Question

Market	Quotation	FX Rate
Zurich	EUR / GBP	0.8832
Chicago	GBP / USD	1.2649
London	EUR / USD	1.1158

1. Is there an arbitrage opportunity? (ignore transactions costs and taxes)
2. If there is an arbitrage opportunity, calculate the profit for 1,000,000 EUR and show all the transactions carried at each market.

Answer 1

(a) Check whether arbitrage opportunity exist or not.

We find out the EUR/USD

EUR/USD = EUR/GBP x GBP/USD = 0.8832 x 1.2649 = 1.11715968 or say 1.1172

but in london market EUR/USD quoted at 1.1158 means rate are not same so arbitrage opportunity exist.

(b) Calculation of arbitrage profit

Arbitrager have 1,000,000 EUR

(1) Zurich Market

so in Zurich market arbitrager buy the GBP at spot rate i.e.0.8832

Arbitrager received GBP = 1,000,000 EURO x 0.8832 = 883,200 GBP

(2) Chicago Market

Arbitrager have GBP so arbitrager buy USD against GBP @1.2649

Arbitrager received USD = 883,200 GBP x 1.2649 = 1,117,159.68 USD

(3) London Market

Now arbitrager convert USD to Euro @ rate EURO/USD = 1.1158

Arbitrager received EURO = 1,117,159.68 USD / 1.1158 = 1,001,218.57 EURO

Arbitrage Profit = 1,001,218.57 EURO - 1,000,000 EURO = 1,218.57 EURO