Triangular arbitrage

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The triangular arbitrage is a variant of the spatial arbitrage and refers to a process for the exploitation of a arbitrage opportunity, resulting from price differences between three different currencies in the currency market yields. With a triangular arbitrage strategy, one starting currency is exchanged for a second, the second is then exchanged for a third, which is then exchanged for the original currency. During the second exchange, the arbitrageur uses the existing price difference, which results from a divergence between the exchange rate on the market and the implied exchange rate, in order to generate a risk-free profit.

Exchange rate divergences

Arbitrage opportunities only arise if the exchange rate required by a bank does not match the implied exchange rate on the market. The following equation shows the calculation of the implied exchange rate (exchange rate resulting from the ratio of two currencies with a different base currency).

(Euro / pound) = (euro / dollar) × (dollar / pound)

If the exchange rate on the market (first term) and the implied exchange rate (second term) match, there is no possibility of arbitrage. Only if there is an imbalance is there an opportunity to generate risk-free profits.

(Euro / pound) ≠ (euro / dollar) × (dollar / pound)

Mechanism of triangular arbitrage

If the exchange rate required by a bank and the implied exchange rate do not match, other banks or traders can use the existing divergence to generate risk-free profits.

Example : A trader has given the following exchange rates:

1.1555 EUR / GBP or 0.86543 GBP / EUR

0.76388 EUR / USD or 1.3091 USD / EUR

1.5386 USD / GBP or 0.64994 GBP / USD

Step 1 : The sum in pounds that the dealer receives when selling 100.00 EUR is:

100.00 EUR × 0.86543 GBP / EUR = 86.543 GBP

Step 2 : If the dealer then sells the GBP 86.543 for USD, he receives an amount of:

86.543 GBP x 1.5386 USD / GBP = 133.155 USD

Step 3 : In the last step, the trader sells the USD 133.155 against EUR and receives:

133.155 USD × 0.76388 EUR / USD = 101.714 EUR

The resulting risk-free profit is the difference between:

101.714 EUR - 100.00 EUR = 1.714 EUR

The return on investment is:

1.714% = (101.714 EUR / 100.00 EUR) - 1st

The equilibrium exchange rate is calculated using the cross rate between USD and GBP:

1.3091 USD / EUR × 1.1555 EUR / GBP = 1.5126 USD / GBP

The given exchange rate (1.5386 USD / GBP) is 1.714% too high compared to the equilibrium exchange rate (1.5126 USD / GBP).

[(1.5386 USD / GBP) / (1.5126 USD / GBP)] - 1 = 1.174%

The measurement of the change in the exchange rate can also be expressed by the following formula:

% Δ USD = [(start price - end price) / end price] × 100 = 1.174%

Individual evidence

  1. ^ Robert J. Carbaugh: International Economics, 10th Edition . Thomson South-Western, Mason, OH 2005, ISBN 978-0-324-52724-7 (English).
  2. ^ Keith Pilbeam: International Finance, 3rd Edition . Palgrave Macmillan, New York, NY 2006, ISBN 978-1-4039-4837-3 (English).
  3. ↑ Yukihiro Aiba, Naomichi Hatano et al .: Triangular arbitrage as an interaction among foreign exchange rates . In: Physica A: Statistical Mechanics and its Applications . tape 310 , issue 4, 2002, pp. 467-479 , doi : 10.1016 / S0378-4371 (02) 00799-9 (English).
  4. ^ Jeff Madura: International Financial Management: Abridged 8th Edition . Thomson South-Western, Mason, OH 2007, ISBN 0-324-36563-2 (English).
  5. ^ Cheol S. Eun, Bruce G. Resnick: International Financial Management, 6th Edition . McGraw-Hill / Irwin, New York, NY 2011, ISBN 978-0-07-803465-7 (English).
  6. ^ Robert C. Feenstra, Alan M. Taylor: International Macroeconomics . Worth Publishers, New York, NY 2008, ISBN 978-1-4292-0691-4 (English).
  7. ^ Maurice D. Levi: International Finance, 4th Edition . Routledge, New York, NY 2005, ISBN 978-0-415-30900-4 (English).
  8. ^ Geert Bekaert, Robert Hodrick: International Financial Management, Second Edition . Pearson, New Jersey 2012, ISBN 978-0-13-284298-3 (English).