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Profit From a Triangular Mispricing, and What Costs Do to It

Quotes: EUR/USD is 1.1000. GBP/USD is 1.2500. EUR/GBP is quoted at 0.8850. The implied EUR/GBP is 1.1000 divided by 1.2500, which is 0.8800. Is there an arbitrage?

Trace the loop starting with 1,000,000 euros. Sell euros for pounds at 0.8850: you receive 885,000 pounds. Sell pounds for dollars at 1.2500: you receive 1,106,250 dollars. Buy euros with dollars at 1.1000: you receive 1,106,250 divided by 1.1000, which is 1,005,682 euros.

Profit: 5,682 euros, about 0.57 percent, in seconds, with no market risk if all three trades execute at the quoted prices.

Now costs. Suppose each leg has a half-pip spread cost on average. Three legs cost roughly 1.5 pips in total, which is about 0.014 percent, or 140 euros on 1 million. The profit exceeds it by a wide margin in this example.

In reality, prices never sit 50 pips off for long. Algorithms scan for such gaps continuously, and mismatches of even a pip or two vanish within milliseconds. A discrepancy of 50 pips would be an error or a stale quote, and the broker would likely cancel the trades.

For a retail trader, this exercise has two uses. It shows how cross rates are tied to the dollar pairs. And it warns that apparent mispricings on your platform may not be tradable.

If you ever see one, check whether the quotes are live and whether your platform delays execution.

Your turn: compute implied cross rates for three pairs and compare with the direct quotes.

Good worked example, with the caveat that a 50-pip gap between quoted and implied EUR/GBP would not survive for more than a moment at a real dealer. Market makers price the crosses from the two dollar legs, so the gaps we actually see in retail feeds are a fraction of a pip and usually come from one leg updating a few milliseconds late.

At that size, the spread on three legs is more than the gap. And if one leg fills late, you're left with an open position, not an arbitrage. That's why retail triangular arbitrage EAs mostly end up trading latency against the broker, which most dealing terms prohibit.

The arithmetic shows how cross rates are tied together. EUR/GBP must equal EUR/USD divided by GBP/USD, or there's a risk free profit available. At 0.8850 against an implied 0.8800, the gap is 50 pips, which is enormous by market standards. In practice, banks and high frequency trading firms run systems that detect discrepancies of a fraction of a pip and close them in milliseconds. So a 50 pip gap on a retail platform would almost certainly be a pricing error, a stale quote, or a feed problem, rather than a real opportunity available to anyone. Treating any large gap as a data problem first is the safer default.

I went looking for triangular gaps on a demo feed one weekend, partly out of curiosity and partly because I had read the same kind of example. Over about three hours on EURUSD, GBPUSD and EURGBP I logged every moment where the implied cross differed from the quoted one by more than the combined spread. It happened a handful of times, the biggest gap was under a pip, and every one of them closed before I could click anything.

What I took from it is that the spread on three legs is the real wall. On my account the total round trip across the three pairs cost more than any gap I recorded, so even a perfect fill would have been a small loss. The few times I tried it on a live micro lot, one leg filled a moment later at a worse price and I was holding a plain directional position, which is exactly the risk the example says is absent.

The part I still use is the check itself. If a cross looks strange compared with the two dollar pairs, I assume the feed is stale and I stay out until the quote catches up.

The point about brokers cancelling trades is worth emphasising. Most client agreements include clauses allowing the broker to void or adjust trades executed at prices that were clearly erroneous or outside the market. A retail trader who exploits a stale quote may find the profits reversed, and repeated attempts can lead to account restrictions. Some traders have tried latency arbitrage, exploiting slow price feeds, and brokers actively detect and block it. So even when a mispricing appears tradable, it's rarely a sustainable source of profit for retail traders. The time is better spent on a strategy with a real, repeatable edge.

The educational value is in understanding how crosses relate to the dollar pairs. When EUR/USD rises and GBP/USD stays flat, EUR/GBP must rise too. When both rise by the same percentage, EUR/GBP stays flat. That helps when analysing cross moves: a strong EUR/GBP move can be decomposed into what the euro and the pound each did against the dollar. It also explains why trading a cross alongside its two dollar legs can create overlapping exposure, since the positions are linked by this arithmetic relationship. A long EUR/GBP plus a long GBP/USD is, in effect, close to a long EUR/USD.