The spot exchange rate is ¥102.30/$, the 180-day forward exchange rate is ¥101.4

Question

The spot exchange rate is ¥102.30/$, the 180-day forward exchange rate is ¥101.40/$, the 180-day dollar interest rate is 4.8% per year, and the 180-day yen interest rate is 3.4% per year. Models suggest that spot will remain close to ¥101.90/$ over the next 180 days.

a. How much profit does investing $5,000,000 (or its yen equivalent) in a covered interest arbitrage between US dollars and Japanese yen yield?

b. How much profit does investing $5,000,000 (or its yen equivalent) in an uncovered interest arbitrage between US dollars and Japanese yen yield?

Explanation / Answer

a) $ 5,000,000 = 5000000*102.3= 511,500,000 Yen

Incovered interest arbitrage forwards are used to hedge risk but in uncovered forwards are not used instead spot rate is used.

Interest earned on yen = 511,500,000*3.4/100*180/365= 8,576,383.56 Yen

Total = 511,500,000+8,576,383.56 = 520,076,383.6 Yen

Using forwards it get converted to dollars at Y 101.4/$ ie 520,076,383.6/101.4= $ 5,128,958.42

Profit from arbitrage = 5,128,958.42-5,000,000= $128,958.42

b) In uncovered arbitrage it get converted at Y101.9/$ ie 520,076,383.6/101.9 = $ 5,103,791.79

Profit from arbitrage = 5,103,791.79-5,000,000= 103,791.79

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