Question

Suppose that the U.S. dollar-pound sterling exchange rate equals to $1.30/f, while the 3-month

forward rate is $1.40/€. The yield on 1-year U.S. and U.K. Treasury bills are 8% and 12%,
respectively:
Calculate the 3-month covered interest differential using the exact formula (f = (i-i*)/(1+
i*)). Are there net gains to be made?

Answer 1

The 3-month covered interest differential calculated using the formula suggests a negative differential, indicating no net gains to be made from covered interest arbitrage when considering the interest rates and forward exchange rate provided.

Step-by-step explanation:

To calculate the 3-month covered interest differential using the exact formula given (which is an application of the interest rate parity condition), we use the domestic and foreign interest rates, as well as the spot and forward exchange rates provided. The formula f = (i - i*) / (1 + i*) is used, where i is the domestic interest rate and i* is the foreign interest rate. Here, 'i' for the U.S. is 8% (or 0.08) for 1 year, and since we need the 3-month rate, we divide by 4 to obtain 0.02 (or 2%). Similarly, 'i*' for the U.K. is 12% for 1 year, and the 3-month rate becomes 0.03 (or 3%). Plugging these into the formula gives us f = (0.02 - 0.03) / (1 + 0.03) = -0.009708, which implies a negative covered interest differential. This suggests that there are no net gains to be made from covered interest arbitrage since investors would incur a loss when factoring in the interest rates and forward exchange rate.

The complete question is:Suppose that the U.S. dollar-pound sterling exchange rate equals to $1.30/f, while the 3-month

forward rate is $1.40/€. The yield on 1-year U.S. and U.K. Treasury bills are 8% and 12%,

respectively:

Calculate the 3-month covered interest differential using the exact formula (f = (i-i*)/(1+

i*)). Are there net gains to be made?

Answer 2

The 3-month covered interest differential using the exact formula is calculated as (0.08 - 0.12) / (1 + 0.12), resulting in approximately -0.0909 or -9.09%. Therefore, there is a net loss rather than gains to be made.

Step-by-step explanation:

The covered interest differential is computed by taking the difference between the domestic interest rate (U.S.) and the foreign interest rate (U.K.) and dividing it by (1 + foreign interest rate). In this case, the calculation is (0.08 - 0.12) / (1 + 0.12), which yields -0.0909 or -9.09%.

A negative covered interest differential signifies that investing in the U.K., even with a higher interest rate, would result in a net loss when considering the exchange rate risk covered by the forward contract.

In practical terms, it indicates that the higher U.K. interest rate is outweighed by the expected depreciation of the pound sterling in the forward market. Consequently, investors would not gain but experience a negative return by engaging in this foreign exchange strategy during the specified period.