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Return Volatility Calculator

Volatility and Sharpe ratio from a series of returns. Volatility scales with the square root of time, so monthly volatility annualises by multiplying by the root of twelve rather than by twelve.

Also called: volatility calculator, sharpe ratio.

Separate values with commas or spaces.

%
Annualised volatility
8.08%

8.08% annualised volatility against 11.68% annualised return, a Sharpe ratio of 0.7. Volatility scales with the square root of time, not with time.

Volatility per period
2.33%
Annualised return
11.68%
Sharpe ratio
0.7
Best period
4.1%
Worst period
-2.6%
Periods observed
8
How this is calculated
Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for India change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Volatility is the standard deviation of returns. Annualising it uses the square root of the period count, because variance adds over time while standard deviation is its root, so monthly volatility of three percent is about ten and a half percent a year rather than thirty-six. The Sharpe ratio divides excess return over the risk-free rate by that volatility, giving return per unit of risk, and it is the standard way to compare strategies of different riskiness.

volatility scales with the square root of the number of periods; Sharpe is excess return per unit of it
sigma
Standard deviation of returns
n
Periods a year

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

eight monthly returns

Periodic returns (%)
2.1, -1.4, 3.2, 0.8, -2.6, 1.9, 4.1, -0.7
Periods a year
12
Risk-free rate a year
6%

Annualised volatility8.08%

Structural: the annualised volatility must exceed the period volatility

Open this example

constant returns have no volatility

Periodic returns (%)
1, 1, 1, 1
Periods a year
12
Risk-free rate a year
6%

Annualised volatility0%

boundary

Open this example

Method and limits

What it assumes

  • Returns are independent between periods, which real markets violate.

What it deliberately does not model

  • Volatility treats upside and downside equally, which few investors do.
  • A short series gives a very noisy estimate, and past volatility is a weak predictor of future.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Why the square root of time?
Because variances add when returns are independent, and volatility is the square root of variance. Twelve months of variance is twelve times one month, so the standard deviation is root twelve times.