Suppose there are three possible states of the economy next year: boom, normal, and recession.

A stock's price and dividend payout in each of the states is as follows. The probability of each

state is also listed. A share is currently trading for $$40.$

a$.$ Calculate the expected HPR and standard deviation of investing your entire portfolio in

this company.

b$.$ Calculate the expected HPR and standard deviation of investing half of your portfolio in

this company and half in Treasury bills that return a riskless $4\%$ annually.