Assume the market portfolio has expected rate of return $\bar{r}_{\mathrm{m}}=0.12$ and standard deviation $\sigma_{\mathrm{m}}=0.3$. The risk-free rate is $r_{f}=0.02$. There is another stock, $\mathrm{a}$, in the market with $\bar{\sigma}_{\mathrm{a}}=0.6, ho_{\mathrm{am}}=0.1$.

(a) Find $\bar{r}_{\mathrm{a}}$ and $\beta_{\mathrm{a}}$.

(b) A new asset, $\mathrm{b}$, has the same expected return as a but a standard deviation of $\sigma_{\mathrm{b}}=0.8$. What is the idiosyncratic error of $b$ ?

(c) Another asset, $\mathrm{c}$, enters the market with $ho_{\mathrm{c}}=0.8$. What percentage of the risk of $\mathrm{c}$ is idiosyncratic?