Eric Falkenstein summarizes what he has found when looking at the relationship between risk and return:
Here’s the bottom line, which apparently is more difficult to understand than the theory, but ultimately much more convincing once you see it.
The negative risk-return relation holds for volatility (cross-sectionally and over time, total and idiosyncratic), beta, options, private investments, leverage, currencies, country returns,yield curves, financial distress, sportsbooks, lotteries, IPOs, junk bonds, and analyst uncertainty.
It’s pretty absent in country returns, commodities, movies, and private investments.
It does work nicely in the the AAA-BBB spread or the short end of the yield curve.
Now, if you were an alien, what’s your generalization, that in general risk is related to return, not related, or the opposite? The Academy teaches that there’s a linear relation, positively sloped!