they use nominal interest rate. why not use the real interest rate? it is more precise. please add some comments . thanks
Jennifer Nance has recently been hired as an analyst at the Central City Bank in the currency trading department. Nance, who recently graduated with a degree in economics, will be working with other analysts to determine if there are profit opportunities in the foreign exchange market.
Nance has the following data available:
US Dollar ($)
UK Pound (£)
Euro (€)
Expected inflation rate
6.0%
3.0%
7.0%
One-year nominal interest rate
10.0%
6.0%
9.0%
Market Spot Rates
US Dollar ($)
UK Pound (£)
Euro (€)
US Dollar ($)
$1.0000
$1.6000
$0.8000
_UK Pound (_£)
0.6250
1.0000
2.0000
_Euro (_€)
1.2500
0.5000
1.0000
Market 1-year Forward Rates
US Dollar ($)
UK Pound (£)
Euro (€)
US Dollar ($)
$1.0000
$1.6400
$0.8082
_UK Pound (_£)
0.6098
1.0000
2.0292
_Euro (_€)
1.2373
0.4928
1.0000
Assume borrowing and lending rates are equal and bid-ask spreads are zero in the spot and forward markets. Using the data above, Nance is asked to calculate the profits in pounds from covered interest arbitrage between the United Kingdom and the United States, assuming an investor starts by borrowing ₤500,000. The answer is:
A) ₤6,585.37. B) ₤6,750.00. C) ₤36,585.37.
Your answer: A was correct!
In this example, covered interest arbitrage involves borrowing pounds at the U.K. interest rate, converting to dollars at the spot rate, investing the dollars at the U.S. interest rate, converting the dollar investment proceeds back to pounds at the forward rate, and repaying the pound loan. Arbitrage profits are the difference between the proceeds from the forward contract and the amount repaid on the loan.
We start by borrowing 500,000. At a borrowing rate of 6.0%, we will have to repay 500,000(1.06) = 530,000 at the end of the year.
We convert the 500,000 pounds to dollars at the spot rate of $1.6000, which gives us 500,000 × 1.6000 = $800,000.
We invest $800,000 for one year at 10.0%, and at the end of the year we receive $800,000(1.10) = $880,000.
This means that initially we must enter into a forward contract at $1.6400 and then at the end of the year convert $880,000 into ($880,000 / $1.6400) = 536,585.37.
We pay back the 530,000 loan balance and our arbitrage profits are 536,585.37 − 530,000 = 6,585.37.
Nance is asked to calculate the one-year forward EUR:USD rate that would preclude profits from covered interest arbitrage between the U.S. dollar and the Euro?
A) EUR:USD 0.7925. B) EUR:USD 0.8073. C) EUR:USD 0.8082.
Your answer: C was incorrect. The correct answer was B) EUR:USD 0.8073.
Interest rate parity implies that, in order to prevent covered interest arbitrage, the one-year forward EUR:USD rate should be equal to $0.8000(1.10) / (1.09) = $0.8073.