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101 Concepts for the Level I Exam

Essential Concept 13: Triangular Arbitrage


A triangular arbitrage opportunity exists if either of these conditions is violated:

  • Dealer cross-rate bid must be lower than the implied interbank cross-rate offer
  • Dealer cross-rate offers must be higher than the implied interbank cross-rate bid

To determine whether a triangular arbitrage opportunity exists, follow these steps:

  1. Calculate the cross-rate implied by the interbank market.
  2. Compare the interbank rate with the dealer rate
  • If dealer bid > interbank offer (DBi G IO) ? buy base currency in the interbank market and sell to the dealer
  • If dealer offer < interbank bid (DO L IB) ? buy base currency from dealer and sell in the interbank market
  1. If you are asked to calculate the arbitrage profit, the additional steps will depend on what currency you start with and the currency in which you need to report the profit.

Example: Consider an interbank quote of 85.76/85.80 on the currency pair A/B. The dealer quotes on the same currency from three dealers are as follows:

Dealer 1 quote: 85.74/85.81

Dealer 2 quote: 85.73/85.75

Dealer 3 quote: 85.81/85.83

When assessing for triangular arbitrage, we suggest using a ‘number line’ format, where the interbank and dealer rates are represented along a number line:

Write the interbank rate within two lines as follows:

85.76             85.80

 

Write all dealer quotes with reference to the interbank quote within the two lines. So, a number less that 85.76 would appear to the left of the interbank quote whereas a number greater than 85.80 would appear to the right of the interbank quote. The three dealer quotes can be represented as follows:

Interbank quote 85.76                  85.80
Dealer 1 quote 85.74 85.81
Dealer 2 quote 85.73                   85.75
Dealer 3 quote 85.81               85.83
Arbitrage condition DO L IB   DBi G IO

 

If the dealer quote falls entirely to the left of the interbank quote, then the DO L IB condition exists, and an arbitrage profit can be made by buying base currency from the dealer and selling it in the interbank market. On the other hand, if the dealer quote falls entirely to the right of the interbank quote, then the DBi G IO condition exists and an arbitrage profit can be made by buying the base currency in the interbank market and selling it to the dealer. Any other arrangement of the dealer quote will not result in an arbitrage opportunity. Therefore, in our example, dealer 1’s quote doesn’t provide an arbitrage opportunity whereas dealer 2’s quote provides an arbitrage opportunity as the DO L IB condition and dealer 3’s quote provides an arbitrage opportunity as the DBi G IO condition.