A Protocol for Factor Identification
47 Pages Posted: 5 Nov 2014
Date Written: November 1, 2014
Several hundred factor candidates have been suggested in the finance literature. We propose a protocol for determining which factor candidates are related to risks and which candidates are related to mean returns. Factor candidates could be related to both risk and returns, to neither, or to one but not the other.
A characteristic such as firm size, or anything else known in advance, cannot be a factor. However, characteristics can be related to mean returns either because they happen to align with factor loadings or because they represent arbitrage opportunities. Pervasive factors with accompanying risk premium should be related to the covariances among returns on assets held in the aggregate market portfolio.
Time variation in both risk premiums and covariances is a challenge, but manageable with recently developed statistical procedures. We illustrate those techniques and also propose a new instrumental variables method to resolve the errors-in-variables problem in estimating factor exposures (betas) for individual assets.
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