Question

Triangular arbitrage (demo version) • Quoted rates Citibank quotes US dollars per euro Barclays Bank quotes U.S. dollars per pound sterling Dresdner Bank quotes euros per pound sterling USD1.3297 = 1 EUR USD1.5585 = 1 GBP EUR1.1722 = 1 GBP • Cross rate based on Citibank and Barclays Bank quotes: GBP/USD 1.5585 EUR/USD 1.1722 = GBP/EUR 1.1721 • This is .0001 less than the Dresdner Bank quote, which results in triangular arbitrage

hello can someone tell me how this calculatipn is done?

Answer 1

First let us put the given data in a tabular format. The quotes are from the dealer's perspective, and mean the dealer buys the 1 unit of base currency (the currency in the denominator) in exchange of price currency units mentioned in the quote

Dealer	Currency Pair	Explanation	Quote
Citi Bank	USD/EUR	USD= US Dollar EUR = Euro	1.3297
Barclays	USD/GBP	USD= US Dollar GBP = pound sterling	1.5585
Dresdner	EUR/GBP		1.1722

$Cross \ rate = \frac{GBP}{USD} \div \frac{EUR }{USD}$

$Cross \ rate = \frac{GBP}{USD} \times \frac{USD}{EUR}$

$\frac{GBP}{EUR} =\frac{1}{1.5585} \times 1.3297$

$\therefore \frac{EUR}{GBP} =\frac{1.5585}{1.3297} = 1.1721$

So basically what the quote that the cross rate implies is 1.1721 while that quoted by Dresdner is 1.1721 so there is an arbitrage opportunity which can lead to a profit of 0.0001

Following example can explain the same:

• Suppose we have USD 10000
• We Sell USD 10000 for GBP
  • GBP 1 = USD 1.5585
  • So USD 10000 = 10000/1.5585 = GBP 6416.43
• We Sell GBP 6416.43 for EUR
  • 1.1722 EUR = GBP 1
  • So GBP 6416.43 = 6416.43 X 1.1722= EUR 7521.33
• Sell EUR 7521.33 for USD
  • 1 EUR = USD 1.3297
  • So EUR 7521.33 =1.3297 X 7521.33 = USD 10001.12
• So we started with 10000 and ended up with 10001.12 which is a profit of USD 1.12