Even though a multifactor linear asset pricing model can be equivalently represented in a Beta or in a stochastic discount factor (SDF) form, its inferential efficiency and pricing accuracy features may differ when estimated by the generalized method of moments (GMM), both in small and in large samples. Using a multifactor linear asset pricing model, we use bootstrapped simulations and analytical approximations to compare and test the estimated variances of the GMM estimators of parameters under the equivalent Beta vs. the SDF representations. We find that the SDF approach is likely to be less efficient but to yield more accurate pricing than the Beta method. We show that the main drivers of this trade-off are the higher-order moments of the factors that play an important role in the estimation process, and that the increased efficiency of the out-of-sample Beta risk premia estimation dominates the SDF increased pricing accuracy. The increased efficiency yielded by the Beta representation risk premia estimation in small samples translates into an increase of the out-of-sample Sharpe ration in a trading exercise.
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