Question

Covered interest arbitrage and IRP. What is the relationship between forward rates and interest rates? If ? = ? and ?௛ ≠ ?௙, is arbitrage possible?

a. Assume the following information:

You have $1,000 to invest:

Current spot rate of Australian dollar = $0.95

180-day forward rate of Australian dollar = $0.94

6-month deposit rate in U.S. = 4%

6-month deposit rate in Australia = 6%

If you use covered interest arbitrage for a 180-day investment, what will be the amount of U.S. dollars you will have after 180 days?

Answer 1

	As per IRPT,
	F = S*(1+rh)/(1+rf)
	Where
	F = The forward rate
	S = Spot rate
	rh = interest rate of home currency
	rf = interest rate of foreign currency
	The forward discount for the AUD = 0.94/0.95-1 =	-1.05%
	Difference in interest rate = 6%-4% =	2.00%
	As the two differ, IRPT does not hold hold good.
	Further, as the interest rate is more than the
	forward discount, it would be profitable to
	invest in the currency having higher interest rate.
	The steps to be taken are:
1)	Convert $1000 into AUD at spot to get 1000/0.95 =	1052.63	AUD
2)	Invest the AUD for 6 months to have a MV of 1052.63*1.06 =	1115.79	AUD
3)	Sell forward 1115.79 AUD at 0.94 to realize after 180 days 1115.79*0.94 =	$     1,048.84
4)	Amount to be had in $ after 180 days =	$     1,048.84
5)	Amount receivable after 180 days if invested directly in $ = 1000*1.04 =	$     1,040.00
6)	Extra amount reaized	$             8.84