Please answer and show work! Much appreciated
1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate fund, and the third is a (riskless) T-bill money market fund that yields a rate of 8%. The probability distributions of the risky funds have the following characteristics: Expected return (%) Standard Deviation (%) Stock fund (Rs) 20 30 Bond fund (RB) 12 15 The correlation between the fund returns is .10. (a) What are the investment proportions in the minimum variance frontier portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return? (b) Tabulate the mean and standard deviations of portfolios of the two risky funds, when you use investment proportions for the stock funds of 0 to 100% in increments of 10%. Draw the mean-variance frontier for portfolios of the two risky funds. (c) Solve numerically for the proportions of each risky asset and for the expected return and standard deviation of the optimal risky portfolio (the portfolio of the risky assets with the highest-reward to variability ratio, or Sharpe ratio). (d) What is the reward-to-variability ratio (Sharpe ratio of the best feasible capital allocation line (CAL)? (e) You require that your portfolio of all three assets yield an expected return of 14% and that it be efficient on the best feasible CAL. What is the standard deviation of your portfolio and what is the proportion invested in each of the three types of assets? (f) If you were to use only the two risky funds, and still require an expected return of 14%, what share would you invest in each? Compare the standard deviation of this portfolio to that of the optimal portfolio found in the previous part (part e). What do you conclude? (g) Solve for the optimal portfolio (of the three assets) of an investor with mean variance preferences U(R) = E(R) 4. Var(R), where R represents the portfolio return, measured in decimal points. 1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate fund, and the third is a (riskless) T-bill money market fund that yields a rate of 8%. The probability distributions of the risky funds have the following characteristics: Expected return (%) Standard Deviation (%) Stock fund (Rs) 20 30 Bond fund (RB) 12 15 The correlation between the fund returns is .10. (a) What are the investment proportions in the minimum variance frontier portfolio of the two risky funds, and what is the expected value and standard deviation of its rate of return? (b) Tabulate the mean and standard deviations of portfolios of the two risky funds, when you use investment proportions for the stock funds of 0 to 100% in increments of 10%. Draw the mean-variance frontier for portfolios of the two risky funds. (c) Solve numerically for the proportions of each risky asset and for the expected return and standard deviation of the optimal risky portfolio (the portfolio of the risky assets with the highest-reward to variability ratio, or Sharpe ratio). (d) What is the reward-to-variability ratio (Sharpe ratio of the best feasible capital allocation line (CAL)? (e) You require that your portfolio of all three assets yield an expected return of 14% and that it be efficient on the best feasible CAL. What is the standard deviation of your portfolio and what is the proportion invested in each of the three types of assets? (f) If you were to use only the two risky funds, and still require an expected return of 14%, what share would you invest in each? Compare the standard deviation of this portfolio to that of the optimal portfolio found in the previous part (part e). What do you conclude? (g) Solve for the optimal portfolio (of the three assets) of an investor with mean variance preferences U(R) = E(R) 4. Var(R), where R represents the portfolio return, measured in decimal points
