fynance.features.metrics.annual_volatility¶
-
fynance.features.metrics.
annual_volatility
(X, period=252, log=True, 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.
- 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
, whereT
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
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])