Alcoa's stock is expected to return 16% in a booming economy, 10% in a normal economy, and -2% in a recession. The probabilities of an economic boom, normal state, or recession are 0.20, 0.70 and 0.10 respectively. Alcoa's beta risk is estimated to be 2.41. Market expecetd retrun is 15% and risk-free is 5%. Show all the steps including formulas to get the answers.

a) What is the expected rate of return on Alcoa?

b) What is the standard deviation of Alcoa?

c) What is the required rate of return on Alcoa?

d) is Alcoa's in equilibrium? why? Is it over-priced, fairly-priced, or underpriced? Would you buy it, do nothing, or sell it?