Risk & returns
Standard deviation measures how widely observations spread around their mean under a defined sample. For returns, it is commonly used as a volatility measure.
Make it click
Two classes can have the same average score while one cluster is tight and the other widely scattered. Standard deviation summarises that spread.
Now put that into markets
Return standard deviation treats positive and negative deviations symmetrically. Annualised figures scale periodic estimates under assumptions.
The sample formula squares deviations, averages them with the chosen denominator and takes a square root. Outliers therefore have strong influence.
State return interval, window, sample or population convention and annualisation. Look at the distribution for skew and heavy tails.
Markets are not reliably normal or stable, and upside variation is not the same harm as downside. One spread statistic cannot describe tail risk.
Takeaway
