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Fama–French Three-Factor Pricing and the Equity Risk Premium

Article Quant Q&A · Author: max
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Summary

The document discusses the equity risk premium as an expected return on the market factor and examines how its estimate behaves in CAPM and Fama–French three-factor asset-pricing tests. It cites a conservative US equity premium estimate of 3–4% and argues that an estimated market premium should be evaluated in light of statistical uncertainty.

The account describes Fama and French’s argument that adding size and value factors improves on a single-factor CAPM: in the cited cross-sectional analysis, the CAPM market-premium estimate is near zero, while including SMB makes it substantially negative. The document raises a methodological challenge: if the negative estimate is evidence against CAPM, it may also cast doubt on the three-factor model. It poses this as a question rather than resolving it, and offers no underlying data or further statistical analysis, so its claims should be read as a summary of a debate rather than a definitive model assessment.

Key ideas

  • The document gives a conservative estimate of the US equity risk premium and emphasizes estimation uncertainty.
  • The Fama–French model adds size and value factors to the market factor.
  • The cited discussion reports that adding SMB shifts the estimated market premium downward.
  • A negative market premium estimate raises a challenge for interpreting the three-factor model, but the document does not resolve it.

Tags

EquitiesFactor investingStatisticsUS markets
Full text
# ERP and FF 3-factor model


# ERP and FF 3-factor model












In a more conservative estimate than a simple historical average, Fama & French estimate (US) equity risk premium at 3-4% (e.g., Equity Risk Premium, JF, 2002).

This suggests that in an APT-like asset pricing test, the estimate of the risk premium on the market factor should be within an estimation error of that range (since the market portfolio has loading of 1 on the market factor and zero on all others).

In their "Cross-Section of Expected Returns" (JF 1992) paper, Fama & French argue that the assets should be priced using a 3-factor APT model (with Market, HML, SMB) rather than CAPM. Their main argument is that in a single-factor cross-sectional regression, the market risk premium estimate is too close to zero (though, given the large estimation error, it's actually within a confidence interval from the 3% per annum).

However, when they add SMB beta to the the cross-sectional regression, the market risk premium estimate becomes quite negative (this time it is too low even allowing for the estimation error). FF argue that this reinforces their point that CAPM is not a good model; while this may be true, isn't this an equally powerful argument against FF3 as an asset pricing model?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.