# What's the meaning of the intercept in asset pricing model?

I would like to understand the role of alpha (intercept) in the regression-based asset pricing model or $n$-factor models; one of the most famous of those one is the Fama-French 3-factor model.

I know that, technically speaking, from an econometric point of view, it should be the value assumed by the dependent variable on average, given the independent variables of the model set to be equal to 0. But, how can you interpret that from an economic point of view?

Does it have to be necessarily significant and equal to zero in order that the model can model properly the asset prices?

I looked some answers for the internet, but I found only contradictory opinions. Thanks for helping.

-

Technically speaking, in factor model $\alpha$ stays for return or risk premia, which asset pays when all factor returns are zero.

Then, to answer question in more details, we have to specify, are we dealing in our model with return ($R_i$ for asset $i$) or with risk premia over risk free ($R_i-R_f$).

In the first case, interpretation of $\alpha$ is straightforward: most probably, it's $R_f$. As for latter case, this is one of white spot in my understanding of modern finance. I don't know correct answer. As far as I understand, in efficient market it should be equal to zero. If not - market is inefficient. Or there is still some risk factor which is priced, but not reflected in the model.

Or may be something else. In fact, for several months after discovering http://quant.stackexchange.com I was going to ask that question myself someday :) So, let me humbly join the questioning crowd.

-
Thanks for the comprehensive answer @Alexander. I knew the first case, in which one analyzes the asset returns, but not the latter. Anyway, in your opinion, by assuming efficient mkt hypothesis, if I find a statistically significant and null α, I theoretically will find a proper model to analyze asset prices, right? – Quantopic Jan 26 '14 at 16:48
I think, even if $\alpha$ would be non-zero and statistically significant, you still will have a tool. It's usual regression story: you need uncorrelated stationary factors, uncorrelated and serially uncorrelated errors (which are interpreted as idiosyncratic risks in factor models of returns), etc., to have a model which satisfactorily describes returns. – Alexander Didenko Jan 27 '14 at 3:41

The factor models are based on the following linear regression model:

$(R_t - R_f)$ = $\alpha$ + $\beta_{mkt}$*$(R_{mkt} - R_f)$ + $\sum\limits_{i=1}^n {x_{k,t}}$ + $\epsilon_t$

$\alpha$ is the regression model intercept and indicates the portfolio performance in excess to the market excess return and the other factor; It has to be strictly positive and significant, in order to be able to measure properly the portfolio performance and the risk-adjusted portfolio returns; look at this [answer] for the joint hypothesis problem1.

$x_{k,t}$ represents the set of variables that can be (or that were been added over time) added following other kind of factor models (see, for instance, the Carhart's 4-factor model (1997)).

-