Suppose that the risk-free rates in the United States and in Canada are 5% and 3%, respectively.The spot exchange rate between the dollar and the Canadian dollar (C$) is $0.80/C$.What should the futures price of the C$ for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs.
A)$1.00/C$
B)$0.82/C$
C)$0.88/C$
D)$0.78/C$

Question

Quizplus · Accepted Answer

To prevent arbitrage opportunities, the futures price of the C$ must reflect the interest rate differential between the US and Canada. The interest rate differential is 5% - 3% = 2%.
Using the formula $F_0=S_0\frac{(1+r_{US})}{(1+r_{C})}$, where $F_0$ is the futures price, $S_0$ is the spot price, and $r_{US}$ and $r_{C}$ are the risk-free rates in the US and Canada, respectively, we get:

$F_0=0.80\frac{(1+0.05)}{(1+0.03)}=0.82$

Therefore, the futures price for a one-year contract should be $0.82/C$. Choice B is the correct answer.

Suppose That the Risk-Free Rates in the United States and in Canada