4) (30%) A pension fund manager is considering two mutual funds, D and E, as follows: Expected return, E(r) Standard deviation, o Stock fund (D) 15% 25% Bond fund (E) 7% 10% Suppose a risk averse investor has a utility function, U = E(r) Ao? (where A = 3). The market risk-free rate (rf) is 5% and PDE = 0. [Note: Show all your calculation steps and express your answers up to 2 decimal points in percentage (e.g., 1.23%) or 4 decimal points in number (e.g., 0.0123)]. a) (6%) Suppose that there is a capital market with risk-free rate borrowing and lending. Now the investor is facing an opportunity set formed by risky assets D and E, and risk-free asset. If PDE = 0, what are the weights of D (XD) & E (XE) invested in the Optimal Risky Portfolio (OP or M), the tangent portfolio of rf on the opportunity curve connecting risky assets DE? b) (6%) What are the expected return and variance (o?) of the Optimal Risky Portfolio (OP or M)? [Note: you are required to compute your answers from XD, XE and XE found in (a) above, not from Xop and XE.) c) (3%) The investor choice her Optimal Complete Portfolio (OC) by maximizing her expected utility. What are the weights of OP (y) & rf (1-y) in her Optimal Complete Portfolio (OC)? d) (5%) What are the expected return and variance (o?) of the Optimal Complete Portfolio (OC)? (4%) Is she a lender (or borrower)? Why? (1%) e) (5%) What is the breakeven coefficient of risk aversion (A*) which causes the investor to change from lender (borrower) to borrower (lender)? Briefly explain the reason for the change. f) (5%) Illustrate your answers in (a) to (d) graphically with proper labeling (i.e., details of expected returns, standard deviations of assets D, E, rf, OP, OC, etc.). 4) (30%) A pension fund manager is considering two mutual funds, D and E, as follows: Expected return, E(r) Standard deviation, o Stock fund (D) 15% 25% Bond fund (E) 7% 10% Suppose a risk averse investor has a utility function, U = E(r) Ao? (where A = 3). The market risk-free rate (rf) is 5% and PDE = 0. [Note: Show all your calculation steps and express your answers up to 2 decimal points in percentage (e.g., 1.23%) or 4 decimal points in number (e.g., 0.0123)]. a) (6%) Suppose that there is a capital market with risk-free rate borrowing and lending. Now the investor is facing an opportunity set formed by risky assets D and E, and risk-free asset. If PDE = 0, what are the weights of D (XD) & E (XE) invested in the Optimal Risky Portfolio (OP or M), the tangent portfolio of rf on the opportunity curve connecting risky assets DE? b) (6%) What are the expected return and variance (o?) of the Optimal Risky Portfolio (OP or M)? [Note: you are required to compute your answers from XD, XE and XE found in (a) above, not from Xop and XE.) c) (3%) The investor choice her Optimal Complete Portfolio (OC) by maximizing her expected utility. What are the weights of OP (y) & rf (1-y) in her Optimal Complete Portfolio (OC)? d) (5%) What are the expected return and variance (o?) of the Optimal Complete Portfolio (OC)? (4%) Is she a lender (or borrower)? Why? (1%) e) (5%) What is the breakeven coefficient of risk aversion (A*) which causes the investor to change from lender (borrower) to borrower (lender)? Briefly explain the reason for the change. f) (5%) Illustrate your answers in (a) to (d) graphically with proper labeling (i.e., details of expected returns, standard deviations of assets D, E, rf, OP, OC, etc.)