Question

Suppose you are the Treasurer of a company that imports goods from England. You estimate that you will have to make two payments: a 5 million pound sterling payment after 6 months and a £6 million payment after another six months (i.e., one year from today). Spot rate S_Ain American terms is $1.26 per pound sterling. You would like to hedge your currency risk exposure.

Question:  A rep from a bank calls you and offers to trade currency forward. To check this guy’s authenticity, you collect today’s interest rates in USA and UK. Next, you compute arbitrage-free forward prices (in American terms) for these four maturities.   

	USD LIBOR (per year)	Sterling LIBOR (per year)	FA[Forward price in American terms
1 month (30 days)	1 %	0.25 %	?
3 months (91 days)	1.17 %	0.32 %	?
6 months (182 days)	1.43 %	0.47 %	?
1 year	1.78 %	0.68 %	?

For simplicity

Assume these rates are continuously compounded annual risk-free interest rates

Day count convention is Actual/365.

Ignore bid/ask spreads

Answer 1

Forward rate (FA) = spot rate*(1+foreign interest rate*(number of days/365))/(1+domestic interest rate*(number of days/365))

where spot rate = $1.26/sterling

domestic interest rate = USD LIBOR

foreign interest rate = Sterling LIBOR

	USD LIBOR	Sterling LIBOR	(n = Number of days/365)	(Den = 1+USD LIBOR*n)	(Num = 1+Sterling LIBOR*n)	(Num/Den)	FA (forward price in USD) (Spot rate*(Num/Den))
1 month (30 days)	1%	0.25%	0.0822	1.00082	1.00021	0.99938	1.25922
3 months (91 days)	1.17%	0.32%	0.2493	1.00292	1.00080	0.99789	1.25734
6 months (182 days)	1.43%	0.47%	0.4986	1.00713	1.00234	0.99525	1.25401
1 year (365 days)	1.78%	0.68%	1.0000	1.01780	1.00680	0.98919	1.24638

Note: For the country with the lower interest rate compared to the other country, its currency is expected to appreciate.