Trading in currencies in the manner described is permissible, subject to the condition that the exchange be completed in the same sitting as the contract is made. It is permissible to sell riyals for euros, subject to the condition that the handover take place in the same sitting as the contract is made. It is also valid to exchange the euros for dollars after that, so long as the same condition is met. So the profit that is made from this transaction is permissible. The evidence for that is the words of the Prophet (peace and blessings of Allaah be upon him): “Gold for gold, silver for silver, wheat for wheat, barley for barley, dates for dates, salt for salt, like for like, hand to hand. If the types are different then sell however you like, so long as it is hand to hand.” Narrated by Muslim, 1587. 

It says in Fataawa al-Lajnah al-Daa’imah (13/458) 

In exchanges of currency it is essential that the exchange be completed in the same sitting as the contract is made. It is not permissible to hand over some straight away and delay some. It is proven that the Prophet (peace and blessings of Allaah be upon him) said: “If the types are different then sell however you like, so long as it is hand to hand.” End quote.