assume you are a bank and have a german exporter who exports to london and would like to sell pounds against Euros. The following market rates prevail:
If your customer wants a cross rate for pound in Euro terms for you, what rate will you quote assuming you want a spread of 0.0020 on the quote.
Shortly in order to exchange pounds into euro a bank has to do two operations,-exchange pounds into dollars and& exchange dollars into euro. Consider this process in details. Let us suppose that exporter exchanges pounds into euro. In this case he must change firstly pounds into dollars. According to the rate of the exchange for 1Pound he gets 1.5209 $. & After this he exchanges this sum of& dollars& into euro. According to the rate for this money he gets 1.5209:1.3266=1.1465 Euro . Consider now the back actions. Exporter has 1Euro and wants to exchange it into pounds. Firstly he exchanges it& into& dollars and according to the rate he& gets 1.3265 $ .After this he exchanges dollars into pounds and according to the rate he receives 1.3265:1.5212=0.8720 Pounds. For getting 1Pound he must pay 1/0.8720=1.1468Euro. So, in this situation the cross rate Pound/Euro of the bank is& equal to 1.1465/1.1468 . Inversing the numbers one can get the cross rate Euro/Pound& 0.8720/0.8722. Thus, a spread equal 0.0020 can not be justified yet.
Answer: Pound/Euro 1.1465/68 or Euro/Pound& 0.8720/22.