---
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.