Supported by empirical examples, this paper provides a theoretical analysis on the impacts of using a suboptimal information set for the estimation of the empirical pricing kernel and, more in general, for the validity of the fundamental theorems of asset pricing. While inferring the risk-neutral measure from options data provides a naturally forward- looking estimate, extracting the real-world one from a stream of historical returns is only partially informative, thus suboptimal with respect to investors’ future beliefs.