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Suppose that six-month interest rates (annualized) in Japan and the United States are 7 percent and 9 percent, respectively
Suppose that six-month interest rates (annualized) in Japan and the United States are 7 percent and 9 percent, respectively. If the spot rate is ¥142:$1 and the ninety-day forward rate is ¥139:$1 and the 180 day forward rate is: ¥152:$1.
Assuming no transaction costs, what would be your arbitrage profit per dollar or dollar-equivalent borrowed?
Expert Solution
Borrow Yen 142 (equivalent of $1) today. Invest Yen in Japan @ 7% for 90 days. Enter into forward agreement (90 day forward) to sell Yen and forward agreement to purchase Yen in 180 days.
Yen investment will give = 142*(1+7%)^(0.25)=144.42 Yen
Selling yen under forward agreement will give = 144.42/139=$1.039009428
Thus, there is an arbitrage profit of $0.039009428 per dollar borrowed in 90 days.
For the next 3 months do the following, invest the dollar in US at 9% for 90 days to get
=1.039009428*(1+9%)^0.25=1.061637163
Sell the dollar to buy Yen = 1.061637163*152=157.9294331 Yen
Pay the bank loan principle and interest = 142*(1+7%)^0.5=146.8859421 yen
The arbitrage profits is 11.04349097 Yen or 0.072654546 $
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