Question 1 [25 Marks] Melusi's utility function is stated as follows: U(W) = a + b [n +$]1_y Where a, b, n and \"y are constants and W is wealth. Use the above information to answer the following questions. (a) Calculate Melusi's risk tolerance coefficient where risk tolerance is the reciprocal of absolute risk aversion. [4] (b) What happens to the Melusi' risk tolerance level as wealth increases. Does that make sense? Justify your answer. [5] (c) Calculate the absolute risk aversion coefcient when 1/ = 0.25 and when y = 0.75. Comment on the impact of 1/ on absolute risk aversion. [6] (d) Discuss the concept of stochastic dominance and explain how it is used in decision making. Please use a relevant diagram in your discussion. [10] Question 2 [25 Marks] (a) Consider a portfolio with 3 assets (A, B and C) with expected returns rA= 0.5, IB=1, rc=1.5, respectively. The covariance matrix for the three assets is given by: CAA CAB CAC 1 0.25 0.5 C = CBA CBB CBC = 0.25 2 0.75 CCA CCB Ccc- L 0.5 0.75 3 Use the above information to answer questions (i) and (ii) below. (i) State the minimization problem required if one is interested in solving for the minimum variance portfolio. [3] (ii) Calculate the expected return and variance for the minimum variance portfolio. [10](b) Are the following statements True, False or uncertain? Briey explain your answer. [12] (i) Proper diversification can reduce or eliminate systematic risk. (ii) Diversication reduces the portfolio's expected return because it reduces the portfolio's total risk. (iii)As more securities are added to a portfolio, total risk would typically be expected to fall at a decreasing rate. (iv) The risk-reducing benets of diversification do not occur meaningfully until at least 30 individual securities are included in the portfolio. Question 3 (a) Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16%. A share of stock sells for R50 today. It will pay a dividend of R6 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year? [3] (b)Are the following true or false? Explain your answer. (i) Stocks with a beta of zero offer an expected rate of return of zero. [4] (ii) The CAPM implies that investors require a higher return to hold highly volatile securities. [4] (iii)You can construct a portfolio with a beta of 0.25 by investing 0.25 of the investment budget in bills and the remainder in the market portfolio. [4] (iv) CAPM says that all risky assets must have positive risk premium. [4] (v) The expected return on an investment with a beta of 2.0 is twice as high as the expected return on the market. [3] (vi) If a stock lies below the security market line, it is under-valued. [3]