Question

1. The annualized US risk-free rate is 8% and the Germany risk-free rate is 5%. Assume that any period rates less than a year can be interpolated (i.e. if you invested for 6 months then you would receive 4% in the US). The spot quote is €0.80/$ while the 3-month forward quote is €0.7994/$.You can borrow either $1,000,000 or €800,000. According to IRP, is the forward quote correct? If not, what should it be?

If the forward quote is not correct, lay out the steps to implement an arbitrage.

Answer 1

	Forward rate= EURO per USD * (1+Interest rate in EURO)/(1+Interest rate in USA)
	Forward rate=	=0.80*(1+0.05/4)/(1+0.08/4)
	Per USD	0.7941
	Since given forward rate is 0.7994, we can see that some arbitrage opportunity is available
	So the funds available are invested in EURO
	Equivelent EURO	=1000000*0.8
		800,000.00
	This is invested in EURO so amount after 3 months	=800000*(1+5%/4)
		810,000.00
	Amount converted back to USD	=810000/0.7994
		1,013,260
	Amount if invested in US after 3 months	=1000000*(1+2%)
		1020000
	So this way there will be loss	(6,740)
	Let's borrow in EURO and invest in US	=800000*(1+5%/4)
		810000
	Amount collected in US after 3 months	=1000000*(1+2%)
		1,020,000.00
	amount converted back to EURO	=1020000*0.7994
		815,388.00
	Gain in EURO	=815388-810000
	Gain in EURO	5,388.00