sigmaquant.performance.risk.annual_vola#

sigmaquant.performance.risk.annual_vola(returns, frequency)#

Compute annualized volatility.

The function computes the sample standard deviation of periodic returns and scales it to annual frequency using the square-root- of-time rule.

Parameters:

  • returns – Time series of periodic returns.

  • frequency – Frequency of the input data.

Returns:

Annualized volatility.

Return type:

float

Notes

  • NaN values are ignored. If fewer than two valid observations are available, NaN is returned.

Let \(r_t\) denote the periodic returns.

Define the sample standard deviation as:

\[s = \sqrt{ \frac{1}{T - 1} \sum_{t=1}^{T} (r_t - \bar{r})^2 }\]

The annualized volatility estimator is:

\[\widehat{\sigma}_{ann} = s \sqrt{N}\]

where \(N\) is the number of periods per year implied by frequency.