OK, right from the very first sentence in this paper I have something to disagree with.
If you read the paper, they looked at stock market from 1990 to 2011 and observed that low volatility stocks had higher returns. So that is actual
realized returns, over a period in the past
But the sentence says higher expected
returns, which is about future
. The paper doesn't show that expectations are higher.
This is very sloppy work. They conflate actual returns and expected returns. Stock A can have higher expected return than Stock B ex-ante, but the actual returns can be reversed ex-post. In fact, over shorter periods this is not unlikely. Most people would say that stocks have higher expected return than bonds, but there have been periods when the actual returns were reversed and bonds beat stocks.
Another thing wrong in the first sentence is that they use the term "low risk stocks" when their research is about "low volatility stocks". They interchange "low risk" and "low volatility". Again, a sloppy substitution of the word risk for volatility which leads to the to-broad conclusion that low risk has higher return.
If I'm confusing anyone here is the problem in a nutshell:.
They say: Low risk stocks have higher expected return.
What they actually showed:
Low volatility stocks had higher actual returns over the period 1990-2011
What they are claiming is very broad and goes against conventional wisdom. What their data actually shows is more narrow and is not at all inconsistent with conventional wisdom.