Question

Initially the US interest rate is 9% per year and the Swiss interest rate is 5% per year, The current spot rate is $0.5/SF and in the next 90 days it is expected to be about $0.505/SF. The franc is expected to appreciate by 1% in the next 90 days so the annual rate of expected increase is 4%. Assume uncovered interest parity holds at these rates. Describe what happens to the spot rate if US interest rate changes from 9% to 12% and Swiss interest rate changes from 5% to 6%?

Answer 1

Uncovered interest rate parity (UIP) theory states that the difference in interest rates between two countries will equal the relative change in currency foreign exchange rates over the same period.

The Formula for Uncovered Interest Rate Parity (UIP) is:

F0 = S0 * [ (1 + i (c) ) / (1 + i (b) ) ]

F0​=Forward rate

S0=Spot Rate

i (c) = Interest rate in Country C

i (b) = Intertest rate in Country B

Now, Since interest rate differential between US and Swiss is 12% - 6% = 6%, the USD will depreciate by 6% pa i.e. 1.5% for 90 days. Thus, Spot rate (90 days forward) would be 0.5 $ * 101.5% = 0.5075 $. i.e. it will depreciate by 1.5% in 90 days time