The EUR/USD and GBP/USD rates imply that the arbitrage free cross rates for the EUR/GBP are:
bid = €1.000/₤2.0100 = €0.4975
ask = €1.0015/₤2.0000 = €0.5008
Since the cross rates given (€0.3985 − €0.4000) are outside of the arbitrage-free cross rates, profitable arbitrage is available.
It takes too few euros to buy 1 pound, so we want our arbitrage trades to go in the direction that will cause us to sell overvalued euros for pounds at the ask rate of €0.4000.
Start with $1,000.
Use the $1,000 to buy euros ($1,000 × €1.000/$) = €1,000.
Use the €1,000 to buy sterling (€1,000 / €0.4000/₤) = ₤2,500.
Use the ₤2,500 to buy dollars (₤2,500 / ₤2.0100/$) = $1,243.78.
(Study Session 4, LOS 14.b)
