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.

Returns:

dtype or np.ndarray([dtype, ndim=1 or 2])

Rolling annualized volatility for each series.

See also

mdd, drawdown, sharpe, annual_return

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

[2]	https://en.wikipedia.org/wiki/Volatility_(finance)

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]])