Consider an economy with two traded assets with returns \(\tilde{r}_{1}\) and \(\tilde{r}_{2}\) together with a market portfolio with return \(\tilde{r}^{m}\). The covariance matrix of the random vector \(\left(\tilde{r}_{1}, \tilde{r}_{2}, \tilde{r}^{m}\right)\) is given by

\[\left(\begin{array}{ccc}0.16 & 0.02 & 0.064 \\0.02 & 0.09 & 0.032 \\0.064 & 0.032 & 0.040\end{array}\right)\]

Moreover, it holds that \(\mathbb{E}\left[\tilde{r}^{m}\right]=1.12\) and \(r_{f}=1.04\). Consider the portfolio \(w\) investing \(3 / 4\) and \(1 / 4\) in the first and in the second assets, respectively.
(i) Compute the \(\beta\) coefficients of the first and of the second asset as well as of the portfolio \(w\) with respect to the market portfolio.
(ii) Write the equation defining the Security Market Line.
(iii) Compute the risk premium of the two assets as well as of the portfolio \(w\).