Now, he caught me being imprecise, so let me be clear: risk is not related to expected returns either. If, with data going back to 1927 in the US, and corporate bonds, currencies, dozens of countries, and with all that data, somehow 'expected' returns are so different than actual returns that they seem orthogonal, it's a rather strange thing. It's like saying one's investments will probably, in their lifetime, not be correlated with one's expectations. So, why waste time studying finance? If the world is that random, that diabolically unpredictable, apply the Serenity Prayer and focus on things were we can make a difference.
The notes that the absence of a robust, intuitive measure of risk that is supposedly omnipresent and important, reminds me of attempts to explain the mysterious absence of the aether in the 19th century, because this was the medium through which light and gravity traveled, it was supposedly everywhere. Like 'risk', no one could measure it, so ever more clever reasons were adduced as to why nature hides what is all around us. See this little piece on Fresnel's coefficient of aether drag, which all seems so reasonable, and uses differential equations (ie, it's science!). Fresnel was able to come up with an equation very much like special relativity, and thus matching reality, but using wrong assumptions, because a good mathematically oriented modeler can always get from assumptions to data if you give him enough time (the degrees of freedom are hidden within the functional form or algorithm). We have a glut of Fresnellian finance going on right now
Anyway, here's Grantham on risk and returns (expected&actual):
In fact, Quality stocks have outperformed the market since 1965 (when our quality data begins) ... On noticing this outperformance, embarrassingly late in my opinion, Fama and French adopted a circular argument rather typical of ﬁnance academics in the 1970 to 2000 era: the market is efﬁcient; P/B and small cap outperform, ergo they must be risk factors. That the result in this case happens to get to the right result is luck. The real behavioral market is perfectly happy not rewarding “risk” when it feels like it, as is shown by the 70-year underperformance of high beta stocks. But this time it worked. Price-to-book, despite its low beta, is a risk factor because of its low fundamental quality and its vulnerability to failure in a depression. This is true with small cap as well. But what about “Quality?” This factor has outperformed forever. (The S&P had a High Grade Index that started in 1925 and handsomely outperformed the S&P 500 to the end of 1965 when our data starts.) Since the market is efﬁcient, to Fama and French quality must be a risk factor! So, by protecting you in the 1929 Crash and in 2008, and by having a low beta for that matter, Quality as represented by Coca-Cola and Johnson & Johnson must be a hidden risk factor. Oh, I know: “The real world is merely an inconvenient special case!”