Suppose that you are considering investing in two stocks for one year: Stock A and Stock B$.$ The current price of stock A is $$60$ and analysts forecast a price of $$80$ in one year if the economy is booming, or $$50$ if the economy enters a recession. The current price of Stock B is $$30$ and analysts forecasts a price of $$36$ in one year if the economy is booming and a price of $$32$ if the economy is in a recession. You believe that the probabilities of a recession is $40\%$ and boom is $60\%.$ Stocks A and B do not pay dividends

$(***$ SHOW all your work for partial credit. If you use Excel, please upload the spreadsheet, OR solve the problem manually and upload a pdf $($preferred$)$ file with answers. Emailing them $*$does not$*$ count for partial credit.$)$ There is no credit for submissions that do not show all the work.

a$)$ Calculate the expected return for each stock based on these forecasts and report your results.

b$)$ Suppose that you decide to invest $$40,000$ in stock A and $$160,000$ in stock B$.$ Find the expected return and standard deviation of the portfolio.

c$)$ Assume that stock A has beta $=1\mathrm{.}5$ and stock B has beta$=1\mathrm{.}1.$ Further, the expected return on the market is $12\%$ and the risk free is $1\mathrm{.}5\%.$ Calculate the expected return for both stocks if they were correctly priced $($i$.$e$.,$ using the CAPM$).$

d$)$ Compare the expected returns given by the analyst $($that you computed in $$a$)$ with those when you calculated in part c in order to identify if these stocks $($Stock A and$/$or Stock B$)$ are undervalued or overvalued and explain why