How does default correlation affect the value of different CDO tranches, and why do equity and senior tranches respond in opposite directions?

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AcadiFi · Accepted Answer

Default correlation is the single most important parameter in CDO pricing, and its effect on different tranches is indeed counterintuitive until you understand the loss distribution mechanics. **The Key Insight:** Higher default correlation doesn't change the *expected* number of defaults, but it changes the *distribution* of defaults. It makes extreme outcomes (very few defaults OR very many defaults) more likely, while reducing the probability of moderate default outcomes. ```mermaid graph TD A[\"Default Correlation\"] --> B{\"Increase Correlation\"} B --> C[\"More probability mass
in the tails\"] B --> D[\"Less probability mass
in the middle\"] C --> E[\"More likely: 0 defaults
(equity tranche safe)\"] C --> F[\"More likely: many defaults
(senior tranche hit)\"] D --> G[\"Less likely: moderate defaults
(only equity tranche hit)\"] E --> H[\"Equity tranche value RISES\"] F --> I[\"Senior tranche value FALLS\"] G --> H ``` **Numerical Example:** Harbourside CDO: 100 reference names, each with 3% annual default probability. Capital structure: Equity 0-5%, Mezzanine 5-15%, Senior 15-30%, Super Senior 30-100%. **Low Correlation (rho = 0.10):** Defaults cluster around the expected value (3 defaults). Distribution is tight. - P(0-5 defaults) = 82% -> equity tranche absorbs losses most of the time - P(>15 defaults) = 0.1% -> senior tranche almost never touched - Equity tranche expected loss: **high** (~60% of notional) - Senior tranche expected loss: **negligible** (~0.05%) **High Correlation (rho = 0.50):** Defaults are either very few or very many. Distribution is bimodal. - P(0-1 defaults) = 35% -> equity tranche survives entirely more often - P(>15 defaults) = 8% -> senior tranche gets hit meaningfully - Equity tranche expected loss: **lower** (~40% of notional) - Senior tranche expected loss: **higher** (~3.5%) **Impact Summary:** | Tranche | Low Correlation | High Correlation | Effect | |---|---|---|---| | Equity (0-5%) | Expected loss 60% | Expected loss 40% | Benefits (value rises) | | Mezzanine (5-15%) | Expected loss 8% | Expected loss 10% | Ambiguous (depends on attachment) | | Senior (15-30%) | Expected loss 0.05% | Expected loss 3.5% | Harmed (value falls) | | Super Senior (30-100%) | Expected loss ~0% | Expected loss 0.8% | Harmed (value falls) | **Trading Implication -- Correlation Trading:** Pre-2008 correlation desks at Thornhill Capital and similar banks ran \"correlation books\" by: - **Buying equity tranche protection** (short correlation) - **Selling senior tranche protection** (long correlation) - Net position: short correlation -- profits when correlation decreases The reverse (\"long correlation\") trade benefits when systemic risk increases. **Why This Matters for Risk Management:** Correlation is notoriously hard to estimate and unstable through time. During the 2008 crisis, correlations spiked dramatically, devastating senior tranche holders who had assumed near-zero loss probabilities based on historical correlations. Study structured credit risk in our FRM resources.

How does default correlation affect the value of different CDO tranches, and why do equity and senior tranches respond in opposite directions?

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Tranche	Low Correlation	High Correlation	Effect
Equity (0-5%)	Expected loss 60%	Expected loss 40%	Benefits (value rises)
Mezzanine (5-15%)	Expected loss 8%	Expected loss 10%	Ambiguous (depends on attachment)
Senior (15-30%)	Expected loss 0.05%	Expected loss 3.5%	Harmed (value falls)
Super Senior (30-100%)	Expected loss ~0%	Expected loss 0.8%	Harmed (value falls)