Q1.

David has the following information on two stocks, Stock A and B. He is wondering if he can build a portfolio with these two stocks which can beat the market portfolio,

	Probibility	Return in Stock A	Return in Stock B
Boom	0.35	16%	40%
Normal	0.5	10%	8%
Recession	0.15	5%	-10%

To beat the market portfolio, David's idea is that his portfolio has to exhibit at least one of the following 2 features: Either it has higher return but the same risk, or it has lower risk but the same return compared with the market portfolio. If he cannot build such a portfolio, he would invest all his money in the market portfolio outright.

Assume CAPM is valid and the two stocks are correctly priced. The expected return on the market and the risk-free rate are 12% and 3% respectively.

• Given that the E(R_A) =11.35% E(R^B) =16.5% , Standard deviation of A=3.81%,Standard deviation of B=18.30%;beta of A:= 0.9278,beta of B =1.5

Davidis examining the following scenarios to ascertain whether he can build a portfolio with these two stocks which can beat the market portfolio,

• i)Hestructureshisportfolioinsuchawaythatithasthesameexpectedreturnasthemarketportfolio.Whatshouldtheportfolioweightsofthesetwostocksbe?Whatistheportfoliobeta?
• ii) Alternatively, he structures his portfolio to have the same risk as the market portfolio. What should the portfolio weights of these two stocks be? What is the portfolio return?

• iii) Based on the answers in part b, conclude if David can build a portfolio with these two stocks that beats the market portfolio. Use CAPM theory to explain your conclusion.