Suppose that the US dollar interest rate and the Swiss Franc interest rate are t

Question

Suppose that the US dollar interest rate and the Swiss Franc interest rate are the same, 5 percent per year, but that there is a risk premium of 1 percent associated with holding Swiss Franc rather than US dollars over the year. (a) What is the relationship (in percentage terms) between the current equilibrium dollar/franc exchange rate and its expected future level? (b) If the expected future exchange rate is $1.12 per franc, what is the equilibrium dollar/franc (spot) exchange rate? Now suppose that the expected future exchange rate, $1.12 US per franc, remains constant as Swiss's interest rate rises to 10 percent per year. (c) If the US interest rate also remains constant, what is the new equilibrium dollar/franc exchange rate?

Explanation / Answer

Ans.

a) The interest rate parity formula is given by:

E = E(e)(1+R*)/ (1+R) (1+q)

Where E = Spot exchange rate in US dollars per Swiss franc. E(e) is expected exchange rate ,R* is interest rate in terms of Swiss franc. R is dollar interest rate and q is risk premium of holding Swiss franc rather than US dollar over a year.

When R*=R = 5% and q =1% the swiss franc is expected to appreciate by 1%p.a. Thus, E(e) must exceed E by 1%.

b) E = E(e)(1+R*)/(1+R)(1+q)

E= (1.12)(1+0.05)/(1+0.05)(1+0.01)

E =1.176/1.0605 = 1.108

The equilibrium exchange rate would be $ 1.108 per Swiss franc , consistent with expected Swiss franc appreciation of 1% per annum.

C) If expected exchange rate remains at $1.12 US per franc.and Swiss franc interest rate rises from 5% to 10% then interest parity formula is satisfied if current exchange rate changes such that there is expected appreciation of dollars equal to 4% i.e E(e) must exceed E by 4% .

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