Using Volatility Regimes in Fama–French Factor Regressions

Summary

The document discusses adding an explicit high- or low-volatility regime to a Fama–French regression for a stock portfolio. The proposed research question is whether a manager’s factor exposures differ by regime, such as favoring quality during high volatility and growth during low volatility. A response suggests using average volatility as a threshold, noting that volatility can rise sharply during market corrections and that the mean may exceed the median or mode under a right-skewed variance distribution. It emphasizes measuring risk at the portfolio level when studying investor behavior, rather than assuming an index’s implied volatility is an adequate proxy. A backward-looking realized-volatility measure, such as a 21-day moving average, is offered as a starting point; a GARCH estimate is presented as a possible next step to capture persistence. The document gives research suggestions, not regression specifications or empirical results. Threshold choice and volatility measure should be justified for the particular hypothesis and portfolio.

Key ideas

• A volatility regime can be represented explicitly in a factor regression with a dummy variable.
• Average volatility is suggested as a possible threshold for classifying high and low regimes.
• Portfolio volatility may better represent investor risk than a broad index’s implied volatility.
• Realized volatility is proposed as a starting measure, with GARCH as a possible extension.
• The regime definition and measure require justification, and no regression results are reported.

Tags

# Fama French regression with dummy variable


# 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.

## Answer by Mild_Thornberry (score 3)

https://quant.stackexchange.com/a/64338

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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