Does the Fama-French five-factor model of stock returns (employing market, size, book-to-market, investment and profitability factors) explain the outperformance of low-volatility stocks. In their July 2016 paper entitled “The Profitability of Low Volatility”, David Blitz and Milan Vidojevic examine whether: (1) any of several models expose a conventional return-for-risk market beta effect for stocks; and, (2) the low-volatility effect is distinct from a low-beta effect. They calculate volatilities for stocks and the market using daily or monthly returns over the past year. They calculate stock betas using these volatilities and daily or monthly stock-versus-market return correlations over the past five years, with shrinkage by 1/3 toward a value of one. They include momentum (return from 12 months ago to one month ago) as an explanatory factor, even though the five-factor model does not. Using data for a broad sample of U.S. common stocks and model factors (excluding extreme outliers) during July 1963 through December 2015, *they find that:*

- Based on monthly regressions between a stock’s beta and its next-month return in excess of the risk-free rate over the entire sample period:
- The Capital Asset Pricing Model (CAPM) does not hold. There is no relationship between a stock’s beta and its future return.
- Controlling for size, value and momentum factors, there is still no relationship between a stock’s beta and its future return.
- Further controlling for profitability and investment factors, there is still no relationship between a stock’s beta and its future return.
- All intercepts are significantly positive, suggesting that every stock earns the equity risk premium regardless of its beta (over long periods).
- Findings are robust to a different way of calculating beta and for two size groups.

- Based on a second round of regressions between a stock’s beta or volatility and its next-month return in excess of the risk-free rate and its beta-predicted return:
- Contrary to CAPM, there is a negative relationship between beta and future return.
- Controlling for other factors, the low-volatility effect dominates the low-beta effect.

In summary, *evidence indicates that the five-factor model does not explain the low-risk effect, and this effect is stronger when measuring risk via volatility rather than market beta.*

Cautions regarding findings include:

- While findings may help an investor decide whether and how to exploit the low-risk effect for stocks, they do not incorporate tests of any realistic strategies.
- The volatility estimation interval (past year) and the correlation estimate interval used in beta calculation (five years) are different, raising the possibility that different look-back intervals introduce differences in volatility and beta regressions. However, one of the authors reports that findings are the same when the intervals match.

See also:

- “Low Risk and High Return?”
- “Systematic Overpricing of High-beta Assets?”
- “Pervasive Outperformance of Low-volatility Stocks”
- “Global Low-volatility Stock Portfolio Performance Predictors”
- “Achieving a Low-volatility Stock Portfolio Efficiently”