.ten questions, please see pdf

the attached PDF has 10 questions

1. Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 20% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%. Calculate the utility levels of each portfolio for an investor with A = 3. Assume the utility function is U = E(r) 0.5 A2. (Do not round intermediate calculations. Round your answers to 4 decimal places.) WBills 0.0 0.2 0.4 0.6 0.8 1.0 WIndex 1.0 0.8 0.6 0.4 0.2 0.0 Worksheet U(A = 3) Difficulty: 2 Intermediate 2. Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client's degree of risk aversion is A = 3.5, assuming a utility function U = E(r) - A. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.) Investment proportion y % b. What is the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) % % Expected return Standard deviation Worksheet Difficulty: 2 Intermediate 3. Refer the table below on the average risk premium of the S&P 500 over T-bills, and the standard deviation of that risk premium. Suppose that the S&P 500 is your risky portfolio. Average Annual Returns Period 1926-2012 1989-2012 1968-1988 1947-1967 1926-1946 S&P 500 Portfolio 11.67 11.10 10.91 15.35 9.40 1-Month T-Bills 3.58 3.52 7.48 2.28 1.04 Risk Premium 8.10 7.59 3.44 13.08 8.36 S&P 500 Portfolio Sharpe Ratio Standard (Reward-toDeviation Volatility) 20.48 0.40 18.22 0.42 16.71 0.21 17.66 0.74 27.95 0.30 Probability* 0.94 0.50 0.24 0.71 Average annual return on large stocks and 1-month T-bills; standard deviation and Sharpe ratio of large stocks over time *The probability that the estimate of the Sharpe ratio over 1926-2012 equals the true value and that we observe the reported, or an even more different Sharpe ratio for the subperiod. a. If your risk-aversion coefficient is A = 4 and you believe that the entire 1926-2012 period is representative of future expected performance, what fraction of your portfolio should be allocated to Tbills and what fraction to equity? Assume your utility function is U = E(r) - 0.5 A2. (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) T-bills Equity % % b. If your risk-aversion coefficient is A = 4 and you believe that the entire 1968-1988 period is representative of future expected performance, what fraction of your portfolio should be allocated to Tbills and what fraction to equity? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.) T-bills % Equity Worksheet % Difficulty: 2 Intermediate 4. In a return-standard deviation space, which of the following statements is(are) true for risk-averse investors? (The vertical and horizontal lines are referred to as the expected return-axis and the standard deviation-axis, respectively.) I) An investor's own indifference curves might intersect. II) Indifference curves have negative slopes. III) In a set of indifference curves, the highest offers the greatest utility. IV) Indifference curves of two investors might intersect. I and II only II and III only I and IV only III and IV only None of the options Multiple Choice Diculty: 2 Intermediate 5. Elias is a risk-averse investor. David is a less risk-averse investor than Elias. Therefore, for the same risk, David requires a higher rate of return than Elias. for the same return, Elias tolerates higher risk than David. for the same risk, Elias requires a lower rate of return than David. for the same return, David tolerates higher risk than Elias. Cannot be determined Multiple Choice Diculty: 2 Intermediate 6. Assume an investor with the following utility function: U = E(r) - 3/2(s2). To maximize her expected utility, she would choose the asset with an expected rate of return of _______ and a standard deviation of ________, respectively. 12%; 20% 10%; 15% 10%; 10% 8%; 10% Multiple Choice Diculty: 2 Intermediate 7. Assume an investor with the following utility function: U = E(r) - 3/2(s2). To maximize her expected utility, which one of the following investment alternatives would she choose? A portfolio that pays 10% with a 60% probability or 5% with 40% probability. A portfolio that pays 10% with 40% probability or 5% with a 60% probability. A portfolio that pays 12% with 60% probability or 5% with 40% probability. A portfolio that pays 12% with 40% probability or 5% with 60% probability. Multiple Choice Diculty: 3 Challenge 8. The standard deviation of the portfolio is always equal to the weighted average of the standard deviations of the assets in the portfolio. True False True / False Diculty: 2 Intermediate 9. Use the below information to answer the following question. U = E(r) - (A/2)s2,where A = 4.0. The variable (A) in the utility function represents the investor's return requirement. investor's aversion to risk. certainty-equivalent rate of the portfolio. minimum required utility of the portfolio. Multiple Choice Diculty: 2 Intermediate 10. Given the capital allocation line, an investor's optimal portfolio is the portfolio that maximizes her expected prot. maximizes her risk. minimizes both her risk and return. maximizes her expected utility. None of the options Multiple Choice Diculty: 2 Intermediate