Question

Covered Interest Arbitrage: The spot rate is currently: 1.6131 $/pound US interest rate 1.0% The 6 month forward is: 1.6022 $/pound UK interest rate 2.5% a.) Is Arbitrage possible? Use the forward as a percentage to show why. What items do you compare to arrive at your answer? Explain fully. b.) Us the forward as a percentage in a sentence that correctly describes what it means. c.) How to Profit. For this part show how the arbitrage would be carried out. What is the excess profit that can be made by carrying out the covered interest arbitrage? Assume that you start with 1.0 million dollars. d.) In which direction would the four numbers at the beginning of this problem need to move to reduce or eliminate the arbitrage? e.) If all numbers are fixed except for the UK interest rate, what would the UK interest rate need to be to totally eliminate the arbitrage?

Answer 1

	Working		Dollar	Pound
		Spot Rate	1.6131	1
		6 month Forward Rate	1.6022	1
		Difference	0.0109
		Base	1.6131
		Time	6 month
		% Change	1.35%
		Interest rate
		US	1.00%
		UK	2.50%
		Yearly interest rate difference	1.50%
		6 monthly interest rate differnce	0.75%
Answers
A)	As interest rate parity theory does not hold good i.e. 8.11%=0.75% .
	Arbitrage is possible.
	Comparision has been done on
	1	Forward rate-spot rate of currencies
	2	Interest rates of two curency
B)	Forward % change		1.35%
	Meaning of Such %
	As such change is negative (Spot - forward) it denotes that home currency going to be stronger against foreing currency.
	It further shows that inflation rate in home county is less than the foreign country.
	Actual Interest rate		1.00%
	Theoritcal interest rate		1.35%
C)	Profitability
	As actual interest rate in home country is lower, borrow in home counntry and invest in foreign country.
	We have		1000000	$
	Spot rate		1.6131 $	for	1 Pound
	We can invest		1000000/1.6131
		=	619924.4	Pound
	Convert in pound	A	619924.4	Pound
	Invest for 6 month and earn interest	B	2.50%
	Interest	C=A X B X 6 MONTHS	7,749.05
	Amount received after six months	D=A + C	627673.4
	Forward rate	E	1.6022
	Convert it in to Pound with forward rate	F=D/E	1005658
	AMOUNT PAYABLE IN DOLLAR
	Borrow	G	1000000
	Interest rate	H	1.00%
	Interest amount	I= G x H	5000
	Amount payable	J=G + I	1005000
	GAIN	F-J	658.36
D)	For removal of arbitrage
	Spot Exchange Rate	Dollar per pound will fall.
	Forward Exchange Rate	Dollar per pound will rise.
	Interest rate of UK	will rise
	Interest rate of US	will fall
	This will continue until removal of arbitrage.
E)	UK interest rate to eliminate arbitrage possibility.
			Dollar	Pound	Pound per Dollar
	Spot Rate		1.6131	1	0.6199
	Forward Rate		1.6022	1	0.6241
	Difference				0.0042
	% Change 6 monhly				1.36%
	Yearly rate to eliminate arbitrage				2.72%