Question

You observed that JPM has bid-ask spread of $1.3655 - $1.3665 for USD/POUND, and Bank of Austria with bid-ask spread of $1.1285 - $1.1295 for USD/EUR. YOu also saw that Barclay has a bid-ask spread of 0.8225 - 0.8235 for POUND/USD. You have access to $20,000,000 line of credits. Show how you can arbitrage to make money of this.

Answer 1

Note: There is a mistake in the above question. After researching, we came to a conclusion that question shall be framed as under. Correction is highlighted in bold and underline.

You observed that JPM has bid-ask spread of $1.3655 - $1.3665 for USD/POUND, and Bank of Austria with bid-ask spread of $1.1285 - $1.1295 for USD/EUR. YOu also saw that Barclay has a bid-ask spread of 0.8225 - 0.8235 for POUND/EUR. You have access to $20,000,000 line of credits. Show how you can arbitrage to make money of this.

SOLUTION

As the question suggests we avail the line of credit of USD 20,000,000
Now, let us perform the traingular arbitrage with the same amount.

Quote 1: $1.1285 - $1.1295 /EUR
Since, we have USD 20,000,000 with us and we want to sell them to buy Euro so the rate to be used will be ASK rate. Ask rate is the selling rate of bank for Euro and buying rate of customers for Euro. We will divide USD 20,000,000 by 1.1295 to arrive at number of Euros.

20,000,000/1.1295= EUR 17706950

Quote 2: GBP 0.8225 - GBP 0.8235 /EUR

Since, we have EUR 17706950 with us and we want to sell them to buy Pounds so the rate to be used will be BID rate. Bid rate is the buying rate of bank for Euros and selling rate of customers for Euro. We will multiply EUR 17706950 by 0.8225 to arrive at number of Pounds

17706950 X 0.8225 = GBP 14563966

Quote 3: $1.3655 - $1.3665 /POUND

Since, we have GBP 14563966 with us and we want to sell them to buy USD so the rate to be used will be BID rate. Bid rate is the buying rate of bank for GBP and selling rate of customers for GBP. We will multiply GBP 14563966 by 1.3655 to arrive at number of USD.

14563966 x 1.3655 = USD 19887096

Now, Subtract the initial investment from the final amount to arrive at gain/loss. There will be an arbitrage loss of USD 20,000,000 -- USD 19887096 = USD 112904