Question

You, as a U.S. investor, find the current annual interest rate in the U.S. is 3% and the annual interest rate in Canada is 5%. The spot exchange rate for Canadian dollar is $0.95 per Canadian dollar, the 90-day Canadian dollar forward exchange rate is $0.928 per Canadian dollar.

Answer 1

US int rate R_USD = 3%

Canada int rate R_CAD = 5%

Spot FX rate S0 = 0.95 USD/CAD

90 day CAD forward exchange rate = 0.928 USD /CAD

First we will determine the 90 day CAD forward exchange rate using the spot price and the US and Canada interest rates

Forward rate = S0*e^{(R_USD -R_CAD )*t}

where S0 is the spot rate, and t is the time period = 90/360 = 1/4

After substituting the given values in the formula, we get

Forward rate = 0.95 * e^(3%-5%)*1/4

Forward rate = 0.9453 USD/CAD

The forward rate that we calculated 0.9453 USD/CAD is higher than the traded 90 day CAD forward exchange rate 0.928 USD /CAD. This means that we are getting less USD per Canadian dollar. Conversely, we are getting more Canadian dollars per USD.

Therefore in order to take advantage of this arbitrage opportunity, we will perform the following steps:

1. we will borrow in Canadian dollars CAD = CAD 1,000,000

2. We will convert CAD to USD using the spot rate = 0.95 USD /CAD * CAD 1 Mn = USD 950,000

3. Invest USD using the prevailing US interest rate for 90 days = 950,000*(1+r) = 950,000 * (1+ 3%*90/360) = USD 957,125

4. Convert USD back to CAD after 90 days using the quoted Forward rate of 0.928 USD/CAD = USD 957,125 / 0.928 USD/CAD = CAD 1,031,385

5. Calculate the accrued interest on the borrowed Canadian dollars in point 1 using prevailing Canada interest rate and calculate the total amount to be returned = CAD 1,000,000 * (1+r) = CAD 1,000,000 * (1+5%*90/360) = CAD 1,012,500

The difference between 4 and 5  will be our profit. = CAD 1,031,385 - CAD 1,012,500 = CAD 18,885

Answer:

The arbitrage profit that we can make is CAD 18,885