$1)$ Consider the following expectations for the market and two stocks in two possible equally likely states:

State Market Return Stock A Stock B

Boom $25\%38\%12\%$

Recession $5\%-2\%6\%$

a$.$ What is the beta of each stock?

b$.$ What is the expected return on each stock?

c$.$ Given that the risk$-$free rate is $6\%,$ draw the Security Market Line $($SML$)$ for this economy, and plot the two securities on the graph.

d$.$ Assuming the CAPM holds, by how many percentage points are the securities located above or below the security market line? State for each of the two stocks if the stock is overvalued, correctly priced, or undervalued according to CAPM?