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Financial Economics and Econometrics

In a recent seminal paper, Steve Ross proposed an attractive strategy to extract the physical distribution and risk aversion from just state prices. However, empirical papers that try to use his Recovery Theorem almost all lead to a depressing conclusion: the recovery theorem does not work. Both the state-price matrix and the recovered physical transition matrix are unreasonable and highly sensitive to subjective speciﬁcations and constraints. Borovička, Hansen and Scheinkman (2016) proposes a widely-accepted explanation for the empirical failure: according to the Hansen-Scheinkman decomposition established in Hansen and Scheinkman (2009), the assumption about the stochastic discount factor in Ross (2015) is equivalent to arbitrarily setting the martingale component to be 1, which is quite unlikely in reality. In Chapter 1, I argue that in contrast to Borovička, Hansen and Scheinkman (2016), the assumption about the stochastic discount factor in Ross (2015) actually does not set the martingale component in the Hansen-Scheinkman decomposition to be 1. What causes the empirical failure is actually a time-homogeneous state-price matrix, which induces quite restrictive implications on the underlying price process and those restrictions are easily violated in reality. In particular, when the underlying price is used as the state variable or as one component of the state vector, this restriction becomes an eigenvalue equation that contradicts the important eigenvalue equation in Ross (2015), which in this case makes the Recovery Theorem not just empirically implausible, but also logically inconsistent.