Question

4. The one year interest rate in Europe is -0.50%. The one year US rate is 0.20%. The EURUSD rate is 1.0700. What should the one year EURUSD forward rate be? GIVE YOUR ANSWER OUT TO FOUR DECIMAL PLACES.(3)

5. If the one year EURUSD forward rate is 1.1000 what are the steps one can take to earn a riskless profit? (3)

Answer 1

EURUSD rate = USD 1.07 per EUR

Therefore EUR is base currency and USD is quoted currency.

Implied forward rate = Spot rate x (1+quoted currency interest rate) / (1+base currency interest rate)

Implied forward rate = Spot rate x (1+US interest rate) / (1+Euro interest rate)

Implied forward rate = 1.07 x (1+0.20%) / (1-0.50%)

Implied forward rate = 1.07 x 1.002 / 0.995

Implied forward rate = 1.07753

Since actual forward rate is not equal to implied forward rate, arbitrage gain is possible.

Since actual forward rate is more than implied forward rate, I would sell EUR in forward contract.

Therefore steps for arbitrage:

Borrow USD @ 0.5%

Convert the borrowed USD to EUR @ USD1.07.

Invest in Europe @ -0.2%

Sell EUR in forward contract @ USD1.10

Therefore for I would borrow money from US @ 0.50% convert it to EUR

Arbitrage Gain = Actual forward rate - implied foward rate

Arbitrage Gain = 1.10 - 1.07753

Arbitrage Gain = USD 0.02247