capture_ratio¶

Defined in fynance.metrics

capture_ratio(X, B, side='up', period=252)[source]

Up- or down-market capture ratio of the strategy against the benchmark.

Restricts to the bars where the benchmark moved in the direction given by side ('up': \(b_t > 0\); 'down': \(b_t < 0\)), annualizes the strategy’s and the benchmark’s compounded return over that same subset of bars, and returns their ratio.

Parameters:

Xnp.ndarray[float64, ndim=1]: Strategy price/level curve.
Bnp.ndarray[float64, ndim=1]: Benchmark price/level curve, same length as X.
side{‘up’, ‘down’}, optional: Which benchmark bars to condition on. Default is 'up'.
periodint, optional: Number of periods per year, default is 252 (trading days).

Returns:

float: The capture ratio, 1.0 when the strategy replicates the benchmark on the selected bars, nan if the benchmark never moves in the requested direction (empty subset).

See also

benchmark_summary, beta

Notes

Let \(\mathcal{T}\) the set of bars with \(b_t > 0\) ('up') or \(b_t < 0\) ('down'), and \(n = |\mathcal{T}|\):

\[ \begin{align}\begin{aligned}annGeo(r, \mathcal{T}) = \left(\prod_{t \in \mathcal{T}} (1 + r_t)\right)^{period / n} - 1\\captureRatio = \frac{annGeo(x, \mathcal{T})}{annGeo(b, \mathcal{T})}\end{aligned}\end{align} \]

A value above 1 ('up') means the strategy out-gained the benchmark on the benchmark’s up bars; a value below 1 ('down') means the strategy lost less than the benchmark on its down bars — both read as “better” for the strategy.

Examples

A strategy identical to its benchmark has both capture ratios equal to 1:

>>> import numpy as np
>>> X = np.array([100., 102., 101., 105., 103., 108.])
>>> round(capture_ratio(X, X, side='up'), 6)
1.0
>>> round(capture_ratio(X, X, side='down'), 6)
1.0