Question

Suppose you observe that 90–day interest rate across the eurozone is 6%, while the interest rate in the U.S. over the same time period is 3%. Further, the spot rate and the 90–day forward rate on the euro are both $1.60.

You have $600,000 that you wish to use in order to engage in covered interest arbitrage.

After 90–days in the bank, your 375,000 euros will have grown to _______ euros (including interest).

Answer 1

Interest rate in Eurozone = 6% | Interest rate in US = 3% | Time to maturity of interest rate = 90 days

Spot rate = Forward rate = $1.60 per Euro

Capital available in USD = $600,000

Convert in Euros, Capital in Euros = Capital available in USD / Exchange rate = 600,000 / 1.6

You started with USD, hence, USD is the home currency and Euros are the foreign currency.

Capital in Euros = $375,000

Invest 375,000 Euros in eurozone bank for 90 days earnings 6% rate.

Value of 375,000 after 90-days = 375,000 * (1 + Foreign interest rate / m)ⁿ / (1 + Domestic interest rate / m)ⁿ

Value of 375,000 after 90-days = 375,000 * (1 + 6% / 365)⁹⁰ / (1 + 3% / 365)⁹⁰

Value of 375,000 after 90-days = 375,000 * 1.014903 / 1.007424

Value of 375,000 after 90-days = 375,000 * 1.007424

Value of 375,000 after 90-days = 377,783.91 Euros (including interest)

Hence, Value of 375,000 Euro in bank for 90 days, is 377,783.91 Euros.