Derivation: Optimal Alpha Model Weights

Choosing alpha-model weights to maximise the model's risk-adjusted mean IC looks like a hard ratio optimisation in two covariance matrices ($\Phi$ for the factors, $\Sigma_{IC}$ for the ICs). It collapses in two moves: the factor matrix cancels out of the ratio entirely, and the remaining problem is scale-invariant, so its first-order condition pins down only a direction — which turns out to be $\Sigma_{IC}^{-1}\overline{IC}$, mean–variance optimisation in IC space. We do the cancellation, work the differentiation in full, and extract the two-factor closed form used in numerical questions.