Question

Question 9 (1 point) Three Exchange Rates are as follows: 1) US Dollars (USD) to Canadian Dollars (CAD) at CAD 1.05 to USD 1 2) CAD to Euros (EUR) at CAD 1.08 to EUR 1 3) EUR to USD at EUR 0.9 to USD 1 Suppose you start with USD 100,000, and do one round of "triangular arbitrage". that is convert make a total of 3 foreign exchange transactions to start from USD and return to USD. What will be your profit in USD? (Note: Profit will be Final USD amount - $100,000. There are not transaction costs.) Your Answer: Answer

Answer 1

Solution:

As per the information given in the question we have:

Availability of USD 100,000

Exchange rates

1. US Dollars (USD) to Canadian Dollars (CAD) at CAD 1.05 to USD 1

CAD / USD = CAD 1.05

2. CAD to Euros (EUR) at CAD 1.08 to EUR 1

CAD / EUR = CAD 1.08

3. EUR to USD at EUR 0.9 to USD 1

EUR / USD = EUR 0.9

Step 1: Sell USD to buy CAD

We have USD 100,000 to look for an arbitrage opportunity              

We know that 1 USD =   CAD 1.05

Thus on sale /exchange of USD for CAD we will have

= USD 100,000 * CAD 1.05 = CAD 105,000

Step 2: Sell CAD to buy EUR

We now have CAD 105,000

We know that 1 EUR = 1.08 CAD

Thus on sale or exchange of CAD for EUR we will have

= CAD 105,000 / CAD 1.08 = 97,222.2222 EUR

Step 3 : Sell EUR to buy USD

We now have 97,222.2222 EUR

We know that 1 USD = 0.9 EUR

Thus on sale or exchange of EUR for USD we will have

= 97,222.2222 EUR / 0.9 EUR

= 108,024.6914 USD

Thus the profit on the arbitrage opportunity = USD 108,024.6914 – USD 100,000

= USD 8,024.6914

Thus the profit in USD = USD 8,024.6914

= USD 8,024.69 ( When rounded off to two decimal places )

= USD 8,025 ( When rounded off to the nearest whole number )