Question

At 6am the next morning, your CFO reports to you all of the new market rates. The EURUSD spot rate has surged to 1.35, and the USD and EUR interest rates are both now 0.1%. Your CFO reports that the forward rate should be 1.35 as well, but is currently being quoted at 1.38!!! A. What is the profit ratio on this arbitrage opportunity? B. If the US interest rate went to ___________% and nothing else changed, the arbitrage would disappear. C. Why is this higher/lower than the current rate of 0.1%? D. If the Euro interest rate went to ___________% and nothing else changed, the arbitrage would disappear. E. If the spot rate went to __________ and nothing else changed, the arbitrage would disappear.

Answer 1

		Spot Rate per EUR	$1.35
		Forward rate per EUR	$1.38
		As per interest rate parity:
		S*(1+id)=F*(1+if)
		S=Spot Rate
		F=Forward Rate(EuroRate)
		id=Domestic interest rate(US rate )
		if=Foreign Interest rate
	A	PROFIT RATIO
		Since forward Euro rate is high
		There is arbitrage i selling Euro at Forward rate :1Euro=$1.38
		Sell 1.001Euro at forward rate of $1.38
		Borrow $1.35   at 0.1% rate of interest
		Buy 1Euro at spot rate =	$1.35
		Invest at 0.1 percent
		Amount received at the end of period=	1.001Euro	(1*1.001)
		On settlement of forward contract you receive	$1.3814	(1.38*1.001)
		Amount payable with interest for borrowing	$1.3514	(1.35*1.001)
		Amount of Profit	$0.03	(1.3814-1.3514)
		Profit RATIO =0.03/1.35=	0.02224444
		Profit RATIO in percentage	2.22%
	B	There will be no arbitrage if US interest rate is as per interest rate parity equation:
		1+id=(F/S)*(1+if)
		F=1.38
		S=1.35
		if=0.001(0.1%)
		1+id=(1.38/1.35)*1.001=	1.02324444
		id=US Interest Rate=0.023244	2.32%
	C	This is higher than current rate of interest of 0.1%
		Because the forward rate is higher
	D	There will be no arbitrage if EURO interest rate is as per interest rate parity equation:
		1+id=(F/S)*(1+if)
		F=1.38
		S=1.35
		id=0.001(0.1%)
		1+if=(1+id)*(S/F)	0.97923913		-0.02076
		if=EURO Interest Rate=0.979239-1=	(0.020761)
		EURO Interest Rate in percentage	-2.08%
	E	There will be no arbitrage if SPOT RATE is as per interest rate parity equation:
		1+id=(F/S)*(1+if)
		F=1.38
		if=0.001(0.1%)
		id=0.001(0.1%)
		S=F*((1+if)/(1+id))
		S=F=$1.38
		Spot Rate =$1.38