Risk Calculator
Measuring How Unpredictable a Return Series Really Is
Two investments can average the identical return over time while one swings wildly month to month and the other barely moves. Standard deviation captures that difference directly — it measures how far individual returns typically stray from the average, which is the standard statistical definition of risk in portfolio analysis.
The Formula
Annualized Risk = Std Dev × √(Periods per Year)
The per-period standard deviation is calculated first from your return series, then scaled up to an annual figure by multiplying by the square root of how many periods occur in a year — 12 for monthly returns, 252 for daily trading returns, and so on.
Why This Matters
- Comparing investments fairly — return alone doesn't reveal how bumpy the ride was to get there; standard deviation fills that gap.
- Input to risk-adjusted metrics — standard deviation is a required input for the Sharpe ratio and other risk-adjusted return calculations.
- Setting expectations — a higher standard deviation means wider swings around the average return are statistically normal, not a sign something is wrong.
Worked Example
A series of six monthly returns: 2.1%, -1.4%, 3.0%, 1.8%, -0.6%, 2.5%.
| Statistic | Value |
|---|---|
| Mean Return | 1.2333% |
| Per-Period Standard Deviation | 1.7941% |
| Annualized Risk (× √12) | 6.2148% |
Annualizing monthly volatility by √12 (about 3.46) is a standard approximation that assumes returns are independent from month to month.
How to Use This Calculator
- Enter your Periodic Returns as a comma-separated list (e.g. monthly percentages).
- Select how many Periods per Year your data represents — monthly (12), quarterly (4), daily (252), or annual (1).
- Select Calculate to see the mean return, per-period standard deviation, and annualized risk.
Related Calculations
Apply this risk figure to estimate potential losses with the Value at Risk Calculator, or see risk-adjusted performance with the Sharpe Ratio Calculator.