This manuscript presents the mathematical relationship between coefficient of variation (CV) and security investment risk, defined herein as the probability of occurrence of negative returns. The equation suggests that there exists a range of CV where risk is zero and that risk never crosses 50% for securities with positive returns. We also found that at least for stocks, there is a strong correlation between CV and stock performance when CV is derived from annual returns calculated for each month (as opposed to using, for example, only annual returns based on end-of-the-year closing prices). We found that a low nonnegative CV of up to ~ 1.0 (~ 15% risk) correlates well with strong and consistent stock performance. Beyond this CV, share price growth gradually shows plateaus and/or large peaks and valleys. The efficient frontier was also re-examined based on CV analysis, and it was found that the direct relationship between risk and return (e.g., high risk, high return) is only robust when the correlation of returns among the portfolio securities is sufficiently negative. At low negative to positive correlation, the efficient frontier hypothesis breaks down and risk analysis based on CV becomes an important consideration.
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