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.
Evidence for triangular arbitrage
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. In observations of triangular arbitrage, the constituent exchange rates have exhibited strong correlation. A study examining exchange rate data provided by HSBC Bank for the Japanese yen (JPY) and the Swiss franc (CHF) found that although a limited number of arbitrage opportunities appeared to exist for as many as 100 seconds, 95% of them lasted for 5 seconds or less, and 60% lasted for 1 second or less. Further, most arbitrage opportunities were found to have small magnitudes, with 94% of JPY and CHF opportunities existing at a difference of 1 basis point, which translates into a potential arbitrage profit of $100 USD per $1 million USD transacted.
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 01:00 and 10:00 UTC, contrasted with a greater number of opportunities and short average duration around 13:00 and 16:00 UTC. 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 00:00 and 10:00 UTC, for Europe around 07:00 and 17:00 UTC, and for America around 13:00 and 23:00 UTC. The overall foreign exchange market is most liquid around 08:00 and 16:00 UTC, and the least liquid around 22:00 and 01:00 UTC. 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 2003 to 2005 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. 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’.” The costs involved in keeping ahead in such a competition present difficulty in consistently beating other arbitrageurs over the long term. 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.
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Ofer Abarbanel is a 25 year securities lending broker and expert who has advised many Israeli regulators, among them the Israel Tax Authority, with respect to stock loans, repurchase agreements and credit derivatives. Founder of TBIL.co STATX Fund.