Question

Suppose 180-day risk-free investments in Britain have a 7% annual return. In the U.S., 180-day risk-free investments have a 5% annual return. The spot exchange rate between U.S. dollars and British pounds is 1.450 dollars per pound. Suppose the interest rate parity holds, what is the forward exchange rate in the 180-day forward market? (Based on a 360-day year)

		1 pound = $1.253
		1 pound = $1.344
		1 pound = $1.436
		1 pound = $0.941
		1 pound = $0.844

Use information in Question 17. The observed forward exchange rate in the 180-day forward market is 1 pound = $1.445. A U.S. investor would profit from an arbitrage opportunity by converting dollars to euros, investing in the British security, and then converting the profit back into dollars in 180 days. Assume the original investment amount is $1,000. What is the investor’s annual rate of return?

		8.30%
		8.10%
		9.20%
		9.30%
		9.50%

Answer 1

a)	Forward Exchange Rate
	= Spot Rate * (1+180Days Interest Rate in US / 1+180 Days Interest Rate in Britain)
	= $1.45 * [(1+5% / 2) / (1+7%/2)]
	= $1.45 * [(1+2.5%) / (1+3.5%)]
	= $1.45 * (1.025 / 1.035)
	= $1.436
b)	Investor's Annual Rate of Return
	= Interest Rate of Investment in Britain + Abitrage Return Rate
	Now,
	1) We have $1000 to convert in £ @ Spot Rate of $1.45
	2) We will receive £689.66 ($1000 / $1.45) to invest @ 7% for 180 Days
	3) After 180 Days we will receive £713.80 [£689.66*(1+7%/2)]
	4) Convert it into $ @ Forward Rate of $1.445
	5) We will get $1031.44 (£713.80*$1.445)
	6) We have to repay $1000 with interest of $25 [1000*(5%/2)]
	7) Arbitrage Profit will be $6.44 ($1031.44 - $1000-$25)
	Arbitrage Return for the Year
	= (Arbitrage Profit / Initial investment)*(360 Days / 180Days)*100
	= ($6.44 / $1000)*2*100
	= 1.29%
	So,
	Investor's Annual Rate of Return
	= Interest Rate of Investment in Britain + Abitrage Return Rate
	= 7% + 1.29%
	= 8.29%
	= 8.3%