I need help solving the problem below. I would like to see the steps taken for e

Question

I need help solving the problem below. I would like to see the steps taken for each part.

The following three banks give 3 quotes listed below.

Bank of L.A                 .8429    $/Canadian $

Bank of Toronto       1.1843    $/Euro

Bank of Spain            .7258      euro/Canadian $

A. Show your work if arbitrage is possible and explain how you know it is possible.

B.Assume you have 1,000,000 US Dollars to start with. What profit can you earn in euros. Show all of the steps.

C.Given your answer to (b) above, what do you think will happen to the quotes of each of these 3 banks in the very near future? Be precise and give the direction that each exchange rate will move.

D.If you could only change the $/euro rate at the Bank of Toronto and the other two rates remain fixed, what rate at the Bank of Toronto would bring the markets into equilibrium?

Explanation / Answer

A. Arbitrage is possible if convergence rates differ.
Suppose I have $1

I convert it to canadian $
$1 = 1/.8429 = 1.1864 canadian $
I convert it to Euro
1 Euro = .7258 Euro
=> 1.1864 canadian $ = 0.8611 Euro
Now I convert it to $
1 Euro = $1.1843
0.8611 Euro = $ 1.019771

So for every $1 invested I am getting $ 1.019771 in return without any risk. Hence arbitrage is possible.

B. starting with $1000000 would give 1000000*1.019771 = $1019771
Profit = $19771
Profit in Euro = 19771/1.1843 = 16694 Euro

C. In near future arbitrage will force these rates to converge to eliminate any chance of arbitrage.
Since 1/ .8429 *.7258 * 1.1843 > 1
Bank of L.A. would increase rate while other two would decrease rate. (Note that rate here is exchange rate as given in question).

D. 1/ .8429 * Bank of toronto rate *.7258 = 1
=> Bank of toronto rate = 1.1613

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