C6
Hedging with Futures and Forwards
Size a futures hedge for one exposure with the minimum-variance hedge ratio, then see what the hedge locks in and what basis risk it leaves. Or use index futures to change a stock portfolio's beta.
Learning focus: a futures hedge swaps price risk for basis risk: the hedger locks in roughly today's futures price plus the basis at close, and ρ² measures how much variance the hedge removes.
Hedge
Exposure and contract
Hedge ratio
At the hedge's close
Futures contracts
37.13
Long hedge: buy 37
Minimum-variance hedge ratio
0.7798
Hedge effectiveness
86.12%
Effective price paid
1.9912
per unit, at S₂ = 2.1000
Basis at start → close
−0.0500 → −0.0300
change 0.0200
Unhedged gain/loss
−320,000.00
Futures gain/loss
217,560.00
Hedged gain/loss
−102,440.00
σ of price change per unit
0.0263 → 0.0098
unhedged → hedged at h*
Hedged and unhedged gain or loss
With the basis at close held at −0.0300, the hedged line is flatter than the unhedged one but keeps a residual price exposure of −446,000 per 1.00 rise in the spot price, and a different basis at close shifts the whole line.