Assume the spot rate for the British pound currently is £.6369 per $1. Also assume the one-year forward rate is £.6421 per $1. A risk-free asset in the U.S. is currently earning 3.2 percent. If interest rate parity holds, what rate can you earn on a one-year risk-free British security?

Question

Quizplus · Accepted Answer

According to interest rate parity, the difference between the domestic and foreign interest rates should be reflected in the forward exchange rate.

Thus, the expected future spot rate, S, can be calculated as:

S = F / (1 + foreign interest rate) / (1 + domestic interest rate)

Plugging in the given values:

S = .6421 / (1 + Rf) / (1 + .032) = .6239

The expected future spot rate indicates that the British pound will appreciate against the dollar (from .6369 to .6239).

To calculate the rate that you can earn on a one-year risk-free British security, you can set up an arbitrage where you convert dollars to pounds, invest in the British security, and then convert back to dollars at the expected future spot rate. The resulting return should be equal to the domestic risk-free rate.

Starting with $1:

1 / .6369 = £1.5688 (convert dollars to pounds) 
£1.5688 x (1 + Rb) = £1.6239 (invest in British security at Rb) 
£1.6239 x .6239 = $1.0128 (convert pounds back to dollars at expected future spot rate)

The return on this arbitrage is $1.0128 / $1 - 1 = .0128, or 1.28%

Since this arbitrage should result in the same return as investing domestically in a risk-free asset, the rate that you can earn on a one-year British security should also be 3.2% + 1.28%, or 4.04%.

Therefore, the best choice is D, 4.04 percent.

Assume the Spot Rate for the British Pound Currently Is