Umbrellas and pace sticks - any drill teachers here?

Teachers of drill, how do you swing your umbrellas? Do you swing it directly forwards or in a semi-circular fashion, like a pace-stick?

The other day I was about and saw someone swinging his umbrella in a semi-circular fashion and I was instantly reminded of a drill NCO measuring pace with a pace stick. I didn’t manage an opportunity to ask, so I ask here.