Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Annualizing a periodic standard deviation scales it by the square root of the number of periods per year, not a straight linear multiplication, so a small monthly volatility figure translates into a meaningfully larger annualized figure than a simple twelve-times multiplication would suggest.
Before you rely on it
What to check
Confirm the annualization used the square-root-of-time scaling rather than a straight linear multiplication of the periodic figure by the number of periods.
The common error
Where people go wrong with investment volatility calculator
Annualizing volatility by simply multiplying a monthly figure by twelve. The correct scaling uses the square root of the number of periods, and the linear shortcut overstates the annualized volatility relative to the mathematically correct conversion.
Sensitivity evidence
How periodic return standard deviation changes the annualized volatility
| Periodic return standard deviation | Annualized volatility | Return-to-volatility ratio | One-standard-deviation lower return |
|---|---|---|---|
| 1.5% | 5.2% | 1.54× | 2.8% |
| 2.5% | 8.7% | 0.92× | -0.660% |
| 3.5%worked example | 12.1% | 0.66× | -4.1% |
| 4.5% | 15.6% | 0.51× | -7.6% |
| 5.5% | 19.1% | 0.42× | -11.1% |
Every input, tested
Which input moves the annualized volatility most
| Input | Tested from | To | Annualized volatility at each end | Swing |
|---|---|---|---|---|
| Periodic return standard deviation | 2.5% | 4.5% | 8.7% to 15.6% | 6.9% (57%) |
| Periods per year | 11 | 13 | 11.6% to 12.6% | 1.0% (8.3%) |
| Annual expected return | 6.0% | 10.0% | 12.1% to 12.1% | none |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Periodic return standard deviation | 3.5% |
| Periods per year | 12 |
| Annual expected return | 8.0% |
| Annualized volatility | 12.1% |
| Return-to-volatility ratio | 0.66× |
| One-standard-deviation lower return | -4.1% |
Where the inputs come from
Periodic return standard deviation is measured from a series of returns, for example the standard deviation of 36 monthly returns. Periods per year converts it to an annual figure: 12 for monthly, 52 for weekly, 252 for daily. Annual expected return is used for the return-to-volatility comparison. Use standard deviation, not variance, and enter it as a percent.
When the result stops applying
The square-root-of-time scaling assumes returns are independent from period to period, which is roughly true for stocks but not for assets with smoothed or autocorrelated returns such as private funds. Volatility treats gains and losses alike and understates the chance of rare, large declines. It depends on the sample period.
What to compare it with
Pair with the Sharpe ratio to see return per unit of risk, with the maximum drawdown page for the worst decline, and with the two-asset risk calculator to see how mixing assets lowers volatility. Compare a bond fund and a stock fund to see the difference in swing.
People also ask
Frequently asked questions
What is a normal level of volatility?
Broad stock indexes have averaged around 15% to 20% a year, while a diversified bond fund is often in the 4% to 8% range.
Why multiply by the square root of periods?
For independent returns, variance adds over time, so standard deviation grows with the square root of the number of periods.
Does high volatility mean high risk?
It measures the size of swings, which is one form of risk. It does not capture the chance of permanent loss, which matters more for individual companies.