#### Previous topic

fynance.features.metrics.roll_annual_return

#### Next topic

fynance.features.metrics.roll_calmar

# fynance.features.metrics.roll_annual_volatility¶

fynance.features.metrics.roll_annual_volatility(X, period=252, log=True, w=None, axis=0, dtype=None, ddof=0)

Compute the annualized volatility of each X’ series.

In finance, volatility is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns [2].

Parameters: X : np.ndarray[dtype, ndim=1 or 2] Time-series of price, performance or index. period : int, optional Number of period per year, default is 252 (trading days per year). log : bool, optional If True then logarithmic returns are computed. Else then returns in percentage are computed. w : int, optional Size of the lagged window of the rolling function, must be positive. If w is None or w=0, then w=X.shape[axis]. Default is None. axis : {0, 1}, optional Axis along wich the computation is done. Default is 0. dtype : np.dtype, optional The type of the output array. If dtype is not given, infer the data type from X input. ddof : int, optional Means Delta Degrees of Freedom, the divisor used in calculations is t - ddof, where t represents the number of elements in time axis. Default is 0. dtype or np.ndarray([dtype, ndim=1 or 2]) Rolling annualized volatility for each series.

Notes

The rolling annualized volatility of returns is computed such that $$\forall t \in [1, T]$$:

$\begin{split}annualVolatility_t = \sqrt{period \times Var(R_{1:t})} \\ \\\end{split}$

Where, $$R_1 = 0$$ and $$R_{2:t} = \begin{cases}ln(\frac{X_{2:t}} {X_{1:t-1}}) \text{, if log=True}\\ \frac{X_{2:t}}{X_{1:t-1}} - 1 \text{, otherwise} \\ \end{cases}$$.

References

Examples

Assume series of monthly prices:

>>> X = np.array([100, 110, 105, 110, 120, 108]).astype(np.float64)
>>> roll_annual_volatility(X, period=12, log=False, ddof=1)
array([0.        , 0.24494897, 0.25777176, 0.21655755, 0.21313847,
0.27344193])
>>> roll_annual_volatility(X.reshape([6, 1]), period=12, log=False)
array([[0.        ],
[0.17320508],
[0.21046976],
[0.18754434],
[0.19063685],
[0.24961719]])