Question

Suppose that you can borrow or lend for one year at 4% in the U.S. in $US and you can borrow or lend in Germany in euros at 2%. Assume there is no risk of default. You see in the newspaper that the spot exchange rate is $1 = .9 euros and the one-year forward exchange rate is $1 = .85 euros. Are there riskless profits to be made? What transactions would you undertake to make such profits? If everyone made such transactions what would happened to interest rates and the spot and forward exchange rates? Give one possible set of values for the interest rates and exchange rates for which there would be no riskless profits.

Answer 1

	This a problem on Interest Rate parity -
	It says that -		F/S =	(1+ia)/(1+ib)
	F = Forward Rate
	S = Spot Rate
	ia =	Interest rate of A
	ib =	Interest rate on B
	If this equation holds good then the exchange rate across the globe will be the same.
	ia =	2%
	ib =	4%
	s =	e/$ =	0.9
	F =	e/$ =	0.85
	Calculate the F as per IRP =
	F/0.9 =	1.02/1.04
	F =	0.980769	x 0.9
	F =	0.8827
	Here the Should be Fwd rate is not equal to the actual fwd rate, there is a opportunity for arbitrage.
	Stepts in Arbitrage -
	Step 1 =	Borrow $ 1000 today for 1 year at 4%
		$ payable at the end of year		$ 1,040.00
	Step 2 =	Convert $ to Euro using exchange rate 0.9 today.
		1000 x 0.9 =		€     900.00
	Step 3 =	Invest these Euro for one year at 2% rate.
		Euro Inflow on maturity =		900 x 1.02
				€     918.00
	Step 4 =	Cover this amount using forward rate-
		Sell euro forward at 0.85.
		$ receivable at the end of 1 year =
		918/0.85		$ 1,080.00
	Profit =	1080 - 1040 =		$       40.00
	If everyone start doing that then the S borrow rate will increase and the euro investment rate will decrease.
	And the forward rate will increase up to .8827
	If Forward exchange rate is 0.8827 there will be no arbitrage opportunity.
	Set of values =
	ia =	2%
	ib =	4%
	s =	e/$ =	0.9
	F =	e/$ =	0.8827
	You can also calculate other values using the formula of IRP.
	Please provide feedback…. Thanks in advance…. :-)