ABSTRACTWe characterize the sets of mimicking positions with returns that can serve in place of factors in an exactK‐factor arbitrage‐pricing relation for a set ofNassets. All of the sets areK‐dimensional nonsingular linear transformations of each other. We interpret three examples of such transformations and discuss empirical considerations. We provide conditions under which the mimicking positions can be expressed as portfolios, and we characterize the relation between mimicking portfolios and the minimum‐variance f