The basis is defined as spot minus futures. A trader is hedging the sale of an asset with a short futures position. The basis increases unexpectedly. Which of the following is true?

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Question restatement: The basis is defined as spot minus futures. A trader is hedging the sale of an asset with a short futures position. The basis increases unexpectedly. Which of the following is true?

Option a: "The hedger’s position improves." In some scenarios, a widening basis could temporarily improve the hedge if the futures move in a favorable direction relative to the spot, but this is not a guaranteed or universal outcome. Since the basis move is unexpected, assuming only improvement would ignore the complex interaction between spot and futures prices and the hedged exposure.

Option b: "The hedger’s position worsens." A larger basis (spot – futures) suggests futures are relatively cheaper compared to spot, or spot is stronger relative to futures. For a trader who is short futures to hedge the sale of the asset, a basis widening does not universally imply a guaranteed worsening; the impact depends on which leg moves and by how much. Therefore stating a definite worsening is too absolute.

Option c: "The hedger’s position sometimes worsens and sometimes improves." This option recognizes basis moves can have mixed effects on hedge effectiveness. When basis widens or narrows, the hedge ratio and effectiveness can change, leading to periods where the hedged position looks better and periods where it looks worse. It reflects the reality of basis risk: hedges are not perfect, and varying basis movements can produce both positive and negative outcomes.

Option d: "The hedger’s position stays the same." This would be incorrect because a change in basis directly affects the relationship between spot and futures prices, which in turn changes the P&L interactions between the cash position and the futures hedge. A basis move almost certainly alters hedge performance rather than leaving it unchanged.

Additional note on concepts: The key idea is basis risk—the possibility that the hedge (short futures against a physical sale) does not move in perfect lockstep with the cash market. Basis changes can alter the degree of hedge effectiveness, sometimes mitigating risk and sometimes amplifying it, depending on how spot and futures prices move relative to each other. The most nuanced, broadly correct characterization among these options is that the hedger’s position can experience both improvements and deteriorations depending on the direction and magnitude of basis changes.

FIN 413 (LEC B01 B02 B03 Winter 2025) Quiz 2

The basis is defined as spot minus futures. A trader is hedging the sale of an asset with a short futures position. The basis increases unexpectedly. Which of the following is true?

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