The 6-month Canadian risk-free rate is 1.55%, while the 6-month US risk-free rate is 0.40%. Both of these rates are in continuous time.

The spot exchange rate is $1.2555 CAD/USD.

(1) What should be the 6-month future exchange rate?

Now, suppose the 6-month future exchange rate is $1.2450.

Is it your first time spotting an arbitrage opportunity in the Forex.

ARBITRAGE TRANSACTIONS:

You borrow $10,000 CAD at 1.55% for 6 months, convert it to $10,000 CAD / 1.2555 CAD/USD = $7,964.95 USD, and invest it at the USD 0.4%.

You enter into a forward contract to sell $7,980.90 USD for 1.2450 CAD/USD to receive $9,936.22 CAD in 6-month.

You plan on earning $10,000 - $9,936.22 CAD in 6 months.

(2) Explain why you will lose money in 6 month rather than gain money.

(3) Fix the ARBITRAGE TRANSACTIONS to actually make money.