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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.

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  • $\begingroup$ 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? $\endgroup$ – shoonya Jun 1 at 13:26
  • $\begingroup$ 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. $\endgroup$ – Mild_Thornberry Jun 1 at 16:14
  • $\begingroup$ 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? $\endgroup$ – shoonya Jun 1 at 16:31
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    $\begingroup$ 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. $\endgroup$ – Mild_Thornberry Jun 1 at 20:36
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I worked on volatility control funds for a few years a while back. Frequently, we would simply use the average as the threshold between high and low vol. That is because volatility is below average in normal times, but can quickly exceed the average during a correction. Mathematically, the fat right tail of an inverse-gamma distribution for an unknown variance makes the average greater than the median/mode.

How an institutional investor perceives risk is another matter. They are looking at their portfolio risk, so you want portfolio volatility. You probably can’t just use S&P 500 implied vols. If you are testing the reaction of investors to realized vol, then you can just do a 21-day moving average realized vol or some backward-looking measure. It may be beneficial to start there, see if it’s significant. Otherwise, the next step may be to estimate vol using a GARCH model to better capture the persistence of realized vol in the future.

Your experiment feels like research more than practical application, so whatever you choose, be sure to justify it.

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