Why does Gandalf have the third elf ring?

[Hot, crispy nice hobbit]

Talking of Rings on Wizards, Saruman had a Ring too!

'But I rode to the foot of Orthanc, and came to the stair of Saruman; and there he met me and led me up to his high chamber. He wore a ring on his finger.

This ring that Saruman wore is obviously of his own manufacture, for he boasted of it to Gandalf:

For I am Saruman the Wise, Saruman Ring-maker, Saruman of Many Colours!

Did Saruman know that Narya was with Gandalf all the while? I don't think so... Yet, is it not significant: that two wizards should have Rings on their fingers, the weaker one blatantly flaunting his power while the stronger concealed his.

P.S. What did Saruman made his own Ring for? Decoration? My, men are becoming more vain each day...