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

1)	The 3 month forward rate per the IRP should be 0.80*1.0125/1.02 =	0.7885
	As the three month forward rate is not same rate as per
	IRP, there is scope for covered interest rate arbitrate.
2)	Forward discount on $ = 0.7994/0.8000-1 =	-0.075%
	3 month interest rate differential = 2.00%-1.25% =	0.75%
3)	As the interest rate differential is more than the forward
	discount, the borrowing should be made in Euro, currency
	having lower interest rate and the investment should
	be made in $, the currency having higher interest rate.
4)	The steps to be taken are:
	Today:
	*Borrow 800000 Euros for 3 months, at 1.25%, the total
	amount repayable being 800000*1.0125 =	€    8,10,000
	*Convert the 800000 Euros into $ at spot to get 800000/0.8 =	€ 10,00,000
	*Invest $1000000 at 2% for 3 months to have a maturity
	value of 1000000*1.02 =	$ 10,20,000
	*Enter into a forward contract for sale of $1020000 after 3
	months to get 1020000*0.7994 =	€    8,15,388
	After 3 months:
	*Receive the maturity proceeds of the deposit of $1,020,000
	*Convert the dollars into euro to get Euros 815,388
	*Pay the euro loan with interest amounting to 810000 Euros
	Profit from arbitrage = 815388-810000 =	€          5,388
	This is riskless profit.