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Traditional asset pricing tests boil down to evaluating the maximum Sharpe ratio obtained from the factors in a given model. This implicitly assumes the linear stochastic discount factor (SDF) that prices the factors as the asset pricing model. We generalize this approach by considering a comprehensive family of nonlinear SDFs pricing the model factors. The relevant metric for model comparison becomes the maximum Sharpe ratio of the mimicking portfolio constructed by projecting the nonlinear SDF onto the test assets. We show that nonlinearities matter empirically for both the absolute and relative pricing performance of leading factor models.