52 Pages Posted: 25 May 2014 Last revised: 22 Apr 2019
Date Written: October 1, 2015
Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk-adjusted discounting, we use Perron-Frobenius Theory to isolate a positive martingale component of the stochastic discount factor process. This component recovers a probability measure that absorbs long-term risk adjustments. 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 empirically relevant martingale components.
Keywords: Perron-Frobenius theory, recovery theorem, stochastic discount factor, martingale decomposition, stochastic stability
JEL Classification: G00, G12, D84
Suggested Citation: Suggested Citation