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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?

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