When the FX triangle looks off but is not tradable

Question

You watch three rates: - EUR/USD = 1.10 (dollars per euro) - USD/JPY = 150 (yen per dollar) - EUR/JPY = 165.10 (yen per euro), quoted in the market Each of the three pairs trades with a round-trip spread of about 3 basis points (0.03\%). Is this a tradable arbitrage?

Accepted Answer

The implied EUR/JPY comes from chaining the units (dollars per euro times yen per dollar equals yen per euro): 	ext{EUR/JPY}{	ext{implied}} = 	ext{EUR/USD} 	imes 	ext{USD/JPY} = 1.10 	imes 150 = 165.00. The market quotes 165.10, a deviation of \frac{165.10 - 165.00}{165.00} \approx 0.0006 = 6 	ext{ basis points}. So the euro looks about 6 bps expensive in yen. In frictionless terms that is an arbitrage. But executing it means crossing all three pairs, and each round-trip costs about 3 bps: 	ext{total cost} \approx 3 + 3 + 3 = 9 	ext{ basis points}. The edge (6 bps) is smaller than th…

When the FX triangle looks off but is not tradable

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