Triangular arbitrage

Triangular arbitrage (also referred to as cross currency arbitrage or three-point arbitrage) is the act of exploiting an arbitrage opportunity resulting from a pricing discrepancy among three different currencies in the foreign exchange market. A triangular arbitrage strategy involves three trades, exchanging the initial currency for a second, the second currency for a third, and the third currency for the initial. During the second trade, the arbitrageur locks in a zero-risk profit from the discrepancy that exists when the market cross exchange rate is not aligned with the implicit cross exchange rate. A profitable trade is only possible if there exist market imperfections. Profitable triangular arbitrage is very rarely possible because when such opportunities arise, traders execute trades that take advantage of the imperfections and prices adjust up or down until the opportunity disappears.

Cross exchange rate discrepancies

Triangular arbitrage opportunities may only exist when a bank's quoted exchange rate is not equal to the market's implicit cross exchange rate. The following equation represents the calculation of an implicit cross exchange rate, the exchange rate one would expect in the market as implied from the ratio of two currencies other than the base currency.

S

a

/

$

=

S

a

/

b

S

b

/

$

{\displaystyle S_{a/\$}=S_{a/b}S_{b/\$}}

where

S

a

/

$

{\displaystyle S_{a/\$}}

is the implicit cross exchange rate for dollars in terms of currency a

S

a

/

b

{\displaystyle S_{a/b}}

is the quoted market cross exchange rate for b in terms of currency a

S

b

/

$

{\displaystyle S_{b/\$}}

is the quoted market cross exchange rate for dollars in terms of currency b

If the market cross exchange rate quoted by a bank is equal to the implicit cross exchange rate as implied from the exchange rates of other currencies, then a no-arbitrage condition is sustained. However, if an inequality exists between the market cross exchange rate,

S

a

/

$

{\displaystyle S_{a/\$}}

, and the implicit cross exchange rate,

S

a

/

b

S

b

/

$

{\displaystyle S_{a/b}S_{b/\$}}

, then there exists an opportunity for arbitrage profits on the difference between the two exchange rates.

Mechanics of triangular arbitrage

Some international banks serve as market makers between currencies by narrowing their bid–ask spread more than the bid-ask spread of the implicit cross exchange rate.