As Fama and French noted in 2004, there is no evidence supporting the contention that Beta is a measure of risk. Nor is standard deviation a measure of risk. Rather the latter is best thought of as a measure of the emotions generated by market volatility. Unfortunately, the investment management industry is built around these two measures and thus they encourage investors to make emotional decisions rather than helping mitigate these decisions. The desire to turn finance into a "science" in early 1960's drove the industry to accept the mathematically elegant CAPM to the determent of making better long-term stock investment decisions. By the way, the primary reason variance is at the center of our finance models is because it is mathematically tractable not because it is a measure of risk.