There are two stocks in the market, stock A and stock B$.$ The price of stock A today is Shs$75.$The price of stock A next year will be Shs$63$ if the economy is in a recession, Shs$83$ if the economy is normal, and Shs$96$ if the economy is expanding. The probabilities of recession, normal times, and expansion are $\mathrm{.}2,\mathrm{.}6,$ and $\mathrm{.}2,$ respectively. Stock A pays no dividends and has a correlation of $8$ with the market portfolio. Stock B has an expected return of $13$ percent, a standard deviation of $34$ percent, a correlation with the market portfolio of $\mathrm{.}25,$ and a correlation with stock A of $48.$ The market portfolio has a standard deviation of $18$ percent. Assume the CAPM holds.a$).$ If you are a typical, risk$-$averse investor with a well$-$diversified portfolio, which stock would you prefer? Why?$(10$ marks$)$b$).$ What are the expected return and standard deviation of a portfolio consisting of $70$ percent of stock A and $30$ percent of stock B$?$c$).$ A good investor should be aware of the Shifting Effect of interest rates in the financial market. Comment on the statement$(5$ marks$)(10$ marks$)$