Question

You are given the following information :

Spot exchnage rate - Canadian dollar 0.665 per Euro

3 months forward rate - Canadian dollar 0.670 per Euro

interest rates - Canadian dollar 9% p.a and Euro is 7% p.a

Required

What operation could you carry out to take advantage of possible arbitrage opportunity?

Answer 1

CANADIAN DOLLAR (CD)

EURO (E)

STRATEGY 1:

TAKE 1000 CANADIAN DOLLAR AT 9% INTEREST.

INTEREST YOU NEED TO PAY AFTER 3 MONTHS = 1000*0.09*3/12 = 22.5CD

CONVERT 1000CD TO E = 1000/0.665 = 1503.76E

INVEST IN EURO AT 7%.

AMOUNT YOU WILL GET AFTER 3 MONTHS = 1503.76(1 + 0.07*3/12) = 1530.08E

CONVERT EUROS BACK TO CD = 1530.08*0.67 = 1025.62CD

PAY THE INTEREST RATE ON CD.

PROFIT = 1025.62CD - 1000CD - 22.5CD = 3.12CD

SCENARIO 2:

TAKE 1000 EUROS AT 97% INTEREST.

INTEREST YOU NEED TO PAY AFTER 3 MONTHS = 1000*0.07*3/12 = 17.5CD

CONVERT 1000E TO CD = 1000*0.665 = 665CD

INVEST IN CANADIAN DOLLAR AT 9%.

AMOUNT YOU WILL GET AFTER 3 MONTHS = 665(1 + 0.09*3/12) = 679.96CD

CONVERT CD BACK TO EUROS = 679.96/0.67 = 1014.86E

PAY THE INTEREST RATE ON E.

PROFIT = 1014.86E - 1000E - 17.5E = -2.64E

AS WE CAN SEE, THERE IS A CLEAR LOSS IN SCENARIO 2. SOWE WILL TAKE SCENARIO 1 TO CARRY OUT AND TAKE THE ADVANTAGE OF ARBITRAGE.