Even in highly liquid markets, volatility encompasses differences of opinions (non-homogenous opinions), and uncertainty including uncertainty around inflation and growth. Inflation and growth then are more directly related to the economy and properly treated as macro-economic factors, whereas "volatility" is much more of a broad paintbrush, a derivative price-related statistic that may have rolled into it idiosyncratic uncertainties, microstructure and supply side dynamics, liquidity related dynamics (lumpiness), as well as proper "macroeconomic" considerations (what the Fed might do or say, inflation uncertainty, growth uncertainty).

Re: also inflation as "bad" for equity returns, if one regresses domestic equity returns to domestic inflation, there tends to be two regimes, one from 0 inflation to "modest inflation" where more inflation is positive for real returns, and much higher inflation where equity *real* returns decline with higher inflation, but not as negative as cash or fixed income. All these things also critically depend on the Fed/ECB responsiveness to tame inflation, making historical data useless were there a paradigm shift moving forward. (Would we look at the Volcker period anti-inflationary measures as representative of the Fed response looking forward? No-- so this is an anomalous period which wouldn't make sense to include in determining statistical relationships).

Finally, re: FF-3 or FF-4, I get they get a lot of respect in academia, but the fact remains that there are hundreds of anomalies now built atop of these 3 and 4 factor models, or atop of this APT model of growth/inflation/volatility. It's rather unimpressive and given too much credit if one understands numerical approximations/math. In the end, if you have enough factors or functions/vectors/tensors that are not fully parallel, you get a pretty good local approximation with 2-3 factors. It is analogous to just the first 2-3 terms in a Fourier/Lagrange/Taylor series. (Same can be said of Miller Modigliani). To someone versed in science/physics/engineering, none of this 'fit' is surprising. One could take three somewhat orthogonal "factors"/anomalies of the hundreds now in existence, and create an alternative FF3/FF4/FF5.

A deeper nuanced understanding in (slow quant) anomalies investing, then starts with understanding the interaction of factors (they have non-linear relationships), and in the linear approximation, understanding orthogonality (for example the greater degree of orthogonality among value-leaning metrics; growth/momentum leaning metrics; liquidity; and "quality" metrics.) An alternative, which is harder to explain to human beings would be taking in all factors, and using a technique like PCA to find 3 truly orthogonal (by design) "factors". The cutting-edge alpha generators, are probably are looking more at nonlinear relationships, global model parameters and tuning, alternative data-sources not well correlated with traditional factors, detecting regime/paradigm shifts.

Much too much time in how traditional finance is taught is centered around these stale finance ideas that are not useful to investment/asset managers (except in a marketing/credibility/signalling sense). Necessary? Perhaps-- one can argue these are fundamental building blocks. I tend to think there is a lot of fluff in finance. A lot of academic patting oneself on the back. But that opinion probably won't garner too much support.