Question

The spot market rate for the euro is 1.4059 Canadian dollars per euro. The 3-month futures (forward) rate on the euro is 1.4147 Canadian dollars per euro. The yield on a 3-month Canadian government security is 1.16 percent (0.0116 decimal), annual percentage rate (APR). The yield on a 3-month euro area security is 0.24 percent (0.0024 decimal), annual percentage rate (APR). Show that interest rate parity (IRP) does not hold by solving for the forward rate that ensures IRP. How would you take advantage of the arbitrage opportunity arising from the actual data (i.e., borrow 1,000,000 euros, convert to Canadian dollars, invest in Canada, sell the proceeds forward and then repay your loan or borrow 1,000,000 Canadian dollars, convert to euros, invest in Europe, sell the proceeds forward and then repay your loan)?

Answer 1

Arbitrage-free forward rate = spot rate * ((1 + r_c) / (1 + r_e))^t,

where r_c = interest rate in Canada

r_e = interest rate in Europe

t = time in years

Arbitrage-free forward rate = 1.4059 * ((1 + 0.0116) / (1 + 0.0024))^3/12

Arbitrage-free forward rate = 1.4091 Canadian dollars per Euro

However, the actual forward rate is 1.4147. Hence, IRP does not hold.

To make an arbitrage profit, the following steps are done :

• Borrow 1,000,000 Euros. Convert into Canadian dollars at the spot exchange rate. Canadian dollars received = 1,000,000 / 1.4059 = 711,288.14 Canadian dollars.
• Invest 711,288.14 Canadian dollars at the Canadian interest rate of 0.24% for 3 months. Canadian dollars received after 3 months = 711,288.14 * (1 + (0.0024*(3/12))) = 711,714.92 Canadian dollars.
• Convert 711,714.92 Canadian dollars back into Euros at the 3-month forward rate. Euros received = 711,714.92 * 1.4147 = 1,006,863.09 Euros.
• Repay the Euro loan with interest at 1.16% for 3 months. Amount to repay = 1,000,000 * (1 + (0.0016*(3/12))) =  1,002,900 Euros.
• Arbitrage profit = 1,006,863.09 - 1,002,900 = 3,963.09 Euros