Working Paper: NBER ID: w31275
Authors: Serhiy Kozak; Stefan Nagel
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.
Keywords: No keywords provided
JEL Codes: G11; G12
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| stochastic discount factor (SDF) (D15) | expected returns (G17) |
| asset characteristics (H82) | expected returns (G17) |
| covariance matrix of stock returns (C10) | heuristic factor models (C38) |
| systematic risk sources (P34) | heuristic methods (C60) |
| hedged factors (G41) | stochastic discount factor (SDF) (D15) |
| dimension reduction methods (C38) | stochastic discount factor (SDF) (D15) |