

  • Dividing tranche loss by pool notional instead of tranche notional.

    Forgetting the question asks for the tranche loss rate.

    Fix: Divide by tranche width times pool notional when a percentage of the tranche is requested.

  • Treating a synthetic CDO as holding the reference assets.

    The word CDO suggests an asset pool.

    Fix: A synthetic CDO takes risk through CDS. Investors in tranches act as protection sellers on the reference portfolio.

  • Confusing implied correlation with base correlation.

    Both are backed out of the Gaussian copula.

    Fix: Implied correlation is tranche-specific. Base correlation uses 0 to detachment equity tranches and is built up sequentially.

Worked examples

Example 1

A CDO pool has notional $1,000 million. Tranches: equity 0%-3%, mezzanine 3%-10%, senior 10%-100%. 12 of 100 equal-sized names default with 40% recovery. What percentage of the mezzanine tranche is lost?

Show the solution
  1. Exposure per name = $1,000m ÷ 100 = $10m.
  2. Pool loss = 12 × $10m × (1 − 0.40) = $72m.
  3. Pool loss as percent = 72 ÷ 1,000 = 7.2%.
  4. Equity absorbs the first 3%, so it is wiped out.
  5. Mezzanine loss = min(max(7.2% − 3%, 0), 7%) = 4.2%.
  6. Mezzanine width = 10% − 3% = 7%.
  7. Percent of mezzanine lost = 4.2 ÷ 7 = 60%.

Answer: 60% of the mezzanine tranche is lost.

Example 2

A risk manager holds the equity tranche and the senior tranche of a Gaussian copula CDO. Default probabilities are unchanged but default correlation rises. What happens to the value of each tranche, and why?

Show the solution
  1. Expected pool loss is unchanged because PD and LGD are unchanged.
  2. Higher correlation makes defaults cluster: more scenarios with very few defaults and more with very many.
  3. Equity is hit by the first losses. With more scenarios of few defaults, its expected loss falls, so its value rises.
  4. Senior is hit only by large losses. Clustering raises the probability of a large joint loss, so its expected loss rises and its value falls.
  5. The changes offset in total because the sum of tranche expected losses equals the fixed pool expected loss.

Answer: Equity tranche value rises and senior tranche value falls. Total expected pool loss is unchanged.

Exam tips

  • Always check whether the question asks for loss in currency or as a percent of the tranche. Read the last line first.
  • Memorize the direction: higher correlation raises equity value and lowers senior value. Treat mezzanine as ambiguous unless told otherwise.
  • Expect questions that contrast cash and synthetic CDOs on funding, assets held and use of CDS.
  • For base correlation questions, remember it uses equity tranches from 0 to each detachment point and gives a more consistent curve than implied correlation.
  • Name the market lesson when asked: super senior tranches were seen as safe but were exposed to correlation and systemic risk.

Practice questions from Credit Derivatives

CDOs and Tranche Structures: frequently asked questions

What is the difference between a cash CDO and a synthetic CDO?

A cash CDO owns the actual loans or bonds and funds them by issuing tranches. A synthetic CDO sells protection through CDS on a reference portfolio and owns no assets. Investors in synthetic tranches take the credit risk without a physical asset pool.

How does default correlation affect CDO tranche value?

Higher correlation raises the value of the equity tranche because few-default outcomes become more likely. It lowers the value of senior tranches because large joint losses become more likely. Expected pool loss stays the same.

What are attachment and detachment points?

The attachment point is the pool loss level at which a tranche starts to lose. The detachment point is the loss level at which the tranche is fully wiped out. The difference is the tranche width.

What is base correlation?

Base correlation is the Gaussian copula correlation that prices an equity-style tranche from 0 to a given detachment point. Values are found step by step using market tranche quotes. It avoids some problems of implied correlation, such as non-unique solutions for mezzanine tranches.