EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 24, Problem 6CP
A
Summary Introduction
To calculate: The sharpe measures and treynor ratio for portfolio X and S&P 500. And explain the X portfolio performance using treynor measure and the sharpe ratio.
Introduction: Sharpe ratio tells about the risk premium with respect to the total risk of the market. Treynor ratio is defined as the risk premium and risk premium is difference of risk rate and return.
A
Expert Solution
Answer to Problem 6CP
The value of Sharpe ratio is 0.222 and 0.462 and Treynor ratio is 6.67 and 6.
Explanation of Solution
The Sharpe ratio of the X portfolio and S&P 500 is calculated below,
Treynor ratio for X portfolio and S&P 500 is calculated below,
B
Summary Introduction
To explain: The Risk management in both portfolios and the reason for the result when using treynor measure versus the sharpe ratio.
Introduction: The risk taking of any portfolio is decided by the value of beta and standard deviation. For low value of beta means low risk in the market.
B
Expert Solution
Answer to Problem 6CP
Portfolio X has low risk as the low beta value.
Explanation of Solution
The risk of portfolios is decided by the value of beta and standard deviation. As from the value portfolio ‘X’ has low beta value. Hence it has lower risk in market. On the other hand the standard deviation value is high for portfolio ‘X’, this means it has high total risk in the market.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
2. An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks,
using both the Treynor and Sharpe measures of portfolio performance. The following
table provides the average annual rate of return for Portfolio X, the market portfolio (as
measured by the Standard & Poor's 500 Index), and U.S. Treasury bills (T-bills) during
the past eight years.
Annual Average
Standard Deviation
Rate of Return
of Return
Beta
Portfolio X
10%
18%
0.60
S&P 500
13
1.00
12
n/a
T-bills
n/a
n/a = not applicable
a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and
the S&P 500. Briefly explain whether Portfolio X underperformed, equaled, or outper-
formed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the
Sharpe measure.
b. Based on the performance of Portfolio X relative to the S&P 500 calculated in part (a),
briefly explain the reason for the conflicting results when using the Treynor measure
versus the Sharpe measure.
An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor’s 500 Index), and U.S. Treasury bills (T-bills) during the past eight years.
Rate Annual Averageof Return
STANDARD DEVIATION OF RETURN
BETA
Portfolio X
10
13
0.40
S&P 500
12
10
1.00
T-bills
7
n/a
n/a
n/a = not applicable
Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place and for the Sharpe measure to three decimal places.
Treynor measure
Sharpe measure
Portfolio X
7.5
S&P 500
5
An analyst wants to evaluate Portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table
provides the average annual rate of return for Portfolio X, the market portfolio (as measured by the Standard and Poor's 500 Index), and U.S. Treasury bills (T-bills) during the
past eight years.
Annual Average Standard Deviation
Rate of Return
of Return
Beta
Portfolio X
11%
18%
0.40
S&P 500
13
14
1.00
T-bills
6
n/a
n/a
n/a = not applicable
a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Round your answers for the Treynor measure to one decimal place
and for the Sharpe measure to three decimal places.
Treynor measure
Sharpe measure
Portfolio X
S&P 500
%
Briefly explain whether Portfolio X underperformed, equaled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe
measure.
Based on the Treynor measure Portfolio…
Chapter 24 Solutions
EBK INVESTMENTS
Ch. 24 - Prob. 1PSCh. 24 - Prob. 2PSCh. 24 - Prob. 3PSCh. 24 - Prob. 4PSCh. 24 - Prob. 5PSCh. 24 - Prob. 6PSCh. 24 - Prob. 7PSCh. 24 - Prob. 8PSCh. 24 - Prob. 9PSCh. 24 - Prob. 10PS
Ch. 24 - Prob. 11PSCh. 24 - Prob. 12PSCh. 24 - Prob. 13PSCh. 24 - Prob. 14PSCh. 24 - Prob. 15PSCh. 24 - Prob. 16PSCh. 24 - Prob. 17PSCh. 24 - Prob. 18PSCh. 24 - Prob. 19PSCh. 24 - Prob. 20PSCh. 24 - Prob. 21PSCh. 24 - Prob. 22PSCh. 24 - Prob. 1CPCh. 24 - Prob. 2CPCh. 24 - Prob. 3CPCh. 24 - Prob. 4CPCh. 24 - Prob. 5CPCh. 24 - Prob. 6CPCh. 24 - Prob. 7CPCh. 24 - Prob. 8CPCh. 24 - Prob. 9CPCh. 24 - Prob. 10CPCh. 24 - Prob. 11CPCh. 24 - Prob. 12CPCh. 24 - Prob. 13CPCh. 24 - Prob. 14CP
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
- Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Period 1927-2021 1927-1950 1951-1974 1975-1998 1999-2021 Average Annual Returns U.S. equity 12.17 10.26 10.21 17.97 10.16 1-Month T-Bills 3.30 0.93 3.59 6.98 1.66 U.S. Excess return 8.87 9.33 6.62 10.99 8.50 Equity Market Standard Deviation 20.25 26.57 20.32 14.40 18.85 Sharpe Ratio 0.44 0.35 0.33 0.76 0.45 Required: a. If your risk-aversion coefficient is A = 4.9 and you believe that the entire 1927-2021 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is u = E(r) 0.5 × Ao². b. What if you believe that the 1975-1998 period is representative?arrow_forwardAn analyst wants to evaluate Portfolio X consisting entirely of US common stocks, using both the Treynor and Sharpe measures of the portfolio performance. The following table provides the average annual rate of return for the portfolio X the market portfolio (as measured by the Standard & Poor's 500 index) and US Treasury billds (Tbills) during the past eight years Average Return Standard deviation Beta Portfolio X 10% 18% 0.6 S & P 500 12% 13% 1 T bills 6% n/a n/a a. Calculate both the Treynor measure and the Sharpe measure for both Portfolio X and the S&P 500. Briefly explain whether portfolio X underperformed, equalled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe measure. b. Based on the performance of…arrow_forwardRefer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Period 1927-2021 1927-1950 1951-1974 1975-1998 1999-2021 Average Annual Returns U.S. equity 12.17 10.26 10.21 17.97 10.16 U.S. Equity Market Standard Deviation 20.25 26.57 20.32 14.40 18.85 1-Month T- Excess return 8.87 9.33 6.62 10.99 8.50 Bills 3.30 0.93 3.59 6.98 1.66 Sharpe Ratio 0.44 0.35 0.33 0.76 0.45 Required: a. If your risk-aversion coefficient is A = 3.5 and you believe that the entire 1927-2021 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is U = E(r) - 0.5 × Ag². b. What if you believe that the 1975-1998 period is representative?arrow_forward
- Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Average Annual Returns U.S. Equity Market U.S. 1-Month Excess Standard Sharpe Period equity T-Bills return Deviation Ratio 1927-2021 12.17 3.30 8.87 20.25 0.44 1927-1950 10.26 0.93 9.33 26.57 0.35 1951-1974 10.21 3.59 6.62 20.32 0.33 1975-1998 1999-2021 17.97 6.98 10.99 14.40 0.76 10.16 1.66 8.50 18.85 0.45 Required: a. If your risk-aversion coefficient is A = 3.7 and you believe that the entire 1927-2021 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is UB-0.5× Ao 2 b. What if you believe that the 1975-1998 period is representative? Complete this question by entering your answers in the tabs below. Required A Required B If your risk-aversion coefficient is A = 3.7 and you…arrow_forwardYou are given the following partial covariance and correlation tables from historical data: Securities J K Market Securities J K Market 1.24 1.11 1.17 1.03 Covariance Matrix K 0.90 J 0.0020480 0.0021600 Also, you have estimated that the market's standard deviation is 4.3 percent. For the coming year, the expected return on the market is 14.0 percent and the risk-free rate is expected to be 4.0 percent. Given this information, determine the beta for Security K for the coming year, assuming CAPM is the correct model for required returns. Correlation Matrix K 0.60 1.00 0.90 1.00 0.60 0.80 Market 0.0020480 0.0021600 Market 0.80 0.90 1.00 Ston sharing Hidel lines Wearrow_forwardBased on the following information, calculate the expected return and standard deviation for each of the following stocks. What are the covariance and correlation between the returns of the two stocks? Calculate the portfolio return and portfolio standard deviation if you invest equally in each asset. Returns State of Economy Prob J K Recession 0.25 -0.02 0.034 Normal 0.6 0.138 0.062 Boom 0.15 0.218 0.092arrow_forward
- Year U.S. Gov’t T-Bills U.K. Common Stocks 2015 0.063 0.150 2016 0.081 0.043 2017 0.076 0.374 2018 0.090 0.192 2019 0.085 0.106 a. Compute the geometric mean rate of return for each of these investments and compare the arithmetic mean return and geometric mean return for each investment and discuss the difference between mean returns as related to the standard deviation of each series.arrow_forwardDuring the 1927-2018 period the Sharpe ratio was greatest for which of the following asset classes? Multiple Choice Long-term U.S. Treasury bonds Small/growth U.S. stocks Bond world portfolio return in U.S. dollars Big/value U.S. stocksarrow_forwardBelow are the annual returns provided by TSCM. Calculate average annual return experienced by an investor over the last five years. Calculate the standard deviation of the portfolio return over this period. (See sheet "TSCM" in the attached Excel.) Period Return 2021 -51.0% 2020 43.0% 2019 61.0% 2018 -5.0% 2017 -19.0% In the year 2022, TSCM return is 21%. Calculate TSCM's Jensen's Alpha for the year period in annual terms. Use the below data. Beta = 2.3 Risk-free rate = 1% Expected Market Return = 8%arrow_forward
- You are analyzing a Time Series of historic market information and found the following information for a particular investment security: the Rate of Return in 2012 was -6.72%; was 18.22% in 2013; was 7.75% in 2014; was 11.45% in 2015; was 4.94% in 2016; and was 18.11% in 2017. What is the arithmetic average rate of return? Show your answer as a percentage rounded to two places (12.34% for example). Group of answer choices 7.64% 8.96% 8.14% 7.24% None of the abovearrow_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 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) 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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning
Intermediate Financial Management (MindTap Course...
Finance
ISBN:9781337395083
Author:Eugene F. Brigham, Phillip R. Daves
Publisher:Cengage Learning
Investing For Beginners (Stock Market); Author: Daniel Pronk;https://www.youtube.com/watch?v=6Jkdpgc407M;License: Standard Youtube License