I too was one of those unhealthy looking, overworked bankers. I was promoted at a young age and had a lot to prove, so I overdid it for a year or two. Then I understood the secret the other MDs had known for years - you just have to look busy, not actually be busy!
When I was working construction many years ago there was an urban legend about a guy that always looked busy running around with some tools, but no one ever saw him actually working. Turned out he used to find himself a hidden spot at the site and sleep there most of the day. Just making sure to walk across the site with tools once in a while.