In the context of Proposition 6.37, let (left(hat{w}_{t} ight)_{t=1, ldots, T}) be an (mathbb{R}^{N+1})-valued predictable process satisfying

In the context of Proposition 6.37, let \(\left(\hat{w}_{t}\right)_{t=1, \ldots, T}\) be an \(\mathbb{R}^{N+1}\)-valued predictable process satisfying \(\mathbf{1}^{\top} \hat{w}_{t}=1\) for all \(t=1, \ldots, T\) and such that, for every \(t=0,1, \ldots, T-1\),

\[\operatorname{Corr}\left(r_{t+1}^{\top} \hat{w}_{t+1}, \mathbf{u}^{\prime}\left(e_{t+1}\right) \mid \mathscr{F}_{t}\right)=\min _{w \in \mathbb{R}^{N+1}: w^{\top} \mathbf{1}=1} \operatorname{Corr}\left(r_{t+1}^{\top} w, \mathbf{u}^{\prime}\left(e_{t+1}\right) \mid \mathscr{F}_{t}\right) .\]