Tim Olson
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53 lines
3.0 KiB
Markdown
53 lines
3.0 KiB
Markdown
---
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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."
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tags: [structured-assets, cdo, carry, tranche-hedging, delta-hedge, spread-differential]
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---
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# Carry — Tranche Hedging
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**Section**: 11.4 | **Asset Class**: Structured Assets | **Type**: Carry / Delta-Hedged
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## Overview
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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.
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## Construction / Mechanics
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**Position:**
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- Long a low-quality tranche (e.g., equity 0–3%): receive high spread S_low
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- Short a high-quality tranche (e.g., senior): pay lower spread S_high
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**Hedge ratio:** The number of high-quality tranche units to short per unit of low-quality tranche is:
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```
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Δ_high = D_low / D_high (488)
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```
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where:
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- D_low = risky duration of the low-quality tranche
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- D_high = risky duration of the high-quality tranche
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**Economics:**
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- Net carry = S_low - Δ_high × S_high (per unit time, before defaults)
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- Since S_low >> S_high, the trade generates positive net carry when spread-neutral
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## Return Profile
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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.
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## Key Parameters / Signals
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| Parameter | Description |
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|-----------|-------------|
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| Δ_high = D_low / D_high | Hedge ratio: risky durations of low vs. high quality tranches |
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| S_low | Spread on low-quality (long) tranche |
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| S_high | Spread on high-quality (short) tranche |
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| Net carry | S_low - Δ_high × S_high |
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| Rehedging | Required as risky durations change with spread moves |
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## Variations
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- Use mezzanine as the hedge instead of senior to change the risk profile.
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- Stack multiple tranche pairs (e.g., equity vs. mezzanine and mezzanine vs. senior) in a ladder structure.
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## Notes
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- 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.
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- 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.
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- The hedge ratio Δ_high changes dynamically; frequent rebalancing is required in volatile credit markets.
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- 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.
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