We report the magnetic response of composites formed by dispersing Fe nanoparticles in a polymer. Transmission electron microscopy reveals the formation of chain-like entities of nanoparticles. The magnetic response (hysteresis, remanence ratio, exchange bias, etc.) is in general nonmonotonic as a function of the particle concentration in the composites. The coercivity and remanence go through a maximum, while the exchange bias and magnetic relaxation rates go through a minimum, with increasing concentration. The effects are interpreted as being a consequence of a competition between an increasing anisotropy due to the formation of the chain-like entities that tends to increase the remanence, etc., and the weakening of these effects at higher concentrations due to the interactions between these entities.