Minimum-variance hedge ratio
You hold an asset and short futures to offset its price moves. The hedge ratio h is how many units of futures you short per unit of exposure. The variance of the hedged position is a parabola in h, minimised at h* = ρ · σ_spot / σ_futures. The deeper the correlation, the more variance the hedge removes — exactly ρ² of it.
Hedge effectiveness 64%. At h* the hedge removes 64% of the unhedged variance, leaving 0.52 of residual (basis) risk you cannot diversify away.
Hedge ratio h*0.96
Optimal contracts N* (exact)19.2
N* rounded to whole contracts19
Hedge effectiveness ρ²64%
Unhedged variance σ_spot²1.44
Minimum variance at h*0.52
Correlation ρ0.8
σ_spot (spot change std dev)1.2
σ_futures (futures change std dev)1
Exposure Q_A (units to hedge)10,000
Contract size Q_F (units per contract)500
h* = ρ · σ_spot / σ_futures · N* = h* · Q_A / Q_F · Var(h) = σ_spot² + h²·σ_futures² − 2·h·ρ·σ_spot·σ_futuresσ_spot and σ_futures are standard deviations of price changes over the hedge horizon. Effectiveness ρ² is the share of spot variance the hedge removes; the rest is basis risk. Contracts are discrete, so N* is rounded to whole contracts in practice.