Definition
Standard deviation quantifies the variability of returns—higher values indicate greater uncertainty and risk. It is the most common risk measure in finance, used in the Sharpe ratio, MPT, and option pricing. Annualized volatility = daily vol × √252. The assumption of normally distributed returns is imperfect—fat tails and skewness mean actual extreme losses occur more often than standard deviation suggests.
functions Formula
σ = √[Σ(Ri − R̄)² / (n-1)]
lightbulb Example
A stock with 20% annual standard deviation and 10% expected return: roughly 68% of the time returns fall between -10% and +30% (one standard deviation), and 95% of the time between -30% and +50% (two standard deviations).
verified_user Key Points
- Primary risk measure in modern finance
- Higher vol = more uncertainty
- Annualize daily vol: multiply by √252
- Fat tails mean extreme events occur more often than predicted