Hedge Ratio Calculator

The hedge ratio is the ratio of the futures position size used to hedge a spot exposure to the value of that exposure. Example: a commodity exposure worth 1,000,000 hedged with 2 futures contracts worth 1,000,000 total means a ratio of 1 to the exposure value. This calculator computes how many contracts are needed, both the naive way and with the optimal hedge ratio.

N = spot exposure value ÷ (futures price × contract size). Example: 1,000,000 ÷ (5,000 × 100) = 2 contracts. The naive method assumes spot and futures prices move in the same direction by comparable amounts.

h* = ρ × (σ_S ÷ σ_F), where ρ is the correlation of spot and futures price changes, σ_S is spot volatility, and σ_F is futures volatility. Example: ρ = 0.8, σ_S = 0.2, σ_F = 0.25 → h* = 0.8 × 0.8 = 0.64. Optimal contract count = h* × naive N = 0.64 × 2 = 1.28 → 1 contract when rounded down.

h* above 1 means the optimal contract count exceeds the naive one, e.g. when spot volatility is larger than futures volatility with high correlation. h* below 1 means fewer contracts are needed, e.g. when futures are more volatile than spot or the correlation is weak.

Basis risk is the risk that the spread between the spot price and the futures price (the basis) changes during the hedge period, so the protection is imperfect. The hedge ratio is computed from historical data, while the future basis may deviate from that historical pattern.

Hedging uses futures contracts to offset the price risk of an exposure you already hold, e.g. a commodity inventory or stock portfolio. Speculation uses futures to profit from the direction of price moves without holding a reference exposure, with P&L, margin, and leverage math as in the futures contract calculator.

Correlation and volatility are computed from past data and can change, so the h* that was optimal yesterday is not necessarily optimal tomorrow. Also, futures contracts only come in whole multiples, so a computed result like 1.28 contracts must be rounded, leaving a small unhedged exposure.