What is the definition of standard deviation in finance?

The definition of standard deviation in finance as the variance of returns is not entirely accurate. Instead, standard deviation is fundamentally linked to measuring the dispersion of a set of data points, specifically the returns in finance.

Standard deviation quantifies how much the returns on an asset deviate from the average or mean return. It essentially provides insight into the volatility of investment returns: a higher standard deviation indicates greater variability in returns, which corresponds to higher investment risk.

While variance is a related concept, representing the average of the squared deviations from the mean, standard deviation is simply the square root of variance, making it a more direct measure of risk as it is expressed in the same units as the original data (i.e., the returns). Thus, the correct characterization of standard deviation as an assessment tool is better captured by stating it as a measure of return risk, aligning closer with the understanding of how risk is evaluated in financial contexts.

This context of return risk involves analyzing the probability and impact of various return outcomes, a key aspect of investment decision-making and portfolio management.