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 4CP
Use the following data in answering CFA Questions 4-6.
Investment Expected Return,E®Standard Deviation, 6
10. 120.30
20. 10.50
30. 210.16
4. 0.24 0.21
Suppose investor “satisfaction” with a portfolio increases with expected return and decreases with variance according to the following “utility” formula: U = E® − ½ A2where A denotes the investor’s risk aversion.
4. Based on the formula for investor satisfaction or “utility,” which investment would you select if you were risk averse with A = 4? (LO 54)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
On the basis of the utility formula below, which investment would you select if you were risk averse with A = 4?
Investment
Expected return E(r)
Standard deviation
σ
1
0.12
0.30
2
0.15
0.50
3
0.21
0.16
4
0.24
0.21
Supposing the return from an investment has the following probability distribution
Return Probability
R (%)
8 0.2
10 0.2
12 0.5
14 0.1
Required:
What is the expected return of the investment?
What is the risk as measured by the standard deviation of expected returns?
Portfolios A and B are both well-diversified. The risk-free rate is 8%. The return for the market is 10%.
Portfolio A has an expected return of 15% and beta of 1.1. Portfolio B has an expected return of 9% and beta
of 0.20. Portfolio A's variance is 9%, whilst Portfolio B's variance is 5.5%.
Calculate for Portfolio A and Portfolio B the following:
1. Sharpe's Measure,
2. Treynor's Measure,
3. Jensen's Measure.
Which is the better portfolio according to each measure?
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
- Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than Blandys standard deviation?arrow_forwardConsider the following information for four portfolios, the market, and the risk-free rate (RFR): Portfolio Return Beta SD A1 0.15 1.25 0.182 A2 0.1 0.9 0.223 A3 0.12 1.1 0.138 A4 0.08 0.8 0.125 Market 0.11 1 0.2 RFR 0.03 0 0 Refer to Exhibit 18.6. Calculate the Jensen alpha Measure for each portfolio. a. A1 = 0.014, A2 = -0.002, A3 = 0.002, A4 = -0.02 b. A1 = 0.002, A2 = -0.02, A3 = 0.002, A4 = -0.014 c. A1 = 0.02, A2 = -0.002, A3 = 0.002, A4 = -0.014 d. A1 = 0.03, A2 = -0.002, A3 = 0.02, A4 = -0.14 e. A1 = 0.02, A2 = -0.002, A3 = 0.02, A4 = -0.14arrow_forwardConsider two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.arrow_forward
- Mean-variance expected utility is given by Eu = e-, where e is expected return, v is the variance of the portfolio and tis risk tolerance. Suppose an investor has risk-loving preferences. What can we say about the value of t? Select one: Ot1 O. t>0 O t=0arrow_forwardAccording to CAPM, the expected rate of return of a portfolio with a beta of 1.0 and an alpha of 0 is:a. Between rM and rf .b. The risk-free rate, rf .c. β(rM − rf).d. The expected return on the market, rM.arrow_forwardd. Interpret your results in (c) above, assuming that the historical average return of 8.5% from the stock is a good benchmark. e. Critically evaluate the strengths and weaknesses of applying the implied rate of return from the RIVM as a proxy of the expected return.arrow_forward
- a) Discuss the difference between a price-weighted index and a value-weighted index. Give one example for the price-weighted index and one example for the value-weighted index and discuss any problems/advantages associated with the specific indices. b) We assume that investors use mean-variance utility: U = E(r) – 0.5 × Ao², where E(r) is the expected return, A is the risk aversion coefficient and o? is the variance of returns. Given that the optimal proportion of the risky asset in the complete port- folio is given by the equation y* = E , where r; is the risk-free rate, E(rp) is the expected returm of the risky portfolio, o, is variance of returns, and A is the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. Aoarrow_forwardWhat are the (a) expected return, (b) standard deviation, and (c) coefficient of variation for an investment with the following probability distribution? Probability Payoff 0.2 19.0% 0.7 9.0 0.1 4.0arrow_forwardAn investor has preferences represented by the utility function U = E(r) - 20². What is her certainty equivalent return for a portfolio with an expected return of 10% and a standard deviation of 15%? Oa. 1.0% O b. 2.5% O c. 0.5% O d. 5.5% O e. 10.0%arrow_forward
- Consider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and σ1=0.2 Asset 2: E[r2]=0.3 and σ2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0. (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.arrow_forwardFollowing is information for the required returns and standard deviations of returns for A, B, and C. The correlation coefficients for each pair also are shown below in a matrix. Which is the portfolio you will recommend AB, AC, or BC, and why? A B C Required Rate of return 7% 10% 20% Standard Deviation 33% 54% 90% Coefficient A,B 0.16 Coefficient A,C 0.19 Coefficient B,C 0.17arrow_forwardAn investor has a portfolio of two assets A and B. The details are shown in the below table. Portfolio Details Asset Expectedreturn Standarddeviation Covariance (A, B) Expected Portfolio Return A 0.06 0.5 0.12 0.1 B 0.08 0.8 Which one of the following statements is NOT correct? a. The portfolio weight in asset A is -100%. b. The correlation of asset A and B’s returns is 0.3. c. The investor can benefit from a fall in the price of asset A. d. The variance of the portfolio is 2.33. e. The order of short selling is borrowing, buying, selling, and returning.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
Portfolio return, variance, standard deviation; Author: MyFinanceTeacher;https://www.youtube.com/watch?v=RWT0kx36vZE;License: Standard YouTube License, CC-BY