You can make a hat into an umbrella but you cannot make an umbrella into a hat.
|Hussein Chalayan hat umbrella|
An umbrella can be cumbersome and hard to hold when you are carrying your shopping bags on a windy day, but a snuggly fitting hat will not blow off your head and allows you to use both hands for the task at hand.
People loose and yes, even steal umbrellas, but they seldom loose or steal hats!
Umbrellas break and blow inside out in gales but well fitting and well made hats last forever.
BUT umbrellas can also be fun and can be useful if you are "singing in the rain".
Check out this article from the New York Times.