The 3-month futures price on a non-dividend-paying stock is $21.22. The risk-free rate is 1.5% and the market rate is 8.9%. What is the spot rate for this stock if spot-futures parity exists?
A)$21.14
B)$21.43
C)$21.51
D)$21.60
E)$21.78

Question

Quizplus · Accepted Answer

The spot price can be calculated using the formula for the futures price in a no-arbitrage situation: $F = S_0 \times e^{rT}$, where $F$ is the futures price, $S_0$ is the spot price, $r$ is the risk-free rate, and $T$ is the time to maturity in years. Rearranging the formula to solve for $S_0$, we get $S_0 = F / e^{rT}$. Given that $F = 21.22$, $r = 1.5\%$, and $T = 3/12$ years, we find $S_0 = 21.22 / e^{0.015 \times 0.25} = 21.14$.

The 3-Month Futures Price on a Non-Dividend-Paying Stock Is $21