Hedging dual-currency perpetual contracts presents unique challenges due to the correlated risk factors between two crypto assets. Below, we break down the process from first principles and provide a generalized formula.
Key Concepts and Assumptions
Assumptions:
- Symbol: ETHUSD
- Multiplier: 0.000001 XBT
- ETHUSD Price: $500
- .BETH (ETH/USD Spot Index): $500
- .BXBT (XBT/USD Spot Index): $10,000
Scenario 1: Short ETHUSD with Hedge
Position Calculation
Short 100,000 ETHUSD Contracts:
- XBT Value:
$500 * 0.000001 XBT * -100,000 = -50 XBT - ETH Value:
-50 XBT / (.BETH / .BXBT) = -1,000 ETH
- XBT Value:
- Hedge: Buy 1,000 ETH at spot price (matching .BETH index).
Outcomes
Case A: Negative Correlation
.BETH ↑ to $750 | .BXBT ↓ to $5,000
- ETHUSD P&L: -25 XBT (-$125,000)
- ETH Spot P&L: +$250,000
- Net Profit: +$125,000
Case B: Positive Correlation
.BETH ↑ to $750 | .BXBT ↑ to $15,000
- ETHUSD P&L: -25 XBT (-$375,000)
- ETH Spot P&L: +$250,000
- Net Loss: -$125,000
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Scenario 2: Long ETHUSD with Hedge
Position Calculation
Long 100,000 ETHUSD Contracts:
- XBT Value:
$500 * 0.000001 XBT * 100,000 = 50 XBT - ETH Value:
50 XBT / (.BETH / .BXBT) = 1,000 ETH
- XBT Value:
- Hedge: Short 1,000 ETH at spot price.
Outcomes
Case A: Negative Correlation
.BETH ↑ to $750 | .BXBT ↓ to $5,000
- ETHUSD P&L: +25 XBT (+$125,000)
- ETH Spot P&L: -$250,000
- Net Loss: -$125,000
Case B: Positive Correlation
.BETH ↑ to $750 | .BXBT ↑ to $15,000
- ETHUSD P&L: +25 XBT (+$375,000)
- ETH Spot P&L: -$250,000
- Net Profit: +$125,000
Summary Table
| Position | Correlation | Outcome |
|---|---|---|
| Short ETHUSD | Negative | Profit |
| Short ETHUSD | Positive | Loss |
| Long ETHUSD | Positive | Profit |
| Long ETHUSD | Negative | Loss |
Investment Horizon
- Short-Term Traders: Dual-currency risk is negligible.
- Long-Term Holders: Correlation shifts significantly impact P&L.
Covariance Considerations
- High volatility + adverse correlation = Amplified losses.
- Regular hedging adjusts exposure but may erode profits.
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FAQ
Q1: What is a Quanto perpetual contract?
A: A derivative where profits are settled in a currency different from the underlying asset (e.g., ETHUSD settled in XBT).
Q2: Why hedge dual-currency contracts?
A: To mitigate cross-currency risk when asset values are correlated.
Q3: How does correlation affect hedging?
A: Negative correlation benefits short positions; positive correlation benefits long positions.
Q4: What’s the role of .BETH and .BXBT indices?
A: They provide benchmark prices for calculating ETH/USD and XBT/USD values.
Q5: Can hedging eliminate all risk?
A: No—it manages but doesn’t eliminate covariance risk.
Q6: How often should I rebalance hedges?
A: Depends on volatility and investment horizon; frequent rebalancing suits active traders.