beta¶

Defined in fynance.metrics

beta(X, B, period=252)[source]

OLS slope of the strategy’s returns on the benchmark’s returns.

Parameters:

Xnp.ndarray[float64, ndim=1]: Strategy price/level curve.
Bnp.ndarray[float64, ndim=1]: Benchmark price/level curve, same length as X.
periodint, optional: Unused by beta itself; accepted for API consistency. Default 252.

Returns:

float: OLS beta of the strategy against the benchmark. 0 when the benchmark has zero variance and the strategy’s covariance with it is also zero, +inf/-inf when the benchmark has zero variance and the covariance is non-zero (see _safe_ratio).

See also

alpha, roll_beta_benchmark

Notes

With \(x\) the strategy’s simple returns and \(b\) the benchmark’s simple returns (see module docstring):

\[\beta = \frac{Cov(x, b)}{Var(b)}\]

period does not affect \(\beta\) (a slope is scale-free); it is accepted for signature consistency with the rest of this module (e.g. alpha calls beta internally).

Examples

>>> import numpy as np
>>> rng = np.random.default_rng(42)
>>> b_ret = rng.normal(0., 0.01, 999)
>>> B = 100. * np.cumprod(1. + b_ret)
>>> B = np.concatenate([[100.], B])
>>> x_ret = 2. * _compute_returns(B, False)[1:]
>>> X = 100. * np.cumprod(1. + x_ret)
>>> X = np.concatenate([[100.], X])
>>> round(beta(X, B), 4)
2.0