Consider the following two scenarios in the economy and the returns in each scenario for the market portfolio, an aggressive stock $A,$ and a defensive stock $B.$

$\backslash$table$[[$Rate of Return$],[$Scenario$,$Market,Aggressive Stock A$,$Defensive Stock B$],[,,,],[$Bust$,-8$ percent,$-10$ percent,$-6$ percent$],[$Boom$,32$ percent,$38$ percent,$24$ percent$],[,,,]]$

Required:

a$)$ Find the beta of each stock. Explain in what way is Stock B defensive.

$(7$ marks$)$

b$)$ If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.

$(6$ marks$)$

c$)$ If the Treasury bill rate is $4$ percent, calculate the CAPM for both stocks

$(4$ marks$)$

d$)$ Based on your answers above, which stock is worth buying Explain your decision.

$(3$ marks$)$