Answer-first summary for fast verification
Answer: $43.33
**Correct answer: B** Using the speculator’s assumed **8% discount rate**, the expected future spot price implied by a fair price can be estimated as the current spot price grown at that rate for one year: \[ E[S(1)] = 40 \times 1.08 = 43.33 \] So the expected future spot price is **$43.33**. > Note: If the question were using a pure no-arbitrage futures-pricing relationship, the risk-free rate would matter. However, this question explicitly gives the speculator’s own discount rate, which points to the expected spot price being **$43.33**.
Author: Manit Arora
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Question 186.3. The spot price and one-year futures price of silver, respectively, is $40 and $47 per ounce; i.e., S(0) = $40.00, F(0,1) = $47.00. The riskless rate is 3.0%. A speculator (investor) assumes a discount rate of 8.0%. From the perspective of this speculator, if she considers the futures price to be fair, what is the expected future spot price of silver in one year, E[S(1)]?
A
$41.22
B
$43.33
C
$47.00
D
$49.41
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