When Do Cross-Sectional Asset Pricing Factors Span the Stochastic Discount Factor?

Serhiy Kozak and Stefan Nagel

No 31275, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: When expected returns are linear in asset characteristics, the stochastic discount factor (SDF) that prices individual stocks can be represented as a factor model with GLS cross-sectional regression slope factors. Factors constructed heuristically by aggregating individual stocks into characteristics-based factor portfolios using sorting, characteristics-weighting, or OLS cross-sectional regression slopes do not span this SDF unless the covariance matrix of stock returns has a specific structure. These conditions are more likely satisfied when researchers use large numbers of characteristics simultaneously. Methods to hedge unpriced components of heuristic factor returns allow partial relaxation of these conditions. We also show the conditions that must hold for dimension reduction to a number of factors smaller than the number of characteristics to be possible without having to invert a large covariance matrix. Under these conditions, instrumented and projected principal components analysis methods can be implemented as simple PCA on characteristics-based portfolios.

JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2023-05
New Economics Papers: this item is included in nep-mfd
Note: AP
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.nber.org/papers/w31275.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberwo:31275

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/w31275

Access Statistics for this paper

More papers in NBER Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().