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I would like to understand the role of alpha (intercept) in the regression-based asset pricing model. What's the meaning of the intercept? Does it have to be necessarily not significant and equal to zero in order that the model can model properly the asset prices? I looked an anwer for the internet, but I found only contradictory opinions. Thanks for helping.

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1 Answer 1

Glad you've asked :)

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.

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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

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