Optimal Hedge Ratio — Smart Financial Analysis
Calculate the optimal hedge ratio h* = ρ × (σs/σf) for minimum variance hedging with futures.
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The optimal hedge ratio (h*) minimizes the variance of a hedged position. Minimum variance hedge minimizes the variance of the combined spot + futures position. Higher |ρ| means more effective hedging. Cross-hedging uses a related but different asset (e.g., crude oil futures to hedge jet fuel).
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Why: The optimal hedge ratio (h*) minimizes the variance of a hedged position. Formula: h* = ρ × (σs/σf), where ρ is correlation between spot and futures, σs is spot volatility, σf i...
How: Enter Spot σ (e.g. 0.03), Futures σ (e.g. 0.05), Correlation ρ (-1 to 1) to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
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📋 Quick Examples — Click to Load
📊 Correlation vs Effectiveness
📈 Effectiveness Curve
🍩 Risk Split
📊 Typical h* by Commodity
Optimal Hedge Ratio
h* = 0.5400, 5 contracts, 81.0% effectiveness.
For educational purposes only — not financial advice. Consult a qualified advisor before making decisions.
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The optimal hedge ratio h* = ρ × (σs/σf) minimizes portfolio variance when hedging spot exposure with futures. It balances correlation and relative volatility. Typical ratios range 0.85–0.95 for well-correlated assets. The global derivatives market exceeds $600T notional. Good hedges achieve ~90% effectiveness (ρ²).
Sources: CME Group, Hull (Options/Futures), CFA Institute, BIS.
Key Takeaways
- • h* = ρ × (σs/σf) minimizes hedged portfolio variance
- • Hedge effectiveness = ρ² (e.g., ρ=0.9 → 81% risk eliminated)
- • Number of contracts = (h* × position size) / contract size
- • Low correlation (<0.7) makes hedging less effective
Did You Know?
How Does Optimal Hedge Ratio Work?
Formula Derivation
Minimize Var(Spot − h×Futures) with respect to h. Setting derivative to zero yields h* = ρ(σs/σf).
Correlation Role
Higher ρ means spot and futures move together—hedge works better. ρ=0 implies no hedging benefit.
Cross-Hedging
When exact futures don't exist, use related asset. Basis risk = spot-futures spread volatility.
Expert Tips
Correlation vs Effectiveness
| ρ | Effectiveness (ρ²) | Risk Eliminated |
|---|---|---|
| 1.0 | 100% | Perfect |
| 0.9 | 81% | Very good |
| 0.7 | 49% | Moderate |
| 0.5 | 25% | Poor |
Frequently Asked Questions
What is optimal hedge ratio?
The optimal hedge ratio (h*) minimizes the variance of a hedged position. Formula: h* = ρ × (σs/σf), where ρ is correlation between spot and futures, σs is spot volatility, σf is futures volatility. It tells you what proportion of your exposure to hedge.
How to calculate hedge ratio?
h* = ρ × (σs/σf). Use historical returns to compute standard deviations and correlation. Number of contracts = (h* × position size) / contract size. Round to nearest whole number for practical execution.
What is minimum variance hedge explained?
Minimum variance hedge minimizes the variance of the combined spot + futures position. The optimal h* is derived by setting the derivative of portfolio variance with respect to hedge ratio to zero. It balances offsetting price movements.
How does correlation affect hedging?
Higher |ρ| means more effective hedging. Hedge effectiveness = ρ². At ρ=0.9, 81% of risk is eliminated. At ρ=0.5, only 25%. Low correlation increases basis risk and reduces hedge value.
What is cross-hedging?
Cross-hedging uses a related but different asset (e.g., crude oil futures to hedge jet fuel). Correlation is critical—typically 0.85–0.95 for effective cross-hedges. Basis risk is higher than direct hedging.
Hedge ratio vs hedge effectiveness?
Hedge ratio (h*) tells you HOW MUCH to hedge. Hedge effectiveness (ρ²) tells you HOW WELL the hedge works. A ratio >1 means over-hedge; <1 means under-hedge. Effectiveness is always 0–100%.
Key Statistics
Official Data Sources
⚠️ Disclaimer: This calculator is for educational purposes only. Past correlations and volatilities may not persist. Not financial advice. Consult a risk professional for hedging decisions.
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