Question

We know that the yen and the swiss franc have a 100yen/ sf 1 exchange rate, meaning one swiss franc buys 100 yen in the spot ER market. The 1 year forward rate is 80 yen /swiss franc , or 1 franc buys 80 yen in the forward market. If the swiss franc has an interest rate of .1, what should the yen rate be for IPT (interest parity theory) to be attained? If the yen rate were 6%, would there be equilibrium? If so, what would transpire? Show both amounts and differentials. Also, show everything in both yen and franc terms.

Answer 1

Solution :

Current exchange rate = 100yen / sf 1 , 1 Year forward rate = 80 yen /1 swiss franc

Swiss franc has interest rate = if = 0.1 = 10% ,

Here domestic currency is Yen and foreign currency is Swiss franc based on the Exchange rate quotation

If we use interest rate parity formula then IPT theory suggests that

Forward rate / Spot rate = (1 + id ) / (1+ if )

80 / 100 = (1 + id ) / (1+0.1)

0.8 * 1.1 = 1 + id  

id = 0.88 - 1 = - 0.12

So Japanese interest rate should be -12%

If Japanese interets rate were 6% then using IPT

Expected Future rate = Spot rate * (1 + id ) / (1+if) = 100 * 1.06 / 1.1 = 96.3636 Yen / Swiss franc

But the forward rate is 80 Yen / Swiss franc

So there is an arbitrage opportunity

Rate = 96.3636 Yen / Swiss franc

Differential = 96.3636 - 80 = 16.3636 Yen / Swiss Franc