Misspecified Recovery

52 Pages Posted: 28 Jul 2015

See all articles by Jaroslav Borovička

Jaroslav Borovička

New York University (NYU) - Department of Economics; National Bureau of Economic Research (NBER)

Lars Peter Hansen

University of Chicago - Department of Economics; National Bureau of Economic Research (NBER)

José A. Scheinkman

Columbia University; Princeton University - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 4 versions of this paper

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

Borovička, Jaroslav and Hansen, Lars Peter and Scheinkman, José, Misspecified Recovery (July 16, 2015). Available at SSRN: https://ssrn.com/abstract=2636416 or http://dx.doi.org/10.2139/ssrn.2636416

Jaroslav Borovička (Contact Author)

New York University (NYU) - Department of Economics ( email )

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Lars Peter Hansen

University of Chicago - Department of Economics ( email )

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José Scheinkman

Columbia University ( email )

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Princeton University - Department of Economics ( email )

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