# Fama French regression with dummy variable

I am looking to run Fama-French regression on a portfolio of stocks. I am looking to specify a regime using a dummy variable. This dummy variable could be a low volatility/ high volatility marker.

Instead of using Markov model, I want to specify it explicitly. So when the vol is high, does the fund manager invest in quality and when the vol is low, does he go to growth stocks.

However how shall this be specified? Any pointers.

• r_(p,t) =α + β_p (r_(m,t) - r_(f,t) ) + β_(SMB ) 〖SMB〗t *D0 + β_HML 〖HML〗_t *D0 +β_UMD 〖UMD〗_t * D0 + β_(SMB ) 〖SMB〗t *D1 + β_HML 〖HML〗_t *D1 +β_UMD 〖UMD〗_t * D1 + ε_t - if i use the equation like this - would this not work? Jun 1, 2021 at 13:26
• That doesn’t look like a dummy variable to me. That’s splitting up your dataset. That’s fine if you want to do that, but then just split it up using the regular Fama-French equation and do 2 regressions. The part that requires thought is in is specifying what constitutes high and low vol, not specifying your equation. If you are looking for a real dummy variable then just use UMD as a regressor. That will tell you what kind of alpha a manager generates in high/low vol regimes. That’s the “active management” piece you’re talking about. Jun 1, 2021 at 16:14
• The high and low vol is confusing. Assume that there are twenty years of fund returns and there are two fund managers - who alternate every year. Now how does one find the alpha for the fund manager? Jun 1, 2021 at 16:31
• Haha, that’s a pretty odd scenario. When you calculate alpha, you do it for the fund. “The manager” is more like the investment decision than the actual person sitting behind the desk. That’s what I meant at least. If you want to know about a manager, that’s still a data filtering issue, not a regression issue. You would split up the dataset into even year manager and odd year manager, then use your dummy to see how their investment decisions generate alpha in high and low vol regimes. Jun 1, 2021 at 20:36