Source
Ang, Hodrick, Xing & Zhang (2006) on idiosyncratic volatility; Blitz & van Vliet (2007) on low volatility; Frazzini & Pedersen (2014) on betting against beta. Our own tests measure volatility, market-independent volatility and beta as three separate signals, and do not follow the construction in any one of those papers.
The claim
Low-volatility and low-beta stocks - those whose prices move least, and those that move least with the market - earn as much as or more than high-volatility, high-beta ones, so risk is not rewarded inside the equity market.
What we ran
Three separate signals, each with the direction declared in advance so that the lower-risk companies were expected to win: how much a share's price moved around over the past 252 trading days, about a year; the part of that movement not explained by the market's own moves; and beta, how strongly the share moves with the market, measured over the same 252 days. Companies sorted into five equal groups on each signal, held one month, drawn from the 1,000 largest US companies by market value excluding financials and utilities, before trading costs. Separately, the same idea was applied not as a standalone signal but as a filter on Purple Turtle's own ranking, the cash-flow and profitability score behind the published books: take twice as many companies as the book needs, then keep the calmer half - either the least volatile or the lowest-beta - at five different book sizes, rebalanced twice a year and after costs.
Window
Monthly, 1998-2026 - 331 monthly observations for the three signals. Reported separately for 1998-2014 and for 2015-2026, the later stretch having been set aside before testing began and not examined while factors were being chosen.
Result
All three signals are flat to mildly opposite to the published direction, and not one of them is distinguishable from zero. Taking the gap between the extreme fifths with the same amount in each company and then weighted by company size: price volatility -0.48% and -3.88% a year (t-statistic -0.09, p-value 0.931); the market-independent part of volatility -0.09% and -4.04% (t-statistic -0.02, p-value 0.986); beta -1.70% and -3.79% (t-statistic -0.29, p-value 0.775). Every one of those measurements is a small fraction of its own margin of error, against a conventional 0.05 threshold, so none can be called a result in either direction. Split across the record, the equal-amount figures ran +1.25% then -2.91%, +1.32% then -2.07%, and -0.08% then -3.97%. The portfolio-level filter behaved differently and is worth reporting separately: keeping the calmer half of a wider pool did cut realised volatility substantially, but it turned a positive return over the index on the held-back years into a negative one. Choosing calmer COMPANIES removed what our own ranking was finding; dividing position sizes by volatility - the same companies, smaller positions in the jumpy ones - did not.
What this does not show
The published low-volatility result is a RISK-ADJUSTED one, and often a leverage-constrained one: the classic claim is a better return per unit of risk, not a higher raw return, and the betting-against-beta version is a market-neutral portfolio that buys low-beta stocks with borrowed money and sells high-beta ones short. We measured raw return gaps between five groups, with no borrowing, no short leg and no risk adjustment, so a flat result here is fully compatible with the published claim. The 2015-2026 half was also led by high-beta mega caps, which loads the dice against any low-risk tilt over exactly the years we held back.