Advice for a disgruntled graduate trainee

I've been working at this international bank for almost two years now in what is perceived to be one of the most prestigious graduate programmes around. The problem I have is that I have been pretty much treated like a temp worker in almost every department I've been posted to. I'm usually given very little responsibility and ownership on projects / tasks that don't have much material impact. The label graduate trainee is in name only and this is certainly not what I have signed up for. The only good thing about the programme is that I get lots of classroom training; though I would rather manage a proper project than to listen to someone talk about how to manage a project. I now have one more year until I "graduate" from the programme and I'm torn between taking up a real job somewhere else (within the bank or not) - where I would be given real responsibility and ownership and concrete targets - or sticking it out so I could earn that guaranteed promotion and pay increase. My question is, should I have a honest chat with my programme manager about this and tell him what I think? What would be the "HR reaction" if someone like me came to you with such a problem? Is it realistic to expect HR to explore solutions for a junior manager like myself?