---
description: "CDO carry strategy that buys a low-quality tranche and delta-hedges by selling a high-quality tranche, earning the spread differential between the two tranches while hedging credit spread exposure."
tags: [structured-assets, cdo, carry, tranche-hedging, delta-hedge, spread-differential]
---

# Carry — Tranche Hedging

**Section**: 11.4 | **Asset Class**: Structured Assets | **Type**: Carry / Delta-Hedged

## Overview
Rather than using the CDS index as the hedge vehicle, this strategy hedges a long position in a low-quality tranche by selling a high-quality tranche. The hedge ratio is calibrated to equate the risky durations of the two positions, and the trader earns the spread differential between the high-yield low-quality tranche and the low-yield high-quality tranche.

## Construction / Mechanics
**Position:**
- Long a low-quality tranche (e.g., equity 0–3%): receive high spread S_low
- Short a high-quality tranche (e.g., senior): pay lower spread S_high

**Hedge ratio:** The number of high-quality tranche units to short per unit of low-quality tranche is:

```
Δ_high = D_low / D_high                                      (488)
```

where:
- D_low = risky duration of the low-quality tranche
- D_high = risky duration of the high-quality tranche

**Economics:**
- Net carry = S_low - Δ_high × S_high (per unit time, before defaults)
- Since S_low >> S_high, the trade generates positive net carry when spread-neutral

## Return Profile
Profits from the spread differential between the low and high-quality tranches. The delta-hedge neutralises small parallel credit spread moves. Residual exposure includes the correlation between the two tranche spreads, curvature (gamma) as spreads shift, and the risk that defaults breach the low-quality tranche while leaving the high-quality tranche intact.

## Key Parameters / Signals
| Parameter | Description |
|-----------|-------------|
| Δ_high = D_low / D_high | Hedge ratio: risky durations of low vs. high quality tranches |
| S_low | Spread on low-quality (long) tranche |
| S_high | Spread on high-quality (short) tranche |
| Net carry | S_low - Δ_high × S_high |
| Rehedging | Required as risky durations change with spread moves |

## Variations
- Use mezzanine as the hedge instead of senior to change the risk profile.
- Stack multiple tranche pairs (e.g., equity vs. mezzanine and mezzanine vs. senior) in a ladder structure.

## Notes
- The correlation between the two tranche spreads is the key residual risk: if the low-quality tranche widens while the high-quality tranche tightens (de-correlation of credit curves), the hedge becomes less effective.
- Unlike the index-hedged strategies (Sections 11.2 and 11.3), there is no single liquid instrument representing the hedge; both legs may have limited secondary market liquidity.
- The hedge ratio Δ_high changes dynamically; frequent rebalancing is required in volatile credit markets.
- This trade is sensitive to the shape of the loss distribution: a bi-modal loss distribution (either very few or very many defaults) affects the two tranches differently.