Where does your authority come from? Is it from your senior title, your strict manner, your sharp dress, your corner office, your first class travel arrangements? Do you find yourself rejecting demeaning work or unworthy tasks because they will dent your authority?
Or does your authority come from within, from your beliefs and values, from you actions and your word?
Both are valid but the former is a weaker form of authority because it is dependant on envionmental paramaters outside of your control. The latter is intrinsic, stronger and will withstand changes to the environment.
You should aim to be big enough to perform all manners of menial tasks without losing your authority.