Another triangular FX arbitrage to spot

Question

Three spot FX rates (ignore bid-ask spreads for now):

EUR/USD $= 1.10$ (dollars per euro)
GBP/USD $= 1.25$ (dollars per pound)
EUR/GBP $= 0.80$ (pounds per euro)

Is there an arbitrage? If so, give the exact sequence of trades and the profit per $1.25M of capital.

Accepted Answer

The no-arbitrage (implied) cross rate is 	ext{EUR/GBP}{	ext{implied}} = \frac{	ext{EUR/USD}}{	ext{GBP/USD}} = \frac{1.10}{1.25} = 0.88 	ext{ pounds per euro}. The market quotes only 0.80, so the euro is too cheap in pound terms. Buy euros with pounds at the cheap cross, then unwind through dollars. Starting with \1{,}250{,}000: 1. Buy GBP with USD at 1.25: receive £1{,}000{,}000. 2. Buy EUR with GBP at 0.80: receive €	frac{1{,}000{,}000}{0.80} = €1{,}250{,}000. 3. Sell EUR for USD at 1.10: receive €1{,}250{,}000 	imes 1.10 = \1{,}375{,}000. Riskless profit: \125{,}000, exactly 10\%, ex…

Another triangular FX arbitrage to spot

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