Consider a world in which there are only two risky assets, $A$ and $B$, and a risk-free asset $F$. The two risky assets are in equal supply in the market; that is, $M=\frac{1}{2}(A+B)$. The following information is known: $r_{F}=10, \sigma_{A}^{2}=04, \sigma_{A B}=01, \sigma_{B}^{2}=02$, and $\bar{r}_{M}=.18$

(a) Find a general expression (without substituting values) for $\sigma_{M}^{2}, \beta_{A}$, and $\beta_{B}$.

(b) According to the CAPM, what are the numerical values of $\bar{r}_{A}$ and $\bar{r}_{B}$ ?