Consider three risky assets with expected returns, standard deviations and correlations with the market portfolio given by the following vectors:

\[\mu=\left[\begin{array}{c}1.07 \\1.08 \\1.1\end{array}\right] \quad \sigma=\left[\begin{array}{c}0.3 \\0.2 \\0.15\end{array}\right] \quad ho=\left[\begin{array}{l}0.2 \\0.4 \\0.8\end{array}\right] \text {. }\]

Suppose that the market portfolio is characterized by expected return \(\mu^{m}=1.09\) and standard deviation \(\sigma^{m}=0.1\).

(i) Does the CAPM relation hold if the risk free rate is equal to \(r_{f}=1.04\) ?

(ii) Compute the risk premium for an asset with \(\beta=-0.5\).

(iii) Show that in equilibrium there cannot exist an asset with expected return \(\mu^{\prime}=\) 1.2 and \(\beta^{\prime}=0.5\).