“The Japanese yen currently trades at .00812. US risk free rate = 4.5%, Jap risk free rate = 2.0%. 3 month forward contract on the yen = .00813. Indicate how you might earn a risk free profit by engaging in a forward contract. Outline your transactions.” I can sort of follow the arbitrage currency process when the forward contract is overpriced, but for some reason when its underpriced I get even more turned around. I know the price should be $0.00817. I also understand the general idea, which is that forward contract is for 1 unit of currency, so you need the equivalent of that much today. However, I don’t understand the specifics about why you do the transactions that you do in this case. Has anyone figured out an easy way to explain or understand this?
F(T) = S*(1+rD)^T/(1+rF)^T Fair F = $0.00812*(1+0.045)^(1/4)/(1+0.02)^(1/4)=$0.00817 (same as your calculation). Quick check: Japanese interest rate is lower -> it appreciates -> F > S (ok) Strategy: if F < fair F -> buy F and sell Spot (borrow foreign, buy domestic) if F > fair F -> sell F and buy Spot (borrow domestic, buy foreign) Since F < Fair F, we should buy forward and sell spot. how do we sell spot? we borrow japanese yen and buy dollar. Borrow 1,000,000 Yen -> convert to dollars -> $8,120 and buy forward in 3 months you have $8,120*(1+0.045)^(1/4)=$8,210 -> convert to Yen at $0.00813 because of forward -> 1,009,840 Yen and pay 1,000,000 Yen with interest = 1,000,000*(1+0.02)^(1/4) = 1,004,963 Yen and keep 4,877 Yen in riskless profit. Does that help?