Covariance between market and security. Capital asset market model If there are two risky assets (A&B) in equal supply in the market M = 1/2(A+B) Show that $\sigma_{AM} = 1/2(\sigma_A^2 + \sigma_{AB})$ THank you

**Hint:** You can treat $A$ and $B$ as (dependent) random variables. Then it is asked to calculate

$$\sigma_{AM}=Cov\left(A,\frac12(A+B)\right)$$

where $Cov(A,A)=\sigma_A^2$ and $Cov(A,B)=\sigma_{AB}$

$\texttt{Additional hint}:$ You can derive the result straightforward if you use the property that the covariance is $\color{blue}{\texttt{bilinear}}$.