Question

Peter Sheffield has Euros (€) amounting to €500,000 and is provided with the following quotes:

        Bank A: Euro/US dollar = €0.8518/$

        Bank A: British pound /US dollar = £0.7548/$

        Bank B: British pound/Euro = £0.8863/€

Determine whether an arbitrage opportunity exists. Show your calculation in the space below and briefly explain (in one or two sentences) why the arbitrage opportunity exists or not.

For example, show your calculation as follows (The currencies used in the example are not applicable to your calculation. It just provide you with information of how you should show your calculation):

Yen/ZAR   = 11.7654/1.3954 = 8.4316

Reason why arbitrage opportunity exists/ does not exist:.........................................................................

Answer 1

        Bank A: Euro/US dollar = €0.8518/$

        Bank A: British pound /US dollar = £0.7548/$

        Bank B: British pound/Euro = £0.8863/€

Basis above mentioned conversion rates, below will be the value on each conversion

Currency pair	Conversion rates	Value post conversion	Remarks
British Pound/Euro	0.8863	£                4,43,150.00	Value post converting 5,00,000 Euro into Pounds
British Pound/US dollar	0.7548	$                5,87,109.17	Value post converting Pounds into USD
Euro/US dollar	0.8518	€                5,00,099.59	Value post converting USD into Euros

Hence arbitrage opportunity exists since there is difference between the original currency value and value post conversion

Second way to look whether arbitrage opportunity exists or not is cross-rate formule i.e.  £/$= £/€ * €/$ which is 0.8863*0.8518 = 0.75495 which is higher than 0.7548 hence the above mentioned £/$ is undervalued so arbitrage opportunity exists