Misspecified Recovery

Asset prices contain information about the probability distribution of future states and the stochastic discounting of these states. Without additional assumptions, probabilities and stochastic discounting cannot be separately identified. Ross (2013) introduced a set of assumptions that restrict the dynamics of the stochastic discount factor in a way that allows for the recovery of the underlying probabilities. We use decomposition results for stochastic discount factors from Hansen and Scheinkman (2009) to explain when this procedure leads to misspecified recovery. We also argue that the empirical evidence on asset prices indicates that the recovered measure would differ substantially from the actual probability distribution and that interpreting this measure as the true probability distribution may severely bias our inference about risk premia, investors' aversion to risk, and the welfare cost of economic fluctuations