fynance.features.metrics.calmar

fynance.features.metrics.calmar(X, period=252, axis=0, dtype=None, ddof=0)

Compute the Calmar Ratio for each X’ series.

Parameters:

X : np.ndarray[dtype, ndim=1 or 2]

Time-series price, performance or index.

period : int, optional

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

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])

Values of Calmar ratio for each series.

See also

mdd, drawdown, sharpe, roll_calmar

Notes

Calmar ratio [3] is the compouned annual return (annual_return) over the maximum drawdown (mdd). Let \(T\) the number of time observations, DD the vector of drawdown:

\[calmarRatio = \frac{annualReturn}{MDD}\]

With, \(annualReturn = \frac{X_T}{X_1}^{\frac{period}{T}} - 1\) and \(MDD = max(DD_{1:T})\).

Where, \(DD_t = 1 - \frac{X_t}{max(X_{1:t})}\), \(\forall t \in [1:T]\).

References

[3]	https://en.wikipedia.org/wiki/Calmar_ratio

Examples

Assume a series of monthly prices:

>>> X = np.array([70, 100, 80, 120, 160, 105, 80]).astype(np.float64)
>>> calmar(X, period=12, ddof=1)
array(0.6122449)
>>> calmar(X.reshape([7, 1]), period=12)
array([0.51446018])