Question

you notice the following quotes: GBP/US dollar = GBP 0.69/US AUD/US dollar = 1.8215/US AUD/GBP = 2.6413/GBP. Ignoring transaction costs, do you have na arbitrage opportunity based on those quotes. If so, what steps would be needed and how much profit if you had 2 million avaliable?

Answer 1

There is no arbitrage opportunity in the given currency exchange quotes; attempting the conversion cycle with GBP 2 million would result in a loss rather than a profit.

Step-by-step explanation:

The student asked if there is an arbitrage opportunity based on the provided currency exchange quotes. The quotes are GBP/USD = 0.69, AUD/USD = 1.8215, and AUD/GBP = 2.6413. To identify a potential arbitrage, we need to check if the product of multiplying these rates differs from 1 after converting currencies in a loop (GBP -> USD -> AUD -> GBP).

If we start with GBP 1 million, at the given GBP/USD rate, we would get USD 1.4493 million (since 1/0.69 = 1.4493). Changing USD to AUD at the AUD/USD rate gives us AUD 0.8188 million (1.4493/1.8215). Finally, converting AUD back to GBP at the AUD/GBP rate results in GBP 0.3097 million (0.8188/2.6413). As GBP 0.3097 million is less than the starting GBP 1 million, there is no arbitrage opportunity; you would incur a loss.

Therefore, with GBP 2 million available, no arbitrage profit could be made, and in fact, a significant loss would occur if this cycle were attempted.