On the Moments of the Stochastic Discount Factor

Ian Martin and Ran Shi

No 21235, CEPR Discussion Papers from Centre for Economic Policy Research

Abstract: We derive new bounds on arbitrary moments of the stochastic discount factor (SDF) that exploit the gap between the true and risk-neutral return distributions. The bounds reveal that SDF moments appear to diverge before the second moment is reached, calling into question the assumption of finite variance that underlies mean-variance analysis. But variance bounds have poor properties even in population, so the question of whether the SDF has finite variance may be unanswerable. We propose alternative measures of SDF variability that are better behaved, supplying stable empirical measures of the attractiveness of investment opportunities and of market risk aversion.

JEL-codes: C58 G12 G13 (search for similar items in EconPapers)
Date: 2026-03
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