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. 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.

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.

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.

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.

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. However, the bid and ask prices of the implicit cross exchange rate naturally discipline market makers.

When banks' quoted exchange rates move out of alignment with cross exchange rates, any banks or traders who detect the discrepancy have an opportunity to earn arbitrage profits via a triangular arbitrage strategy.

For example, Citibank detects that Deutsche Bank is quoting dollars at a bid price of 0.

Citibank itself is quoting the same prices for these two exchange rates. While the quoted market cross exchange rate is 1. Although the market suggests the implicit cross exchange rate should be 1.

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The following steps illustrate the triangular arbitrage transaction. Research examining high-frequency exchange rate data has found that mispricings do occur in the foreign exchange market such that executable triangular arbitrage opportunities appear possible.

Tests for seasonality in the amount and duration of triangular arbitrage opportunities have shown that incidence of arbitrage opportunities and mean duration is consistent from day to day. However, significant variations have been identified during different times of day.

Transactions involving the JPY and CHF have demonstrated a smaller number of opportunities and long average duration around Such variations in incidence and duration of arbitrage opportunities can be explained by variations in market liquidity during the trading day.

For example, the foreign exchange market is found to be most liquid for Asia around The overall foreign exchange market is most liquid around The periods of highest liquidity correspond with the periods of greatest incidence of opportunities for triangular arbitrage. This correspondence is substantiated by the observation of narrower bid-ask spreads during periods of high liquidity, resulting in a greater potential for mispricings and therefore arbitrage opportunities.

However, market forces are driven to correct for mispricings due to a high frequency of trades that will trade away fleeting arbitrage opportunities. Researchers have shown a decrease in the incidence of triangular arbitrage opportunities from to for the Japanese yen and Swiss franc and have attributed the decrease to broader adoption of electronic trading platforms and trading algorithms during the same period.

Such electronic systems have enabled traders to trade and react rapidly to price changes.

Forex triangle patterns every trader must know

The speed gained from these technologies improved trading efficiency and the correction of mispricings, allowing for less incidence of triangular arbitrage opportunities. Mere existence of triangular arbitrage opportunities does not necessarily imply that a trading strategy seeking to exploit currency mispricings is consistently profitable.

Electronic trading systems allow the three constituent trades in a triangular arbitrage transaction to be submitted very rapidly. However, there exists a delay between the identification of such an opportunity, the initiation of trades, and the arrival of trades to the party quoting the mispricing. Even though such delays are only milliseconds in duration, they are deemed significant.

For example, if a trader places each trade as a limit order to be filled only at the arbitrage price and a price moves due to market activity or new price is quoted by the third party, then the triangular transaction will not be completed.

In such a case, the arbitrageur will face a cost to close out the position that is equal to the change in price that eliminated the arbitrage condition.

In the foreign exchange market there are many market participants competing for each arbitrage opportunity; for arbitrage to be profitable a trader would need to identify and execute each arbitrage opportunity faster than competitors. Competing arbitrageurs are expected to persist in striving to increase their execution speed of trades by engaging in what some researchers describe as an "electronic trading 'arms race'.

Other factors such as transaction costs , brokerage fees, network access fees, and sophisticated electronic trading platforms further challenge the feasibility of significant arbitrage profits over prolonged periods. From Wikipedia, the free encyclopedia.

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