Question

3. Interest rate parity: The annual, riskless, nominal interest rate in the Eurozone is [– 0.5%]. The spot rate between the euro (EUR) and the dollar (USD) is USD 1.1074 / EUR and the 90-day forward rate between the euro and the dollar is USD 1.0930 / EUR.

a) What is the annual, riskless, nominal interest rate in the US if interest rate parity holds?

b) What happens if interest rate parity is violated? Explain. (7 points) a) Calculate annual, riskless, nominal interest rate in US: b) Answer the question here:

Answer 1

a]

As per interest rate parity, forward rate = spot rate * [(1 + quote currency rate) / (1 + base currency rate)]ⁿ

where forward and spot rates are quoted as number of USD per EUR. Therefore quote currency is USD and EUR is base currency. n = number of years until date of forward rate

1.0930 = 1.1074 * [(1 + US rate) / (1 + (-0.5%)]^90/360

[(1 + US rate) / 0.995]^1/4 = [1.0930 / 1.1074]

(1 + US rate)^1/4 = [1.0930 / 1.1074] * (0.995)^1/4

US rate = [[1.0930 / 1.1074] * (0.995)^1/4]⁴ - 1

US rate = -0.05575, or -5.575%

b]

If interest rate parity is violated, there is an arbitrage profit that can be made (assuming no transaction costs).

The higher yielding currency (Euro) will be invested in by borrowing in the lower yielding currency (USD). Simultaneously, the Euro will be sold forward. The borrowed USD will be converted into EUR at the spot rate, and the proceeds after 90 days will be converted back into USD at the forward rate. The original loan USD will be paid back, and the remaining amount is the arbitrage profit