annual_volatility¶

Defined in fynance.features.metrics

annual_volatility(X, period=252, log=True, axis=0, dtype=None, ddof=0)[source]

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:

Xnp.ndarray[dtype, ndim=1 or 2]

Time-series of price, performance or index.

periodint, optional

Number of period per year, default is 252 (trading days per year).

logbool, optional

If True then logarithmic returns are computed.
Else then returns in percentage are computed.

axis{0, 1}, optional

Axis along wich the computation is done. Default is 0.

dtypenp.dtype, optional

The type of the output array. If dtype is not given, infer the data type from X input.

ddofint, 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]): Values of annualized volatility for each series.

See also

mdd, drawdown, sharpe, annual_return

Notes

Let \(Var\) the variance function of a random variable:

\[annualVolatility = \sqrt{period \times Var(R_{1:T})}\]

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)
>>> annual_volatility(X, period=12, log=True, ddof=1)
0.2731896268610321
>>> annual_volatility(X.reshape([6, 1]), period=12, log=False)
array([0.24961719])