Concept explainers
Based on current dividend yields and expected
a. If you currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? Explain.
b. If instead you e0u1d invest only in T-bills and one of these portfolios, which would you choose?
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Essentials Of Investments
- Based on current dividend yields and expected capital gains, the expected rates or return on portfolios A and B are 12% and 18%, respectively. The beta of A is 0.7 while that of B is 1.6. The T-bill rate is currently 4% while the expected rate of return of the S&P500 Index is 13%. The standard deviation of portfolio A is 14% annually, while that of B is 26%, and that of the index is 15%. If instead you could invest only in bills and one of these porfolios, which would you choose? Use the sharpe ratio to make your desicion.arrow_forwardBased on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 13% and 15% respectively. The beta of A is 0.8 while that of B is 1.3. The T-bill rate is currently 7% while the expected rate of return of the S&P500 index is at 14%. The standard deviation of portfolio A and B are 20% and 41%, and that of the index is 30%. Compare the performance of the two portfolios relative to the market using the four performance measures: Sharpe ratio, Treynor ratio, Jensen's Alpha and M?. Comment on the calculated results. а. b. Would you choose to add A or B to your holdings if you currently hold a market-index portfolio? Justify your decision. Which portfolio would you choose if instead you could invest only in Treasury bills and one of these portfolios? Explain your answer. с. Could a portfolio show a higher Sharpe ratio but a lower M² measure at the same time? Explain your answer. с.arrow_forwardConsider two types of assets: market portfolio (M) and stock A. The expected return is 8% and standard deviation of the market portfolio is 15%. The risk-free rate is 2%. The standard deviation of market portfolio returns is 15%. The standard deviation of stock A is 30%, and the beta coefficient is 1. Draw the capital market line and show the position of stock A.arrow_forward
- 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 21% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 2%. Calculate the utility levels of each portfolio for an investor with A=2. Assume the utility function is U = E(r) Note: Do not round intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be indicated by - 0.5 × Ag². a minus sign. 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 U(A = 2)arrow_forwardConsider 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 31% per year. Assume these values are representative of Investors' expectations for future performance and that the current T-bill rate is 3%. Calculate the utility levels of each portfolio for an Investor with A = 2. Assume the utility function is u = E(r) - 8.5 x Ao². Note: Do not round Intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be Indicated by a minus sign. W Bills 0.0 0.2 0.4 0.6 0.8 1.0 Windex 1.0 0.8 0.6 0.4 Oo 0.2 0.0 U(A = 2)arrow_forwardConsider 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 28% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%. Calculate the utility levels of each portfolio for an investor with A-2. Assume the utility function is U = E(r) - 0.5 x Ao². (Do not round intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) 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 U(A=2)arrow_forward
- 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 21% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 4%. Calculate the utility levels of each portfolio for an investor with A = 3. Assume the utility function is u = E(r) - 0.5 × Ao². (Negative amounts should be indicated by a minus sign. 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 U(A = 3)arrow_forwardConsider 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 33% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 4%. Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U = E(r) Note: Do not round intermediate calculations. Round your answers to 4 decimal places. Negative amounts should be indicated by a minus sign. - 0.5 × Ag². X Answer is complete but not entirely correct. WIndex U(A = 2) 0.0111 0.0504 0.0808 x 0.1026 0.1164 X 0.1200 X WBills 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.8 0.6 0.4 0.2 0.0arrow_forwardSecurity F has an expected return of 10 percent and a standard deviation of 43 percent per year. Security G has an expected return of 15 percent and a standard deviation of 62 percent per year. Required: (a) What is the expected return on a portfolio composed of 30 percent of Security F and 70 percent of Security G? (b) If the correlation between the returns of Security F and Security G is .25, what is the standard deviation of the portfolio described in part (a)?arrow_forward
- Solve step by steparrow_forwardConsider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 90 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 = round intermediate calculations. Round your answers to 4 decimal places.) E(r) 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 U(A = 3) 0.5 × Ao². (Do notarrow_forwardThe Treasury bill rate is 3%, and the expected return on the market portfolio is 14%. According to the capital asset pricing model: a. What is the risk premium on the market?b. What is the required return on an investment with a beta of 1.8? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)c. If an investment with a beta of 0.8 offers an expected return of 8.2%, does it have a positive or negative NPV?d. If the market expects a return of 12.9% from stock X, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places.)arrow_forward
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