Question

Suppose you are using a fundamental model to forecast the exchange rate of British pound in a quarter: et+10.02+-0.2INT,+-0.2 INF, where e,1 is the expected percentage change in the exchange rate over the next quarter. INT is the quarterly interest rate differential and INF is the quarterly inflation rate differential. The quarterly data are not available, so you obtained annual data instead and plan to convert them to quarterly data. The most recent annual interest rates are 3.94% in the U.S. and 3.86% in the U.K. The most recent annual inflation rates are 2.6 % in the U.S. and 3.44% in the U.K. Today the spot rate is $1.1565. Estimate the exchange rate in a quarter. Round to four decimal places. Example $1.1234

Answer 1

The most recent quarterly interest rates are

1.0394^0.25 - 1 in the US and

1.0386^0.25 - 1 in the UK

therefore the most recent quarterly interest rate differential is

INT_t = (1.0394^0.25 - 1) - (1.0386^0.25 - 1 ) = 1.0394^0.25 - 1.0386^0.25

Similarly the most recent quarterly inflation rate differential is

INF_t =  (1.026^0.25 - 1) - (1.0344^0.25 - 1 ) = 1.026^0.25 - 1.0344^0.25

Therefore the expected percentage change in the exchange rate over the next quarter is

e_t+1 = 0.02 + 0.2x( 1.0394^0.25 - 1.0386^0.25)+ 0.2x(  1.026^0.25 - 1.0344^0.25) = 0.019628135 i.e 1.9628135 %

There the estimated exchange rate in a quarter is 1.1565x1.019628135 = $1.1792