Standard deviation (σ) measures the dispersion of investment returns around their average (mean). In finance, it is the primary measure of total risk (both systematic and unsystematic).
Interpretation: - A higher standard deviation = wider spread of returns = more volatile/riskier investment. - A lower standard deviation = returns cluster closer to the mean = less volatile.
Normal distribution properties: - ~68% of returns fall within ±1 standard deviation of the mean. - ~95% of returns fall within ±2 standard deviations. - ~99.7% of returns fall within ±3 standard deviations.
Example: A fund has an average annual return of 10% with a standard deviation of 15%. - There's a 68% chance annual returns fall between −5% and +25% (10% ± 15%). - There's a 95% chance annual returns fall between −20% and +40% (10% ± 30%).
Standard deviation vs. beta:
| Measure | Measures | Risk Type | |---|---|---| | Standard deviation | Total volatility | Total risk (systematic + unsystematic) | | Beta | Relative market volatility | Systematic risk only |
Coefficient of variation (CV): Standard deviation ÷ Mean return = risk per unit of return. Useful for comparing investments with different expected returns.
> Exam tip: Standard deviation = total risk; beta = systematic risk. For a well-diversified portfolio, unsystematic risk is largely eliminated, so standard deviation approaches beta-driven risk. Sharpe ratio uses standard deviation; Treynor ratio uses beta.