Let \(\mu>A / C\) and consider the following optimization problem:

\[\begin{equation*}\max _{w \in \Delta_{N}} \frac{w^{\top} e-\mu}{\sqrt{w^{\top} V w}} \tag{3.56}\end{equation*}\]

corresponding to the maximization of the Sharpe ratio with respect to the reference rate of return \(\mu\) over the set of all portfolios investing in the \(N\) risky assets. Prove that, for any \(\mu>A / C\), the solution \(w^{*}\) to problem (3.56) is given by \[\begin{equation*}
w^{*}=g+h \frac{\mu A-B}{\mu C-A}=\frac{V^{-1}(e-\mathbf{1} \mu)}{\mathbf{1}^{\top} V^{-1}(e-\mathbf{1} \mu)} . \tag{3.57}
\end{equation*}\]