Section A This section is made up two questions. Answer BOTH questions. Question 1 [30 Marks] (a) Consider a portfolio with 3 assets (A, B and C) with expected returns rA= 0.5, rB=1, rc=l.5, respectively. The covariance matrix for the three assets is given by: C .4 .4 3:! C33 Bf" 1/4 2 3/4 CAB CW 1 1/4 1/2 C C CO Cm CFC 1/2 1/4 3 C: Use the above information to answer questions (1') and (if) 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. [12] (b) An agent faces a risky situation in which she can lose amount of money with probabilities given in the following table: Loss (in South African Rands) Probability 1000 0.1 2000 0.2 3000 0.35 5000 0.20 6000 0.15 The agent has a utility function of wealth of the form: W\"? U(W)=1_? +2 , where W is the agent's wealth. His initial wealth is R10 000 and his 7 is equal to 1.2. (i) Calculate the certainty equivalent amount of this prospect for this agent? [5] (ii) Calculate risk premium for this agent. [3] (iii) What would be the certainty equivalent amount for this agent if the agent was risk neutral'? [3] (c) Describe the risk premium of an agent whose utility of wealth has the form implied by the following properties: U'(W) > 0 and U\"(W) > 0. [4] Question 2 [30 Marks] (a) Show that risk aversion implies diminishing marginal utility of wealth. Please use a diagram in your demonstration. [10] (b) In Machina (1987) it is shown that the VNM expected utility function is linear in probabilities. Individuals A and B have different levels of risk tolerance. Individual A has a utility function which is such that: U[E(W)]>E[U(W)]. Individual B has a utility function which is such that: U[E(W)]