  We consider a new framework of predictable relative forward performance
processes (PRFPP) to study portfolio management within a competitive
environment. Each agent trades a distinct stock following a binomial
distribution with probabilities for a positive return depending on the market
regime characterized by a binomial common noise. For both the finite population
and mean field games, we construct and analyse PRFPPs for initial data of the
CARA class along with the associated equilibrium strategies. We find that
relative performance concerns do not necessarily lead to more investment in the
risky asset. Under some parameter constellations, agents short a stock with
positive expected excess return.
