Question

A corporate treasury working out of Vienna with operations in New York simultaneously calls Citibank in New York City and Barclays in London. The two banks give the following quotes at the same time on the euro:
Citibank NYC Barclays London
$0.7551-61/€ $0.7545-75/€
Required:
A) Using $1 million or its euro equivalent, show how the corporate treasury could make geographic arbitrage profit with the two different exchange rate quotes.

Answer 1

Answer:

Given $1 million and the following quotes:

Bank C - $0.7551-61/€

Bank B - $0.7545-75/€

There are two different arbitrage strategies that can be attempted. The first is to buy euros from bank B, and then sell them to bank C:

Buy euros Bank B:

Euros to be bought = $1,000,000 x  Euro / $ 0.7575

Euros to be bought = 1,320,132.01 Euros

Sell euros Bank C:

Euros to be sold = 1,320,132.01 euros x $0.7551 / Euro

Euros to be sold = $996,831.68

The profit/loss can be calculated by subtracting the original starting amount of dollars by the post-arbitrage amount:

Profit/loss = $996,831.68 - $1,000,000

Profit/loss = -$3,168.32

The second strategy involves buy euros from bank C and selling them to bank B: Buy euros Bank C:

Euros to be bought = $1,000,000 x  Euro / $ 0.7561

Euros to be bought = 1,322,576.38 Euros

Sell euros Bank B:

Euros to be sold = 1,322,576.38 euro x 0.7545 / Euro

Euros to be sold = $997,883.88

The profit/loss can be calculated by subtracting the original starting amount of dollars by the post-arbitrage amount:

Profit/loss = $997,883.88 - $1,000,000

Profit/loss = -$2,116.12

In both instances a loss is made by the arbitrage. The arbitrager cannot make a profit using these quotes.

Answer 2

Answer:

stage/case 1 : -$2116.12

stage/case 2 : -$3168.32

Explanation:

Citibank NYC : $0.7551-61 = €1 ------------------ bank A

Barclays London : $0.7545-75 = €1 ------------- bank b

Given : $1000000

There are two ways Corporate treasury can make arbitrage profit i.e either buying Euro from Bank A and selling to Bank B or Buying Euro from Bank B and selling to Bank A

stage 1:

buying euro from bank A

$0.7561 = €1

$1000000 = € ( 100000 / 0.7561 ) = €1322576.38

selling to bank B

$0.7545 = €1

€1322576.38 = $ ( 1322576 / 0.7545 ) = $997883 .88

Profit made = $997883.38 - $1000000 =  -$2116.12

stage 2:

buying euro from bank B

$0.7575 = €1

$1000000 = € ( 1000000 / 0.7575 ) = € 1320131.01

selling to bank A

$0.7551 = €1

€1320131.01 = $ ( 1320131.01 * 0.7551 ) = $996831.68

profit made = $996831.68 - $1000000 = - $3168.32

in both cases/stages the treasury company didn't make any geographic arbitrage profit.