Portia's Disguise in Merchant of Venice

I chose this clip because the disguises used by Shakespeare in his plays has intrigued me all semester. After looking back on The Merchant of Venice I had completely forgot that Portia's disguise even fooled her husband. Because of this I wanted to see how a movie would visually represent this. My question is one that I don't have an answer to but hopefully others may: What effect and what measures were taken by Shakespeare to disguise his actors? Was it merely a hat and fake mustache relying on the audiences interpretation or were the disguises more elaborate leaving less to the audience's imagination?

http://www.youtube.com/watch?v=UOji4H3Jgfw