Misspecified Recovery
52 Pages Posted: 28 Jul 2015
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Misspecified Recovery
Misspecified Recovery
Misspecified Recovery
Misspecified Recovery
Date Written: July 16, 2015
Abstract
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. To understand this identification challenge, we extract a positive martingale component from the stochastic discount factor process using Perron-Frobenius theory. When this martingale is degenerate, probabilities that govern investor beliefs are recovered from the prices of Arrow securities. 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. Also empirical evidence on asset prices suggests that the recovered measure differs from the actual probability distribution. Even though this probability measure may fail to capture investor beliefs, we conclude that it is valuable as a tool for characterizing long-term risk pricing.
Keywords: Perron-Frobenius theory, recovery theorem, stochastic discount factor, martingale distribution, stochastic stability
JEL Classification: G00, G12, D84
Suggested Citation: Suggested Citation