
Explanation:
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:
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.
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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