Some note that if we are in bull markets, it is better to be in high beta stocks. I would agree that if you know you are in a bull market--that is, you know the stock market will be up at the end of this month--then it is preferable to be in high beta stocks. Yet, implementing this timing rule is not straightforward because even abstracting from the variance drag of high volatility stocks, the dominance of low vs. high beta changes whether you are using contemporaneous or ex ante indicators. That is, it makes a big difference if you use data from today to determine tomorrow's portfolio, or data from tomorrow night.
Low vol is pretty much like low beta. and betas are actually pretty straightforward to predict. Low beta stocks move less than high beta stocks. In up markets, low beta stocks go up less than the average, and much less than the high beta stocks. In down markets, low beta stocks go down less than high beta stocks. Here's my data on beta portfolios since 1962 using monthly data, using the separation of whether the contemporaneous S&P return that month was up or down. Bottom line: if you know markets are going up, go into high beta stocks.
Now, what about volatility? In above average volatility using the same, ex post, end of month data point, one finds that in the tranquil, below average volatility months, markets rise and higher beta stocks dominate; in higher-than-average volatility it's better to be in low beta stocks.
We know that monthly returns are pretty uncorrelated, yet, monthly volatility is highly correlated, and so, perhaps, low volatility periods are better for high volatility stocks?! Alas, no. Looking forward, it goes the other way. That is, using last month's volatility, lower-than-average vol means it's better to be in low volatility, and the opposite in high volatility regimes.