Question

S(EUR/USD) = EUR/USD 1.1

Annual interest rate in Euro zone = 0.5%

Annual interest rate in US = 2%

Bank A offers: F(EUR/USD) = EUR/USD 1.2.

Check for the presence of an arbitrage opportunity (Covered interest

Answer 1

Direct quote, S = USD 1.1 / Euro; F = USD 1.2 / Euro

As per the covered interest rate, the no arbitrage forward rate, F* = Spot rate x (1 + i_US) / (1 + i_Euro) = 1.1 x (1 + 2%) / (1 + 0.5%) = USD 1.1164 / Euro

Since F* and F are not equal, there is indeed an arbitrage opportunity. And that is:

At t = 0

Borrow 1 USD in US @ 2%

Convert it into Euro today = 1 / 1.1 = Euro 0.9091

Lend this Euro in Euro zone @ 0.5%

At t = 1

Maturity proceeds from lent position = 0.9091 x (1 + 0.5%) = Euro 0.9136

Convert it into USD using the forward rate offered by the bank = 0.9136 x 1.2 = USD 1.0964

Liability towards the borrowed USD 1 = 1 x (1 + 2%) = USD 1.02

Hence, arbitrage profit = USD 1.0964 - 1.02 = USD 0.0764 per USD of investment