Question

Assume the following information:

You have $1,500,000 to invest.

Current spot rate of pound = $1.61.

90-day forward rate of pound = $1.57.

3-month deposit rate in U.S. = 2.39%.

3-month deposit rate in U.K. = 5%.

Does the covered interest parity hold? If you use covered interest arbitrage for a 90-day investment, what will be the amount of U.S. dollars you will have after 90 days?

Answer 1

Solution--

Forward rate =Spot rate∗(1+Interest rate for foreign currency​)/ (1+Interest rate for Domestic currency​)​

1.57 = 1.61 * (1+2.39%/4) / (1+5%/4)

1.57 = 1.61 * 1.005975 / 1.0125

1.57 = 1.599624

Forward rate is not equal to calculated Forward rate. Hence Covered interest rate parity does not hold.

If we use covered interest arbitrage than our money will grow as below:

$1500000 = $1500000/1.61 = Pound 931677.02

We can invest this pound value at interest rate at 5% in UK for 90 days

Pound 931677.02 * (1+5%/(90/365))

Pound 943163.45

Afer 90 days we can convert the pound in $ amount at provided exchange rate

=Pound 943163.45 * 1.57

= $1481017.08

If interest rate parity have hold than this amount should have grown to

Pound 943163.45 * 1.5996244 = 1508962.50

Hence it shows interest rate parity does not hold.