Question

1. The current interest rate in the US is 8% per year, while it is 10% in the UK. Currently, in the spot market, US $1 can be exchanged for GBP 0.875. Calculate the amount of 120-days forward exchange rate between US $ and GBP? Do you think the GBP exchange rate is classified as a premium or discount?

Answer 1

a)	As per Interest Rate Parity Theorem,
	(1+Rate of Interest in Domestic Country)/(1+Rate of Interest in Foreign Country)
	= Forward Exchange Rate / Spot Exchange Rate
	here,
	Domestic Country = UK
	Foreign Country = US
	Rate of Interest in UK = 10% per year
	Rate of Interest in UK for 120 Days = 10%*120/365 = 3.2877%
	Rate of Interest in US = 8% per year
	Rate of Interest in US for 120 Days = 8%*120/365 = 2.6301%
	Spot Exchange rate = GBP 0.875 / $
	So,
	(1+Rate of Interest in Domestic Country)/(1+Rate of Interest in Foreign Country)
	= Forward Exchange Rate / Spot Exchange Rate
	(1+Rate of Interest in UK for 120 Days)/(1+Rate of Interest in US for 120 Days)
	= Forward Exchange Rate / Spot Exchange Rate
	(1+3.2877%)/(1+2.6301%) = Forward Exchange Rate / 0.875
	1.032877 / 1.026301 = Forward Exchange Rate / 0.875
	1.006407 = Forward Exchange Rate / 0.875
	Forward Exchange Rate = 1.006407 * 0.875
	Forward Exchange Rate = 0.881
	Forward Exchange Rate = GBP 0.881 / $
b)	As per Interest Rate Parity Theorem, if interest rate in a country in relation
	to other country is high then its currency would depreciate and vice-versa.
	In the given problem rate of interest of UK (10%) is higher than the rate of
	interest in US (8%), so GBP will be depreciate and $ will appreciate.
	GBP will be depreciate means GBP exchange rate is classified as
	discount.
	Rate of Discount
	= [(Forward Rate - Spot Rate)*365Days /120Days]*100
	= [(0.881-0.875)*365/120]*100
	= [0.006*365/120]*100
	= 0.01825*100
	= 1.825%