Question

1. Suppose the expected annual rate of inflation for the coming year is 8% for the US and 4% for Switzerland. The current spot exchange rate is $:SFr=2. The one-year interest rate is 10% in the US. Using the precise form of the international parity relations, compute the one-year interest rate in Switzerland, the expected Swiss franc to pound exchange rate in one year, and the one-year forward exchange rate.

2. A US investor likes to invest in the foreign exchange market. After an analysis of US dollar to British pound exchange rate data over the past decade, he has come up with his own model to forecast the £:$ exchange rate one year ahead. Based on this model, the forecast for the one-year-ahead exchange rate is $1.5315 per £. The spot £:$ is equal to 1.5620. The annual one-year interest rates 2% in dollars and 4.25% in pounds.

a) What is the one-year forward £:$ exchange rate?

b) If the US investor invests based on his model, which currency would he buy forward?

Answer 1

1. From International parity,

Real rate of interest in USA = Real rate of Interest in Switzerland

=(1+nominal interest rate in USA)/(1+inflation rate in USA) -1 =(1+nominal interest rate in Switzerland)/(1+inflation rate in Switerland) -1

=> 1.10/1.08 -1 =  (1+nominal interest rate in Switzerland)/1.04 -1

=> nominal interest rate in Switzerland = 1.1*1.04/1.08-1 = 0.059259 or 5.93% (One year interest rate in Switzerland)

From Interest rate parity theorem

Expected Spot rate after one year / Spot rate = (1+nominal interest rate in Switzerland)/(1+nominal interest rate in USA)

=>Expected Spot rate after one year = 2*1.059259/1.10 = 1.9259 Swiss Fr/$

or $:SFr= 1.9259

The Expected one year forward rate and the expected spot rate in one year are the same in this case

Hence, Expected One year forward rate = 1.9259 SFr/$