Proposition IA.1, p. IA2 — mean-optimal intensity tends to one

Fix the number of stocks $N$, risk aversion $\gamma$, population variances $\sigma_g^2$ and $\psi^2$, GMV mean $\mu_g$, and robustness weight $\lambda$. If $N\geq2$, $\gamma>0$, $\sigma_g^2>0$, and $\psi^2>0$, then the mean-maximizing intensity in (IA3) obeys

This gives the asymptotic mean benchmark for the robust shrinkage intensity.

Formalization Note The paper omits the necessary condition $\psi^2>0$: at $\psi^2=0$, formula (IA3) gives $\kappa_E(T)=0$. The estimator-consistency sentence requires a sample-portfolio model and is outside this closed-form result. The OOSU moments are the closed forms from Proposition IA.1 and Proposition 1; their probabilistic identification is outside this mission.