Are Fama French Factors market neutral?

I was wondering whether the famous fama-french factors such as e.g. SMB and HML are market neutral? I know that they are long-short factors in the sense that the net investment is essentially zero, but I was wondering if this also makes them market neutral?

If not, how to make them market neutral?

Bonus: is it also possible to make them beta neutral?

• Thank you for the reply. The FF factors are not constructed based on a regression though, but rather on those double sorts (first sort stocks on size and then on value), this way essentially creating long-short portfolios. In that case, are they market neutral?
– Rik
Feb 19 '20 at 15:28

Given that the Fama-French factors are long-short portfolios, it might be reasonable to expect that $$\beta_{Mkt}$$ for these portfolios would be close to zero. However, the underlying factors may cause significant differences in $$\beta_{Mkt}$$ for the long and short portfolio. So, for example, small stocks are likely to have a significantly different $$\beta_{Mkt}$$ to large stocks, and the resultant SMB factor will have an overall $$\beta_{Mkt}$$.
If you wish to make the resultant portfolios $$\beta_{Mkt}$$ neutral, you can calculate the $$\beta_{Mkt}$$ for all of the constituents and reweight the members of each of the 6 subportfolios so that all 6 have a $$\beta_{Mkt}$$ of 1. There are many ways of doing this if you have access to an optimizer. Any long-short portfolios constructed from those portfolios will then have a $$\beta_{Mkt}$$ of 0.