We characterize when physical probabilities, marginal utilities, and the discount rate can be recovered from observed state prices for several future time periods. We make no assumptions of the probability distribution, thus generalizing the time-homogeneous stationary model of Ross (2015). Recovery is feasible when the number of maturities with observable prices is higher than the number of states of the economy (or the number of parameters characterizing the pricing kernel). When recovery is feasible, our model allows a closed-form linearized solution. We implement our model empirically, testing the predictive power of the recovered expected return and other recovered statistics.

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