$4.$ Consider the following table, which gives a security analyst$$s expected return on two stocks for two particular market returns:

i$.$ What are the betas of the two stocks?

ii$.$ What is the expected rate of return on each stock if the market return is equally likely to be $5\%$ or $20\%?$

iii. If the T$-$bill rate is $8\%$ and the market return is equally likely to be $5\%$ or $20\%,$ draw the SML for this economy.

iv$.$ Plot the two securities on the SML graph.

v$.$ What are the alphas of each?

vi$.$ What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm$$s stock?