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Question 3 Part 1 Given the information of a portfolio comprised of three stocks X, Y and Z as shown below: State of Economy Probability Stock X Stock Y Stock Z of State of Rate of Rate of Rate of Economy Return Return Return Boom 0.18 0.03 0.28 0.40 Normal 0.54 0.05 0.17 0.15 Bust 0.28 0.09 -0.16 -0.33 Required: (a) If the portfolio is invested 35 percent each in Stock X and Y, as well as 30 percent in Stock Z respectively, what are the portfolio's expected return, variance and standard deviation? (6 marks) (b) If the above portfolio has a positive investment in Stock X, Y and Z, is the expected return of the portfolio always greater than the expected return of each individual Stock of X, Y and Z? Illustrate with relevant calculations and conclude your answer within 40 words. (7 marks) (c) Based on CAPM, the expected returns on Stock X, Y and Z are 8.1 percent, 10.5 percent and 16.9 percent, respectively. Assume that the expected rate of return from the Treasury Bill is 2.5 percent and Stock Y's price tends to move with the same magnitude of the overall market. Under the market equilibrium state, calculate the betas of Stock X and Z respectively with explanations in 45 words. (10 marks) Part II On Monday, 1 Mar, Del Luna Hotel's board of director declares a dividend of $2.53 per share payable on Wednesday, 14 April, to shareholders as of Wednesday, 31 Mar that the holders of record are determined Required: (a) When is the ex-dividend date? You purchased 5,000 shares of Del Luna Hotel at $150 per share. The stock sells for $193 per share just before the ex-dividend date. Assuming no taxes, how much will your stock value in total be worth on the ex-dividend date? (6 marks) (b) The stock price of another hotel is currently selling at S150 per share. Assuming no market imperfections or tax effects exist, what will be the stock price per share after: i) Del Luna Hotel has a four-for-six stock split? (2 marks) (ii) Del Luna Hotel has a 29.5 percent stock dividend? (2 marks)