Misspecified Recovery

TL;DR

This paper uses Perron-Frobenius Theory to isolate a key component of the stochastic discount factor, revealing challenges in accurately inferring investors' beliefs from asset prices due to long-term risk adjustments.

Contribution

It introduces a method to extract a probability measure from the stochastic discount factor that accounts for long-term risks, highlighting potential misinterpretations in belief inference.

Findings

The recovered probability measure absorbs long-term risk adjustments.

Misinterpreting the martingale component can distort risk-return analysis.

Many asset price models include empirically relevant martingale components.

Abstract

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.