Hedge Ratio Calculator
Print| Number of Futures Contracts Needed | 0 |
Whether you are an airline hedging against jet fuel price spikes, a farmer locking in crop prices, or a fund manager insulating a stock portfolio against market crashes, hedging involves taking an offsetting position in a financial derivative. However, taking a 1:1 dollar hedge is rarely optimal if the derivative asset doesn’t move in perfect lockstep with your underlying spot asset.
Our free Hedge Ratio Calculator determines the Minimum Variance Hedge Ratio (MVHR). By analyzing the correlation and volatility between your spot asset and futures contracts, you can calculate the exact number of contracts required to minimize portfolio variance.
How to Calculate Optimal Hedge Ratio
The Minimum Variance Hedge Ratio (h*) minimizes the variance of the combined hedged position value.
1. Optimal Hedge Ratio Formula (h*)
h* = ρ × (σᶣ / σᶡ)
- ρ (Rho): Correlation coefficient between changes in spot price (ΔS) and changes in futures price (ΔF).
- σᶣ (Sigma Spot): Standard deviation (volatility) of spot price changes.
- σᶡ (Sigma Futures): Standard deviation (volatility) of futures price changes.
2. Number of Futures Contracts (N*) Formula
To find the exact number of futures contracts needed to execute the hedge:
N* = h* × (Value of Portfolio to Hedge / Value of One Futures Contract)
Step-by-Step Futures Hedging Example
Imagine an equity fund manager wanting to hedge a $10,000,000 stock portfolio using S&P 500 futures contracts.
- Portfolio Value: $10,000,000
- Single S&P 500 Futures Contract Value: $250,000
- Correlation (ρ) between portfolio and futures: 0.90
- Portfolio Volatility (σᶣ): 18.0%
- Futures Volatility (σᶡ): 15.0%
| Hedging Component | Formula / Math | Result |
|---|---|---|
| Optimal Hedge Ratio (h*) | 0.90 × (0.18 / 0.15) = 0.90 × 1.20 | 1.08 (108%) |
| Unhedged Contracts Needed | $10,000,000 / $250,000 | 40 Contracts |
| Optimal Futures Contracts (N*) | 1.08 × 40 Contracts | 43.2 (Sell 43 Contracts) |
Because the portfolio is 20% more volatile than the futures index, the manager must short 43 futures contracts (rather than 40) to achieve minimum variance protection.
Frequently Asked Questions (FAQ)
What is Basis Risk in hedging?
Basis Risk is the financial risk that the spot price of the asset and the futures contract price do not move in perfect alignment. Basis risk arises when the correlation (ρ) is less than 1.0, or when the hedge is closed prior to the futures contract expiration date.
Can a hedge ratio be greater than 1.0?
Yes. If the underlying spot asset is significantly more volatile than the futures contract (σᶣ > σᶡ), the optimal hedge ratio (h*) will exceed 1.0, requiring a larger dollar position in futures than the underlying spot position value.
What is Delta Hedging in options trading?
In options trading, the Delta represents the hedge ratio. A call option with a Delta of 0.60 requires selling 60 shares of underlying stock to create a delta-neutral hedge for a 100-share option contract.