Before revision:   When the martingale component is not trivial, using this same approach recovers a probability measure, but not the one that is used by investors. We refer to this outcome as "misspecified recovery." We show that the resulting misspecified probability measure absorbs long-term risk adjustments. Many structural models of asset prices have stochastic discount factors with martingale components.
After revision:  When the martingale is not degenerate, surmising that this recovered probability captures investors' beliefs distorts inference about risk-return tradeoffs. Stochastic discount factors in many structural models of asset prices have stochastic discount factors with martingale components.