Consider an economy with (N) risky assets with returns (left(tilde{r}_{1}, ldots, tilde{r}_{N} ight)) and a risk free

Consider an economy with \(N\) risky assets with returns \(\left(\tilde{r}_{1}, \ldots, \tilde{r}_{N}\right)\) and a risk free asset with return \(r_{f}\), with \(r_{f}<\mathbb{E}\left[\tilde{r}_{n}\right]\) for all \(n=1, \ldots, N\). Show that the tangent portfolio \(w^{\mathrm{e}}\) is diversified if the risky asset returns are uncorrelated.