An advanced degree in finance/economics/mathematics, an MBA, a CFA...these are all reasonable paths to a career in portfolio management. An MFE works too, especially if you are interested in more actively managed funds. But as Alain noted, there aren't many openings for PM's without experience, but that experience can vary. For example, I have seen people move from ops to portfolio management after passing the CFA; I have seen financial developers become PM's after building a track record of successful, analytical systems; even people with experience working for data vendors.
Here are a couple examples of what I have seen in terms of landing a PM role:
1. Working as an Analyst for a PM provides a path to becoming a PM down the road. I would say you usually need a quantitative master's and some strong grounding in finance to have a good shot at being an Analyst for a PM.
2. If you are someone that has strategies with verifiable results, then you could be looking at PM roles. It really helps if you are soup to nuts, meaning you have strategies (and are able to come up with new ones), you have implemented them and executed them in the past. Someone like that would be in great demand.
As an example, one of our clients who's a fund incubator (meaning they are providing the infrastructure and capital to enable individuals to start funds) is looking for someone that fits #2 above. So someone like that would come in, run the fund and once it grows to a certain size, they can spin-off into an independent hedge fund. Very appealing indeed if you have the right skills to pull it off.