qis.regimes.compute_regime_kappa

qis.regimes.compute_regime_kappa(af, tail_prob=0.16, nu=None)[source]

Kappa of the symmetric three-bucket partition, the Sharpe cost of one unit of correlation.

kappa = sqrt(af) phi(z_{1 - tail_prob}) under the Gaussian null: 0.487 at af = 4 and 0.843 at af = 12 on the one-sigma cut. A unit-variance Student-t margin puts more mass near the centre and in the far tails, so at the one-sigma cut its kappa lies below the Gaussian value and rises to it as nu grows, while at tail probabilities of 10% and less it lies above and falls to it.

Parameters:

  • af (float) – annualisation factor of the periodic returns

  • tail_prob (float) – probability of each tail bucket, in (0, 0.5)

  • nu (float | None) – degrees of freedom of a joint Student-t null; None is the Gaussian null

Returns:

kappa, the Bull loading and minus the Bear loading

Raises:

ValueError – if tail_prob is outside (0, 0.5)

Return type:

float