---
description: "CDO carry strategy that buys a low-quality tranche and delta-hedges with a single-name CDS, using the CDS risky duration as the hedge ratio denominator rather than the index."
tags: [structured-assets, cdo, carry, cds-hedge, single-name, delta-hedge]
---

# Carry — CDS Hedging

**Section**: 11.5 | **Asset Class**: Structured Assets | **Type**: Carry / Delta-Hedged

## Overview
Instead of hedging a long low-quality tranche position with the CDS index (Section 11.2) or a high-quality tranche (Section 11.4), this strategy uses a single-name CDS as the hedging instrument. The single-name CDS typically pays a lower premium than the long tranche, generating positive carry. The hedge ratio uses the risky duration of the CDS as the denominator.

## Construction / Mechanics
**Position:**
- Long a low-quality tranche: receive high spread S_tranche
- Short a single-name CDS (protection buyer): pay lower spread S_CDS

**Hedge ratio:**

```
Δ_CDS = D / D_CDS                                            (489)
```

where:
- D = risky duration of the low-quality tranche (Eq. 486)
- D_CDS = risky duration of the single-name CDS

Note: Eq. (489) is Eq. (487) with D_ix replaced by D_CDS.

**Economics:**
- Premium received on the long tranche > premium paid on the short single-name CDS
- Net carry = S_tranche - Δ_CDS × S_CDS

## Return Profile
Earns positive carry from the spread differential between the tranche and the CDS. The hedge approximately neutralises single-name credit spread sensitivity. Residual risks include basis risk between the tranche and the CDS (they do not move in perfect lockstep), default event risk (the CDS may not pay out at the same time or magnitude as tranche losses), and gamma risk.

## Key Parameters / Signals
| Parameter | Description |
|-----------|-------------|
| Δ_CDS = D / D_CDS | Hedge ratio: tranche risky duration / CDS risky duration |
| S_tranche | Spread received on long tranche |
| S_CDS | Spread paid on short single-name CDS |
| Net carry | S_tranche - Δ_CDS × S_CDS |
| D_CDS | Risky duration of the CDS instrument |

## Variations
- Use multiple single-name CDS (one per reference entity or a basket) for more precise hedging across the reference pool.
- Combine with an index hedge (Section 11.2) to address both systematic and idiosyncratic credit spread risk.

## Notes
- Single-name CDS has more precise default coverage for specific reference entities than the index, but may not be available for all names in the pool.
- Basis risk between the tranche and the single-name CDS is a key risk: the tranche spread reflects pool-wide correlation dynamics, while the CDS spread reflects individual credit risk.
- Liquidity of single-name CDS varies widely; less-liquid names may have wide bid-ask spreads that erode carry.
- The tranche remains exposed to correlated defaults (systemic events) even when individual names are hedged.