A bit of both. The market is white hot right now, so there's a better than usual chance of getting something. Of course there's still a lot of applicants so it's useful to have the right degree.

The thing to do is talk to headhunter firms. I've always maintained a number of relationships with the leading firms in my area (quant trading) and they'll call now and again. But if you don't know them, get in touch and they'll usually tell you if you're useful to them.