Psychology class

Today I learned about dreams about death in psychology class, and I have a dream where I'm being chased and eventually killed in an attic. Its a reoccurring dream that I've had at both points of view, the killed and the killer. No matter what P.O.V. is I'm always being killed (so sometimes I'm killing myself as a different person.) 
So I wonder if it means that I'm my own worst enemy? or something worse. It never scared me, I always felt calm in the dream, but I wonder if I shouldn't be. Then again it might just be something completely stupid, of that I wouldn't be surprised.