A show reel for a make up artist seems to be the norm these days, instead of just a physical portfolio, they are utilising other types of media.
Videos have their qualities, where you can see the artist in action and it gives you the chance to add a little personality along the way. The music you choose, the font, the editing and the content you choose, will define you as a make up artist. It can be both a benefit and a hinderance, as the viewer may not enjoy your video.
I am going to have a go at doing my showreel representing myself as a graduate make up artist :) look out on my youtube channel for this one.
My YouTube Channel