I'm wondering is that possible to get insignificant beta estimates in the time-series context, but highly significant risk premium associated with that beta in the cross-sectional regression?
Any help would be greatly appreciated!
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up.
Sign up to join this communityI'm wondering is that possible to get insignificant beta estimates in the time-series context, but highly significant risk premium associated with that beta in the cross-sectional regression?
Any help would be greatly appreciated!
I prefer thinking in terms of well measured vs. poorly measured rather than significant vs. insignificant: arbitrary p-value cutoffs and ignoring sensible priors can both be problematic. On the question, "can poorly measured betas from time-series regressions give rise to well measured factor premiums from cross-sectional regression?" The abstract answer is yes, but you have several problems working against you.
Let $F_t$ denote some factor. You can estimate the beta for a return $R_i$ on the factor with a time-series regression:
$$ R_{it} -R^f_t = \alpha_i + \beta_i F_t + \epsilon_{it}$$
The key idea behind all these factor models is that expected returns should be linearly increasing in the regression beta on the factor. To estimate factor premium $\gamma_F$, you'd like to run the regression:
$$R_{it} - R^f_t = \gamma_0 + \gamma_F \beta_i + u_{it} $$
To do this sensibly, you need to confront several problems: