What it means
The principle is the "law of one price": the same thing should cost the same everywhere. If one bank quotes a currency a little differently from another, or if three related exchange rates do not line up mathematically, a trader can buy cheap and sell dear in quick succession and keep the difference.
Triangular arbitrage uses three currencies, for example the dollar, euro and pound. If the euro-to-pound rate quoted directly does not match the rate implied by the euro-dollar and pound-dollar quotes, trading around the triangle returns more dollars than you started with.
Locational arbitrage is simpler. It involves buying a currency from a dealer quoting a low price and selling it to another dealer quoting a higher one at the same moment.
In practice, opportunities are small and short-lived. Automated systems scan quotes thousands of times a second, and as soon as a gap appears, the trades push prices back into line.
Costs and speed decide whether any gap is worth chasing. Spreads, commissions and the delay between placing each leg of the trade can wipe out the profit, so only firms with fast technology and tight costs benefit.
For a corporate finance team, the lesson is that large, lasting mispricings are rare and any quote that looks too good should be checked. Banks' quoted cross rates are normally consistent, so the main use of the concept is to understand why rates stay aligned.
In practice
Real-world examples.
Example
A proprietary trading firm's software detects that a bank's EUR/GBP quote is out of line with the EUR/USD and GBP/USD quotes. It executes three trades in a few milliseconds and locks in a profit of a fraction of a cent per euro. Repeated thousands of times in size, those fractions add up, but only if the costs are tiny.
Example
A currency dealer in Hong Kong quotes a slightly higher price for US dollars than a dealer in London at the same moment. A fast trader buys from the cheaper dealer and sells to the dearer one. The gap closes within seconds as other traders spot the same difference.
Example
A company's treasurer receives two quotes for a large euro purchase and finds they differ by 0.15%. She does not call it arbitrage, since she cannot resell at the higher price, but she uses the gap to negotiate a better deal. The cheaper bank wins the order, and she records the saving against her budget.
Formula
Calculation
Implied cross rate EUR/GBP = EUR/USD / GBP/USD
Profit = final amount - starting amount, before costs
Suppose EUR/USD is 1.2000 and GBP/USD is 1.5000, so the implied EUR/GBP rate is 1.2000 / 1.5000 = 0.8000. A bank quotes EUR/GBP directly at 0.8100, which means one euro buys 0.8100 pounds, more than the implied 0.8000.
Start with $1,200,000 and buy euros at 1.2000: 1,200,000 / 1.2000 = 1,000,000 euros. Sell the euros for pounds at 0.8100: 1,000,000 x 0.8100 = 810,000 pounds. Sell the pounds for dollars at 1.5000: 810,000 x 1.5000 = $1,215,000. The profit is 1,215,000 - 1,200,000 = $15,000 before costs, a return of 1.25%.Case study
Seen in the real world.
Quickstep Markets is an illustrative, fictional trading firm that built an automated system to look for triangular arbitrage. In testing, the system found hundreds of apparent opportunities a day, each worth only a few dollars on paper.
When the firm included spreads, commissions and the delay in the second and third trades, most of the gaps disappeared. A handful remained profitable, but only when trades were made in large size with the fastest connections.
The illustrative lesson is that paper profits can be an illusion. The firm concentrated on the few real opportunities and invested in lower latency, since speed and costs were the true edge. The firm also set strict limits on how long any one leg could stay open, because a delay turned a small profit into a loss.
Watch out
Common mistakes.
- Ignoring transaction costs, when spreads and fees can easily exceed the tiny profit from a price gap.
- Assuming arbitrage is risk-free in practice, when a price can move between the first and last leg of the trade.
- Believing retail traders can compete with automated firms on speed, when the gaps usually close before a manual order is placed.
Questions
People also ask.
Is forex arbitrage legal?
Yes, it is a legitimate trading strategy, though brokers may restrict accounts that exploit stale prices from their own platform. Check the broker's terms before relying on any such strategy.
What is triangular arbitrage?
It is a trade that goes through three currencies in a loop, such as dollars to euros to pounds and back to dollars, to profit from inconsistent quotes.
Why do arbitrage opportunities disappear so fast?
Because many traders and algorithms look for them at the same time, and their buying and selling quickly pushes the quotes back into line. In effect, the act of exploiting a mispricing is what removes it.
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