Triangular consistency: EURUSD, USDJPY, EURJPY

[Shadow Trader]

Three pairs are linked by arithmetic: EURUSD times USDJPY should equal EURJPY. In theory, the relationship holds at all times, otherwise someone is arbitraging it away in milliseconds.

In practice, the pairs update at slightly different speeds. EURUSD and USDJPY, being the most liquid, lead. EURJPY, a cross, follows a fraction of a second later, because its price is derived or traded in smaller volume.

That lag creates tiny moments where the cross is out of line. Retail feeds show them. The gap is rarely more than a pip, and executing on it is impossible for most accounts, because the broker's cross price is built from the same legs anyway.

But the relationship is useful in a different way. When EURJPY moves and neither EURUSD nor USDJPY did, something odd is happening, such as a thin-market spike. When the legs move together and the cross hasn't, the cross is about to move.

Using the legs as a leading signal for the cross is more realistic than trying to arbitrage them.

Can the leg-lead on crosses like EURJPY or GBPJPY be turned into entries, or is it too small after costs?