Answer-first summary for fast verification
Answer: As time to maturity (t) approaches zero (0), F(t) converges to S(t) such that F(0) ~ = S(0)
The defining relationship is **convergence at expiration**: as time to maturity approaches zero, the futures price converges to the spot price of the underlying asset. - At expiration, there is no time left for expectations or carrying costs to matter, so **futures price ≈ spot price**. - Choice **A** states this correctly. - Choice **B** is incorrect because spot price does not converge to its expected value at maturity. - Choice **C** is not generally true at any given time; futures prices are related to expected future spot prices plus carry, not necessarily equal to the expectation. - Choice **D** incorrectly uses today's spot price as the convergence target. Therefore, the correct answer is **A**.
Author: Manit Arora
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Question 143.1. Which of the following is most likely to be TRUE in regard to the relationship between futures and spot prices, F(X) and S(X)?
A
As time to maturity (t) approaches zero (0), F(t) converges to S(t) such that F(0) ~ = S(0)
B
As time to maturity (t) approaches zero (0), S(t) converges to E[S(t)] such that S(t) ~ = E[S(t)]
C
At any given time, E[S(t)] is approximately equal to F(t), such that E[S(t)] - F(t) ~ = 0
D
At any given time, F(t) converges toward S(0) such that E[F(t)] ~ = S(0)
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