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Hedging Basis Risk

Let's study the case of the hedger who takes a short position in futures at time t = 1 and knows that he will close out this position at time t = 2. The basis at t = 1 is therefore b₁ = S₁ – F₁, while the basis at t = 2 is b₂ = S₂ – F₂. In the case of our cattle rancher, the market price received for selling his herd would be S₂ and the profit on his futures position when he closes it out would be F₁ – F₂. The effective price he receives is therefore S₂ + (F₁ – F₂), which by definition equals F₁ + b₂.

The value of F₁ is known at t = 1, but the basis b₂ at t = 2 is not. Were it so, then we would have constructed the perfect hedge. In fact, for the case in which the futures position is closed out on the delivery date and the hedging asset is the underlying, then the basis would be zero at t = 2. Since this is not always the case, then the final profit or loss includes b₂ as a risk. To see this more clearly, let S₂′ be the spot price of the asset used for hedging. Adding and subtracting this from the effective price the hedger receives at t = 2, which from before, is S₂ + (F₁ – F₂), we get:

The two terms in parentheses are the components of the basis risk. S₂ – S₂′ is the part of the basis represented by the imperfect hedging choice, and S₂′ – F₂ represents the nonconvergence in the spot to the futures price. If the asset hedged were identical to the hedging asset, ...