Tim Olson
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description, tags
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|---|---|---|---|---|---|---|---|
| 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. |
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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.