Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 5, Problem 1CP
A portfolio of nondividend-paying stocks earned a geometric mean return of 5% between 1, January 1, 2010, and December 31, 2016. The arithmetic mean return for the same period was 6%. If the market value of the portfolio at the beginning of 2010 was $100, 000, what was the market value of the portfolio at the end of 2016? (LO 5-1)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Stocks A and B have the following historical returns:
Stock A's Returns
(24.25%)
18.50
38.67
14.33
39.13
Year
2015
2016
2017
2018
2019
Assume the risk-free rate during this time was 3.5%. What are the Sharpe ratios for
Stocks A and B and the portfolio over this time period using their average returns?
Answers:
a) Sharpe ratio for Stock A
b) Sharpe ratio for Stock B
0.5332
0.8839
c) Sharpe ratio for Portfolio AB
Stock B's Returns
5.50%
26.73
48.25
(4.50)
43.86
Note: enter your answers with 4 decimal places
Using the data in the table, consider a portfolio that maintains a 35% weight on stock A and a 65% weight on stock B.
a. What is the return each year of this portfolio? (2010-2015)
b. Based on your results from part (a), compute the average return and volatility of the portfolio.
c. Show that (i) the average return of the portfolio is equal to the (weighted) average of the average returns of the two stocks, and (ii) the volatility of the portfolio equals the same result as from the calculation in Eq. 11.9.
d. Explain why the portfolio has a lower volatility than the average volatility of the two stocks.
Stocks A and B have the following historical returns:
Year
Stock A’s Returns
Stock B’s Returns
2015
(24.25%)
5.50%
2016
18.50
26.73
2017
38.67
48.25
2018
14.33
(4.50)
2019
39.13
43.86
Assume the risk-free rate during this time was 3.5%. What are the Sharpe ratios for Stocks A and B and the portfolio over this time period using their average returns?
Answers:
a) Sharpe ratio for Stock A =
b) Sharpe ratio for Stock B =
c) Sharpe ratio for Portfolio AB =
Chapter 5 Solutions
Essentials Of Investments
Ch. 5 - Prob. 1PSCh. 5 - The real interest rate approximately equals the...Ch. 5 - When estimating a Sharpe ratio, would it make...Ch. 5 - You’ve just decided upon your capital allocation...Ch. 5 - Prob. 5PSCh. 5 - The stock of Business Adventures sells for $40 a...Ch. 5 - Prob. 7PSCh. 5 - a. Suppose you forecast that the standard...Ch. 5 - Using the historical risk premiums as your guide,...Ch. 5 - What has been the historical average real rate of...
Ch. 5 - Consider a risky portfolio. The end-of-year cash...Ch. 5 - For Problems 12-16, assume that you manage a risky...Ch. 5 - For Problems 12-16, assume that you manage a risky...Ch. 5 - For Problems 12-16, assume that you manage a risky...Ch. 5 - For Problems 12-16, assume that you manage a risky...Ch. 5 - For Problems 12-16, assume that you manage a risky...Ch. 5 - Prob. 17PSCh. 5 - You manage an equity fund with an expected risk...Ch. 5 - What is the reward-to--volatility (Sharpe) ratio...Ch. 5 - A portfolio of nondividend-paying stocks earned a...Ch. 5 - Which of the following statements about the...Ch. 5 - Which of the following statements reflects the...Ch. 5 - Use the following data in answering CFA Questions...Ch. 5 - Prob. 5CPCh. 5 - Lise the following data in answerifng CFA Question...Ch. 5 - Use the following scenario analysis for stocks X...Ch. 5 - Prob. 8CPCh. 5 - Use the following scenario analysis for stocks X...Ch. 5 - 10. Probabilities for three states of the economy...Ch. 5 - 11. An analyst estimates that a stock has the...Ch. 5 - Prob. 1WMCh. 5 - Prob. 2WMCh. 5 - Prob. 3WM
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Similar questions
- You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%.a. What are the betas of Stocks X and Y?b. What are the required rates of return on Stocks X and Y?c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?arrow_forward9. You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, Stock A and Stock B, have the following historical returns: Return Year Stock A Stock B 2014 -0.2 -0.05 2015 0.42 0.15 2016 0.2 -0.13 2017 -0.08 0.5 2018 0.25 0.12 a. Calculate the average rate of return for each stock during the 5-year period. b. Suppose you held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? c. Calculate the standard deviation of returns for each stock and for the portfolio.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 34% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 2%. x Ao². Calculate the utility levels of each portfolio for an investor with A = 2. Assume the utility function is U = E(r) - 0.5 × 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 0.2 0.0 U(A = 2)arrow_forward
- You have the following rates of return for a risky portfolio for several recent years: 2013 35.23% 2014 18.62% 2015 —9.82% 2016 23.45% If you Invested $1000 alike beginning 2013, what would your investment be worth at the end of 2016 (using geometnc average return)arrow_forwardIf D1 = $1.25, g (which is constant) = 5.5%, and P0 = $44, what is the stock's expected total return for the comingyear?arrow_forwardIf D1 = $1.5, g (which is held constant) = 6.5%, and Po = $56, what is the stocks expected capital gains yield for the coming year? Bond valuation related problems should be solved by using a financial calculator or MS excel spreadsheet. Accordingly, you must show the values of all relevant time valu of money variablesarrow_forward
- Using the data in the following table, and the fact that the correlation of A and B is 0.06, calculate the volatility (standard deviation) of a portfolio that is 70% invested in stock A and 30% invested in stock B. The return of stock A is ☐ %. (Round to two decimal places.) Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Realized Returns Year Stock A Stock B 2017 15% 24% 2018 12% 22% 2019 9% 10% 2020 -4% -4% 2021 4% -3% 2022 11% 22%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 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) 0.5 × Ao². Note: 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_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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,
Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan ProfessorPublisher:McGraw-Hill Education
Essentials Of Investments
Finance
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:9780134897264
Author:KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:Pearson,
Fundamentals of Financial Management (MindTap Cou...
Finance
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i...
Finance
ISBN:9780077861759
Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:McGraw-Hill Education
Portfolio return, variance, standard deviation; Author: MyFinanceTeacher;https://www.youtube.com/watch?v=RWT0kx36vZE;License: Standard YouTube License, CC-BY