Tim Olson
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69 lines
3.8 KiB
Markdown
69 lines
3.8 KiB
Markdown
---
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description: "Volatility carry with two ETNs shorts VXX (short-maturity VIX futures ETN) and buys VXZ (medium-maturity VIX futures ETN) to harvest the contango roll loss differential, with the hedge ratio determined by serial regression."
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tags: [volatility, carry, vxx, vxz, etn, contango, roll]
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---
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# Volatility Carry with Two ETNs
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**Section**: 7.3 | **Asset Class**: Volatility | **Type**: Carry
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## Overview
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VXX and VXZ are exchange-traded notes (ETNs) tracking VIX futures. VXX tracks short-maturity (months 1-2) futures and suffers greater roll/contango losses than VXZ (months 4-7), because the VIX futures curve is steepest at the short end in contango. The strategy shorts VXX (captures the larger roll loss as profit) and buys VXZ as a hedge (offsets some exposure to VIX spikes), earning the contango roll differential.
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## Construction / Mechanics
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**VXX**: tracks a constant-maturity position in months 1-2 VIX futures. Each day, a fraction of the front-month futures is sold and replaced with the next-month futures. In contango, the next-month is more expensive → daily roll loss → VXX decays over time.
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**VXZ**: tracks months 4-7 VIX futures. Same roll mechanism but in a less steep part of the contango curve → lower roll loss than VXX.
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**Basic strategy**: short VXX, long VXZ.
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**Hedge ratio** h (number of VXZ units per VXX shorted):
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```
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h = β = ρ · σ_X / σ_Z
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```
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where:
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- ρ: historical pairwise correlation between VXX and VXZ returns
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- σ_X: historical volatility of VXX
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- σ_Z: historical volatility of VXZ
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- β: slope of serial regression of VXX returns on VXZ returns (with intercept)
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The position: short 1 unit of VXX, long h units of VXZ.
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## Payoff / Return Profile
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- Earns the differential roll loss between VXX and VXZ: the strategy benefits because VXX decays faster than VXZ in contango.
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- The VXZ long position partially hedges against VIX spikes (which cause VXX to spike more sharply than VXZ).
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- Profitable in normal, low-volatility, contango environments.
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- Experiences sharp drawdowns during sudden VIX spikes (equity market selloffs), as VXX spikes more violently than VXZ in the short term.
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## Key Parameters / Signals
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- Contango in VIX futures curve: the necessary condition for the strategy to profit
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- h = ρ · σ_X / σ_Z: hedge ratio (number of VXZ units per 1 unit of VXX shorted)
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- Roll loss differential between VXX and VXZ: the carry being harvested
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- VIX level and slope of futures curve: risk indicators
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## Variations
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### 7.3.1 Hedging Short VXX with VIX Futures
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Instead of using VXZ to hedge, use a basket of N medium-maturity VIX futures (e.g., months 4-7) directly. The optimal weights w_i for the N futures:
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```
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w_i = σ_X Σ_{j=1}^N C_{ij}^{-1} σ_j ρ_j (432)
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```
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where:
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- ρ_j: historical correlation between futures j and VXX returns
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- C_{ij}: N×N sample covariance matrix of the N futures returns (C_{ii} = σ_i²)
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- σ_X: historical volatility of VXX
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Dollar-neutral constraint (optional): Σ_i w_i = 1 (Eq. 433). Some w_i may be negative; can impose w_i ≥ 0 if short futures is undesirable.
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Portfolio can be rebalanced monthly or more frequently. This variation allows finer control over the hedge than using VXZ alone.
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## Notes
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- VXX spikes (which occur during equity market selloffs) can be large and sudden, causing substantial short-term P&L drawdowns even if the strategy is profitable overall.
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- The hedge ratio h should be recalibrated periodically using updated historical data.
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- The corresponding VXZ spikes are typically smaller, providing only partial protection during stress.
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- Transaction costs (bid-ask spread on VXX/VXZ) and ETN management fees must be accounted for in return estimates.
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- In sustained backwardation periods, both VXX and VXZ can rise; the strategy may lose money if VXX rises faster than VXZ.
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