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gateway/knowledge/trading/strategies/structured-assets/carry-equity-tranche.md

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+---
+description: "CDO carry strategy that buys the equity (lowest quality) tranche and delta-hedges credit spread risk by selling the CDS index, earning the spread differential between tranche premium and index cost."
+tags: [structured-assets, cdo, carry, equity-tranche, delta-hedge, cds-index]
+---
+
+# Carry — Equity Tranche with Index Hedging
+
+**Section**: 11.2 | **Asset Class**: Structured Assets | **Type**: Carry / Delta-Hedged
+
+## Overview
+The equity tranche (e.g., 0–3%) of a CDO pays the highest periodic premium of all tranches because it absorbs the first losses in the reference portfolio. By buying this tranche and delta-hedging the credit spread exposure through a short position in the CDS index, the trader earns the premium differential between the equity tranche and the index hedge cost while neutralising systematic spread movements.
+
+## Construction / Mechanics
+**Position:**
+- Long the equity (0–3%) tranche (protection seller): receive spread S_equity
+- Short the CDS index (protection buyer): pay spread S_index
+
+**Delta (hedge ratio):** The number of index units to short per unit of equity tranche is:
+
+```
+Δ_ix = D / D_ix                                              (487)
+```
+
+where:
+- D = risky duration of the equity tranche (Eq. 486 from Section 11.1)
+- D_ix = risky duration of the CDS index
+
+**Economics:**
+- Premium received from the equity tranche > premium paid on the short index position
+- The net carry = S_equity × M_tr - S_index × Δ_ix × M_index (per unit time, before defaults)
+
+## Return Profile
+The trade earns positive carry (net spread income) as long as defaults do not erode the equity tranche beyond its detachment point. The hedged position is approximately spread-neutral to small parallel moves in credit spreads. The primary remaining risk is convexity: large spread moves change Δ_ix and require rehedging.
+
+## Key Parameters / Signals
+| Parameter | Description |
+|-----------|-------------|
+| Δ_ix = D / D_ix | Hedge ratio: equity tranche risky duration / index risky duration |
+| S_equity | Spread on the equity tranche (higher premium) |
+| S_index | Spread on the CDS index (lower premium) |
+| Net carry | S_equity - Δ_ix × S_index (approximately) |
+| Rehedging frequency | Required as spreads move (risky durations change) |
+
+## Variations
+- Leave the position partially unhedged to maintain more credit spread exposure (higher carry but more market risk).
+- Use individual CDS names in the reference pool instead of the index for more precise hedging.
+
+## Notes
+- The equity tranche has the highest spread income but is the first to lose principal if defaults occur in the reference pool; this is the primary tail risk.
+- Δ_ix changes as spreads widen or tighten, requiring dynamic rehedging; gamma (convexity) cost reduces net carry.
+- During credit crises, equity tranche spreads can blow out dramatically; the hedge may not keep pace if the index and tranche spreads move non-proportionally.
+- The strategy is exposed to correlation risk: if default correlations in the reference pool increase (systemic stress), equity tranche losses occur faster than priced.