# foreign currency forwards arbitrage

Hi, Can somebody please help me understand the following question please in layman terms Japanese yen trades at .00811. Us RFR= 5.5% JPy RFR=3% 3month forward contracts quoted at .00814 Indicate how you earn a riskfree profit by engaging in a forward contract. OUTLINE your transaction (please explain this part in simple terms) Appreciate it.

The first two points tell you what you need to do. The third one is a list of necessary transactions. 1) estimate fair price of foward contract: F = S*(1+F)^t/(1+D)^t = \$.00811*(1+3%)^.25/(1+5.5%)^.25=0.00806 2) since forward is traded at a higher price, you should sell it and buy spot. 3) That would involve selling forward, borrowing money in the US, converting that amount to Japanese Yen, collecting interest rate, than sell Yen at .00814 (delivering forward), paying back interest in the US, etc. Does that help?

the arbitrage free forward price is spot*(1+rfr\$)^(3/12)/(1+rfr yen)^(3/12) = 0.00816 since the quoted forward price is lower, the yen is undervalued and hence you would buy forward yen (long yen) if you are long yen, you would buy 1 yen 3 months from now through the forward contract you could therefore borrow 0.99264 yen today at 3% rfr. the repayment would be 1 yen [0.99264*(1.03)^(3/12)] - 3 months from now. this can be repaid through the 1 yen you would be buying through the forward contract 0.99264 yen today can be converted to 0.99264*0.00811=\$0.00805 at todays spot rate invest \$0.00805 at 5.5% for 3 months = 0.00805*(1.055)^(3/12) = \$0.00816 - 3 months from now of the \$0.00816 you get 3 months later, use \$0.00814 to purchase 1 yen through the forward contract and repay the 0.9926 yen borrowed at t(0) - repayment with interest = 1 yen that leaves you with \$0.00002 - arbitrage free profit

oops, I miscalculated forward price. Jen should appreciate sinice its interest rate is lower. sorry about that.

Yeah, the rule here is to calculate arbitrage-free forward price (in this case 0.00816) and determine if the forward is underpriced or overpriced. You buy if the forward is low (underpriced), and sell if itâ€™s high (overpriced).