The Efficiency vs. Pricing Accuracy Trade-Off in GMM Estimation of Multifactor Linear Asset Pricing Models

Even though a multifactor linear asset pricing model can be written equivalently in Beta or Stochastic Discount Factor (SDF) form, the two representations need not deliver the same inferential properties when estimated by the generalized method of moments (GMM). Using a multifactor linear asset pricing model, we combine bootstrapped simulations with analytical approximations to compare the sampling variances of GMM estimators under the two equivalent representations. We find that the SDF approach is generally less efficient–i.e., yields higher variance estimators–but provides more accurate pricing than the Beta method. We show that the primary source of this trade-off lies in the higher-order moments of the factors, which shape identification differently across the two representations. Notably, in out-of-sample portfolio applications, the efficiency gains of Beta-GMM in estimating risk premia outweigh the pricing-accuracy benefits of SDF-GMM, leading to higher Sharpe ratios for Beta-based trading strategies.