Question

A large commercial bank observes the annual return on 90-day Canadian dollar denominated bonds (RC$) is 1.94% and the annual return on 90-day euro denominated bonds (R€) is 1.58%. Suppose the spot €/C$ exchange rate is 0.74, and € is traded at a forward premium of 0.8% per year. Note: Keep your answers to 4 decimal points if necessary. a) Based on the above information, is there any arbitrage opportunity? If yes, describe how the commercial bank could capture this arbitrage profit. (10 points) b) Suppose the commercial bank has the ability to “move” the market (i.e. affecting spot exchange rate, the forward exchange rate, and the returns on bonds in both countries), what happens to these variables after the transactions in part (a)? Explain. (10 points) c) Instead of affecting the interest rates and the 90-day forward exchange rate as in part (b), suppose the spot exchange rate bears all the burden of adjustments, find the spot €/C$ exchange rate that would eliminate interest arbitrage. (5 points)

Answer 1

As per the interest rate parity theory, the forward rate shall be function of current relative interest rates . We are given the following info:

Canadian Interest Rate (I_C) = 1.94% p.a. or 1.94%*(90/365) = 0.4784% for 90 days

Euro Interest Rate (I_E) = 1.58% p.a. or 1.58%*(90/365) = 0.3896% for 90 days

Spot rate is 0.74 Euro for every 1 Canadian Dollar. A forward premium of 0.8% per annum will mean for 90 days = 0.74 * (1+(0.8%*90/365)) = 0.7415

As per the interest rate parity the forward rate should be : 0.74 * (1+0.0.3896%)/(1+0.4784%) = 0.7393

Since the current forward rate is different from expected forward rate, there is an arbitrage opportunity and it can used as below:

• Since the current forward rate reflects higher depreciation for Canadian dollar than as per interest rate parity, we should do as below
• We borrow PV of Euro for 90 days which will be (100/1+0.3896%) = 99.6119
• Convert this into CAD at 0.74 and get (99.6119/0.74) = 134.6107
• Invest this 134.6107 in Canadian dollars for 90 days at 0.4784%
• Book forward to convert the CAD back to Euro at 0.7415 atfer 90 days
• After 90 days, receive in CAD = 134.6107 * (1+0.4784%) = 135.2546
• Convert into Euro at forward rate = 135.2546 * 0.7415 = 100.2859
• Repay Euro 100 loan taken at initiation and 0.2859 is the riskless arbitrage profit

If the bank can move the markets, then due to its activities, the demand for CAD in spot will increase and supply for CAD in forward market will decrease leading the rates to converge to a level where the arbitrage it zeroised.

If the entire burden will have to borne by adjustment in the spot price, then we work backwards - the forward rate remains 0.7415 . Lets denote the no arbitrage spot rate to be X. Then we have :

X * (1+0.0.3896%)/(1+0.4784%) = 0.7415 ; solving for X,we get X = 0.7421