Does holding your breath under water improve your stamina?

Just speaking from personal experience, yes. I heard about this from a friend, so I decided to try it. After only a few weeks and a lot of practice, I've been able to work up to over a few minutes underwater without taking a breath, and noticed that it has definitely improved my stamina when working out, running, etc... I can do that "extra few" push ups, and run that extra lap now.

My educated guess is that is has something to do with increasing oxygen levels in the blood - the more 02 in the blood, the more stamina, and the longer you can hold your breath.