I've been following studies such as Kempf & Osthoff (2007) and Statman & Glushkov (2009) in building a methodology measuring ESG portfolio performance centred around the Carhart 4-Factor Model. I've been using factors from the Kenneth French database and regressing in Microsoft Excel to get my coefficients and p-values.

My understanding of the intercept term in the Model is that it is representative of the alpha, or excess return of the portfolio. However, when running these regressions on returns and factor data over a 5 year period, my alpha is statistically significant, but is miniscule, at -.40%, when the true return in excess of R(f) is much greater. As such, my primary question is how to interpret this alpha, and what is the reasoning behind its significant difference from the true return in excess of R(f)?

Find both above referenced studies below:



Edit: As I am running the regression on daily returns and factor datapoints, is the intercept indicative of daily alpha, in which case I should annualise returns for the yearly periods under investigation?

  • 4
    $\begingroup$ There's nothing wrong working with daily data, but you have to keep track of units. Something you may find is that betas are quite different if estimated at the weekly or monthly frequency due to small but meaningful correlation for less liquid securities between daily returns and lagged daily market or other factor returns. $\endgroup$ Jun 23, 2021 at 16:50

1 Answer 1


The idea behind any of these factor models (whether it be the CAPM, Fama-French 3 Factor Model, Carhart 4 Factor Model etc...) is that expected returns are linear in covariance with variables of hedging concern to investors. The economic idea is that there are macroeconomic risks investors do not wish to hold, and to entice investors to hold these risks, investors are compensated in the form of higher expected returns. Covariance with variables of hedging concern is risk that obtains a positive market price. The more covariance, the more risk, and the higher the expected return. (How this theory meshes with reality is of course highly nuanced and debatable.)

Anyway, in a time-series regression of excess returns on other returns series (i.e. tradable factors), the intercept term (i.e. the alpha estimate), is the difference between the average return of the portfolio and what can be explained by covariance with some set of factors. A negative alpha implies that the mean return is lower than what would be expected given factor model.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.