Question

Suppose that the spot and the forward exchange rates between the UK pound (£) and the Euro (€) are S0=0.5108 £/€ and Ft=3 months=0.5168 £/€. The time to maturity of the forward contract is 3 months. The annual interest rate of £-denominated Eurocurrency market deposits is 4.08%. The annual interest rate of €-denominated, 3-month Eurocurrency market deposits is 3.15%.
a) Examine whether there exists an arbitrage opportunity.
b) Devise an arbitrage strategy. Describe the transactions and calculate the arbitrage profits.

Answer 1

Forward rate= Pound per Euro * (1+Interest rate in Pound)/(1+Interest rate in Euro)
Forward rate=	=0.5108*(1+(4.08%*3/12))/(1+(3.15%*3/12)
Per Euro	£            0.5120
Since given forward rate is 0.5168, we can see that some arbitrage opportunity is available
Since Pound is stronger, it is advisable to loan in Pound and invest in Euro.
Assumed loan taken in Pound=	£ 1,000,000.00
Equivelent Euro	=1000000/0.5108
	€ 1,957,713.39
This is invested in EURO so amount after 3 months	=1957713.39*(1+3.15%*3/12)
	€ 1,973,130.38
Amount converted back to Pound	=1973130.38*0.5168
	£ 1,019,713.78
Amount payable in Pound after 3 months	=1000000*(1+4.08%*3/12)
	£ 1,010,200.00
So this way there will be Gain	1019713.78-1010200
So this way there will be Gain	£         9,513.78