information_ratio¶

Defined in fynance.metrics

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

Annualized mean active return over the tracking error.

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

Returns:

float: Annualized information ratio, or 0.0 when the tracking error is zero.

See also

tracking_error, beta

Notes

With \(x\)/\(b\) the strategy’s/benchmark’s simple returns and \(TE\) the tracking error (tracking_error):

\[IR = \frac{period \times E[x - b]}{TE}\]

Zero-tracking-error convention. Unlike sharpe/calmar (which return +inf/ -inf on a zero denominator), a zero tracking error means the strategy is the benchmark bar-for-bar — there is no active bet to size a ratio on — so IR is defined as 0.0 regardless of the (necessarily zero) numerator, rather than propagating a signed infinity.

Examples

A strategy identical to its benchmark has a zero information ratio (no active risk to be compensated for):

>>> import numpy as np
>>> X = np.array([100., 102., 101., 105., 110.])
>>> information_ratio(X, X)
0.0