Diagnosing Unexpected Fama–MacBeth Factor Risk Premia

Summary

The document describes a two-stage Fama–MacBeth analysis of stock returns using market, size, and value factors. The first stage estimates each stock’s factor betas from time-series regressions; the second runs cross-sectional regressions at each date and averages the resulting risk-premium estimates. The author reports an unexpected pattern: the market and value premiums are negative but statistically insignificant, while the size premium is positive and significant. The estimated alpha is also positive and significant.

As diagnostic checks, the author repeats the analysis across subperiods, including a pre-crisis interval, and compares a market-only model and a model that adds size with the three-factor model. These checks do not resolve the apparent anomaly: value does not turn positive in the selected earlier period, and alpha is lower in the one-factor specification. The post describes symptoms and checks, not their resolution; it supplies no data, regression output, or details about standard errors, portfolio construction, or implementation, so the results cannot be independently assessed.

Key ideas

• The first Fama–MacBeth stage estimates factor betas for each stock using time-series regressions.
• The second stage estimates date-specific cross-sectional premiums and averages them over time.
• The reported market and value premiums are negative and statistically insignificant, while size is positive and significant.
• The author checks subperiods and alternative factor specifications but does not explain the unexpected estimates.
• The post does not provide enough methodological detail or output to diagnose the results independently.

Tags

# Fama-Macbeth Regression: Weird Risk Premia


# Fama-Macbeth Regression: Weird Risk Premia












I just conducted a Fama-Macbeth regression where in the first step I calculated a time-series regression for each individual stock to get three betas (for mkt-rf, smb, hml) for each stock. Then I ran a cross-sectional regression with the returns of all companies at each timepoint as my dependent variable and the all the estimated betas of all companies as the independent variables. This gave me a time-series of the different risk premia of which I took a simple average.

Unfortunately, the results are very weird from my perspective. As I cannot find a mistake in my regression, I'd like to ask if anyone of you can somehow explain the results:

The risk premium of Mkt-Rf is -0.11% per month (but not statistically significant), SMB is 0,62% (significant) and HML -0,14% (not significant). Additionally I get a (in my opinion very high) alpha of 1.05% which is statistically significant.

While this is already very strange as I expected HML and especially Mkt-Rf to be positive, at least they're not significant.

But even worse, I tried to double check my results.

- I checked four subperiods as e.g. the Value-Premium/HML wasn't performing since the financial crisis 2007. Not even the Pre-crisis era from 2000-2007 in which HML performed really well.

- Instead of the three-factor model I caluclated CAPM and a two-factor model just with SMB. Against all my expectations the Alpha was lower in the One-factor-modell than in the other two although two factors where added which should increase the explanatory power and decrease the alpha.

Has anyone of you a logical explanation for the results? Otherwise I probably should check my calculcations again.

Thanks

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