Risk & Performance
Volatility (Standard Deviation)
A measure of how widely returns vary around their average, indicating investment risk and variability.
Formula
σ = √[Σ(Rᵢ − R̄)² ÷ n]
Variables
σ- Standard deviation (volatility)
Rᵢ- Individual return
R̄- Average return
n- Number of observations
Worked Example
Scenario: Daily returns of 2%, 1%, 3%, −1%, 2% have volatility (standard deviation) of approximately 1.58%.
Steps:
- Calculate average: (2 + 1 + 3 − 1 + 2) ÷ 5 = 1.4%
- Calculate deviations from average: 0.6%, −0.4%, 1.6%, −2.4%, 0.6%
- Square deviations: 0.36, 0.16, 2.56, 5.76, 0.36
- Sum squares: 9.2
- Divide by n: 9.2 ÷ 5 = 1.84
- Take square root: √1.84 = 1.36%
When to Use This Formula
- Measure investment risk
- Annualize daily or monthly volatility (multiply by √252 for daily)
- Compare risk levels between investments
Limitations & Assumptions
- Treats upside and downside variability equally
- Historical volatility may not predict future volatility
- Assumes normal distribution of returns (real markets don't always)
- Sensitive to outliers and time period selected
Common Questions
Does 20% volatility mean a 20% loss?
No. Volatility is dispersion around average return, not a directional prediction or loss ceiling.
How do I annualize daily volatility?
Multiply by √252 (approximate trading days). Monthly volatility: multiply by √12. This assumes returns are independent.
Volatility and how it is priced
- VolatilityDefinition
- Historical volatilityDefinition
- IV crushDefinition
- Volatility smileDefinition
- Implied volatility skewGuide
Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.