Consider the following: $$\begin{array} { l l l }
\text { Risk-free rate in the United States } & 0.04 / \text { year } \
\text { Risk-free rate in Australia } & 0.03 / \text { year } \
\text { Spot exchange rate } & 1.67 \mathrm {~A} \$ / \$
\end{array}$$ If the futures market price is 1.63 A$/$, how could you arbitrage?
A) Borrow Australian dollars in Australia, convert them to dollars, lend the proceeds in the United States, and . enter futures positions to purchase Australian dollars at the current futures price.
B) Borrow U.S. dollars in the United States, convert them to Australian dollars, lend the proceeds in Australia, . and enter futures positions to sell Australian dollars at the current futures price.
C) Borrow U.S. dollars in the United States, invest them in the U.S., and enter futures positions to purchase Australian dollars at the current futures price.
D) Borrow Australian dollars in Australia and invest them there, then convert back to U.S. dollars at the spot price.
E) There is no arbitrage opportunity.

Question

Consider the following: $$\begin{array} { l l l } 
\text { Risk-free rate in the United States } & 0.04 / \text { year } \
\text { Risk-free rate in Australia } & 0.03 / \text { year } \
\text { Spot exchange rate } & 1.67 \mathrm {~A} \$ / \$
\end{array}$$ If the futures market price is 1.63 A$/$, how could you arbitrage?
A) Borrow Australian dollars in Australia, convert them to dollars, lend the proceeds in the United States, and . enter futures positions to purchase Australian dollars at the current futures price. 
B) Borrow U.S. dollars in the United States, convert them to Australian dollars, lend the proceeds in Australia, . and enter futures positions to sell Australian dollars at the current futures price. 
C) Borrow U.S. dollars in the United States, invest them in the U.S., and enter futures positions to purchase Australian dollars at the current futures price. 
D) Borrow Australian dollars in Australia and invest them there, then convert back to U.S. dollars at the spot price. 
E) There is no arbitrage opportunity.

Quizplus · Accepted Answer

To arbitrage, we need to find a discrepancy between the current futures price and the fair value of the futures contract. The fair value of the futures contract can be found by adding the risk-free rate of Australia to the spot exchange rate and subtracting the risk-free rate of the United States, all for the maturity of the futures contract.

In this case, the fair value of the futures contract can be calculated as follows:

Fair value = (1.67 * e^(0.03*3/12)) / e^(0.04*3/12) = 1.657 A$

Since the futures market price is below the fair value, we could buy Australian dollars at the futures price of 1.63 A$/$ and enter into a futures contract to sell Australian dollars at the fair value of 1.657 A$/$. We can also borrow U.S. dollars in the United States, convert them to Australian dollars, lend the proceeds in Australia at 0.03 / year, and make a profit.

Therefore, Choice B is the correct answer.

Consider the Following If the Futures Market Price Is 1