numeraire.core.stats.grs_test

numeraire.core.stats.grs_test(assets: DataFrame, factors: DataFrame) → GRSResult

Gibbons-Ross-Shanken (1989) test that all time-series alphas are jointly zero.

assets are (date x N) test-asset excess returns, factors (date x K) factor excess returns on the identical index. The statistic (multifactor form):

F = (T - N - K) / N * (a' Sigma^-1 a) / (1 + Sh(F)^2)  ~  F(N, T - N - K)

with Sigma the MLE residual covariance and Sh(F)^2 = mu' Omega^-1 mu the factors’ max squared sample Sharpe (MLE moments). Requires T > N + K.