Given the information of a portfolio comprised of three stocks X, Y and Z as shown below:

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? (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.

(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 Ys 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.

State of Economy Probability of State of Economy 0.18 0.54 0.28 Stock X Rate of Return 0.03 0.05 0.09 Stock Y Rate of Return 0.28 0.17 -0.16 Stock Z Rate of Return 0.40 0.15 -0.33 Boom Normal Bust