In financial contexts, variance and standard deviation are often used to quantify risk. Variance measures the dispersion of returns around the expected value, while standard deviation is the square root of variance and provides a measure in the same units as the returns. It's important to note that while variance and standard deviation can indicate the degree of risk (the more spread out the returns, the greater the risk), they do not capture the direction of that risk (whether it's upside or downside risk). Additionally, risk can also encompass other factors such as liquidity risk, credit risk, and operational risk, which are not solely captured by variance or standard deviation. read more >>

In a literal sense, the standard deviation is a measure of how far from the expected value the actual outcome might be. Two stocks may have the same expected return, but have different levels of risk, as measured by variance and standard deviation. ... Both stocks have the same expected return.read more >>