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# fynance.features.metrics.sharpe¶

fynance.features.metrics.sharpe(X, rf=0, period=252, log=False, axis=0, dtype=None, ddof=0)

Compute the Sharpe ratio for each X’ series.

Parameters: X : np.ndarray[dtype, ndim=1 or 2] Time-series of prices, performances or index. rf : float, optional Means the annualized risk-free rate, default is 0. period : int, optional Number of period per year, default is 252 (trading days). log : bool, optional If true compute sharpe with the formula for log-returns, default is False. 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] Value of Sharpe ratio for each series.

Notes

Sharpe ratio [7] is computed as the annualized expected returns (annual_return) minus the risk-free rate (noted $$rf$$) over the annualized volatility of returns (annual_volatility) such that:

$\begin{split}sharpeRatio = \frac{E(R) - rf}{\sqrt{period \times Var(R)}} \\ \\\end{split}$

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 a series X of monthly prices:

>>> X = np.array([70, 100, 80, 120, 160, 80]).astype(np.float64)
>>> sharpe(X, period=12)
0.24475518072327812
>>> sharpe(X.reshape([6, 1]), period=12)
array([0.24475518])