Question

Question 1

Bank of Montreal (BMO) trades on both the Toronto Stock Exchange (TSX) and the New York Stock Exchange (NYSE). On a given day, let's assume the stock trades for $72.85CAD on the TSX and $54.21USD on the NYSE. Let's further assume the exchange rate of USD/CAD is $1.37, meaning that $1USD = $1.36CAD, where $54.21USD = $73.71CAD.

A) Explain how a trader can profit through arbitrage? (4 points) Show what his per-share profit would be in this case. (2 points)

B) If the British pound (£) is worth 1.60USD, while the Euro (€) is worth 1.14 USD when cross-transaction using triangular arbitrage is used what is the value of the British pound when compared with the Euro? (4 points) Explain your answer. (2 points)

Answer 1

A.)

Consider the following -

A trader wants to buy 100 BMO shares. In the US, he will have to pay $5421USD and in Canada, he will have to pay $7285 CAD.

Given that the exchange rate USD/CAD is $1.37, his investment if he buys the shares in the US would be worth $7427 CAD ($5421USD x 1.37).

Hence, for him, it will be beneficial if he buys the shares in the Toronto Stock Exchange for $7285 CAD and then sells them in the New York Stock Exchange for $7427 CAD. His profit will thus be $7427 CAD - $7285 CAD = $142 CAD or $104 USD. This will amount to a $1.04 USD profit per share.

B.)

The exchange rates given are as follows -

1 Pound = USD 1.60

1 Euro = USD 1.14

Using triangular arbitrage, the cross-exchange rate can be established as follows -

Let us say that a trader wants to convert 1000 Pounds to euros. First, he will convert the 1000 pounds to USD at the rate give. This will be equal to 1000 x 1.60 USD = 1600 USD.

Next, he will convert this 1600 USD to euros at the given rate. That will amount to 1600/1.14 euros = 1404 euros.

Thus, we can now see that 1000 pounds equal 1404 euros, which means the exchange rate will be established at -

1 pound = 1404/1000 euros

=> 1 pound = 1.404 euros