Optimal Hedge Ratio Calculator
Compute the optimal hedge ratio = correlation × (spot price SD ÷ futures price SD), the share of exposure to hedge with futures.
Input Data
Results
At a glance:The optimal hedge ratio minimises the variance of a hedged position. h* = correlation × (spot SD ÷ futures SD). It is the fraction of the spot exposure that should be covered by a futures contract.
Formula
Optimal hedge ratio = correlation × (spot standard deviation ÷ futures standard deviation).
$$h^* = \rho \times \dfrac{\sigma_s}{\sigma_f}$$$$N_{contracts} = h^* \times \dfrac{V_{spot}}{V_{futures}}$$How to Use
- Enter the correlation between spot and futures moves.
- Enter the spot and futures price standard deviations.
- Read the optimal hedge ratio.
FAQ
What is the minimum-variance optimal hedge ratio?
It is the hedge ratio that minimises the variance (risk) of the hedged position, commonly estimated as the slope of a regression of the spot price change on the futures price change: h* = ρ × (σₛ / σ_f). It balances the hedge effectiveness against basis risk, and is more accurate than a naive 1:1 ratio when the spot and futures do not move perfectly together.
Why would the hedge ratio be less than 1?
Because the spot asset and the futures contract are not perfectly correlated and may differ in volatility. If ρ < 1 or the spot is less volatile than the futures, h* < 1, meaning a smaller futures position is enough to offset most of the spot risk. Over-hedging with a 1:1 ratio can actually add basis risk instead of reducing it.
What data do I need to estimate it?
You need a history of paired spot and futures price changes (or returns) over the same period: their standard deviations σₛ and σ_f, and their correlation ρ. The more representative and longer the sample, the more stable the estimate; very short or abnormal periods can distort ρ and the ratio.
Does this apply to Hong Kong's futures and spot markets?
Yes. It is commonly used for Hong Kong's flagship Hang Seng Index futures against a spot portfolio, and for commodities (gold, oil) hedging. Given cross-market basis risk, estimating h* with local data is more reliable than blindly using 1. Note that exchanges such as HKEX set position limits and margin rules, so actual hedging must also comply with those.
What are the limitations of the optimal hedge ratio?
It is a statistical estimate, not a guarantee. It assumes historical volatility and correlation persist, which breaks down in crises; it minimises variance but not necessarily downside loss; it ignores transaction costs, margin and rollover; and it relies on the chosen sample window. Treat it as a reference for position sizing, and review it as market conditions change.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.