Question

Suppose that three month interest rates (annualized) in Japan and the US are 7% and 9% respectively. If the spot rate yen 142 :$1 and the 90 day forward rate is the yen 139 : $1 what is the three month arbitrage profit?

A. 5.5%

B. 1.7%

C. 2.6%

D. 1.2%

Answer 1

>>>>

3 month interest rate for Japan = 7%*3 / 12 = 1.75%

3 month interest rate for US = 9%*3 / 12 = 2.25%

Spot rate = Yen 142:$1

90 day forward rate = Spot rate * (1+3 month interest rate for Japan) / (1+ 3 month interest rate for US)

= Yen 142: $1 * (1+1.75%) / (1+2.25%)

= Yen 142: $1 * 1.0175 / 1.0225

= Yen 141.305623: $1

Actual 90 day forward rate = Yen 142: $1

Arbitrage profit = Actual 90 day forward rate - 90 day forward rate

= Yen 141.305623 : $1 - Yen 139: $1

= Yen 2.305623 : $1

Arbitrage Profit Percentage = Arbitrage profit / 90 day forward rate

= Yen 2.305623 : $1 / Yen 139: $1

= 0.0165872158

= 1.65872158%

Therefore, three month Arbitrage profit is 1.66% (near to 1.67%)