Below are three different investment alternatives, along with information on their expected return and return standard deviation. Suppose investors have the following utility function: U = E(R) - 12A0² The coefficient of risk aversion (A) for Alice is 1.5, and that for John is 2.5. Which investment will each investor pick? (hint: Find the investment giving the investor the highest utility level). Expected Return E[r] Standard Deviation o Investment 1 0.10 0.02 2 0.25 0.05 3 0.30 0.15 4 0.35 0.40 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

Below are three different investment alternatives, along with information on their expected return and return standard deviation. Suppose investors have the following utility function: U = E(R) - 12A0² The coefficient of risk aversion (A) for Alice is 1.5, and that for John is 2.5. Which investment will each investor pick? (hint: Find the investment giving the investor the highest utility level). Expected Return E[r] Standard Deviation o Investment 1 0.10 0.02 2 0.25 0.05 3 0.30 0.15 4 0.35 0.40 For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter3: Risk And Return: Part Ii

Section: Chapter Questions

Problem 2P: APT An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk-free...

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Investment Expected Return Standard Deviation1 0.12 0.302 0.15 0.503 0.21 0.164 0.24 0.21Based on the utility formula we covered in lectures,a. Calculate the utility of each investment alternative for an investor with risk averse A=4:The utility of Investment 1The utility of Investment 2The utility of Investment 3The utility of Investment 4b. State which investment you would select if you were risk averse with A=4: Blank 5. Fill in the blank, read surrounding text. c. State which investment you would select if you were risk averse with A=2: Blank 6. Fill in the blank, read surrounding text.. d. State which investment you would select if you were risk neutral: Blank 7. Fill in the blank, read surrounding text.
(corrected problem) NEW Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The CORRELATION COEFFICIENT between the two is 0.084. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio?
3.1 Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio?
9. A risk averse, wealth maximising, investor is faced with a choice between four investments (P, Q, R and S) that have profiles as follows:   Mean return (%) Variance (%) P 19 18   Q 16 17  R 22 16   S 20 16   Between which pair of these investments would the investor find it impossible to distinguish on the basis of the above information? A. P and Q   B. R and S   C. P and S   D. Q and R
Portfolio Expected return Standard deviation Q 7.8% 10.5% R 10.0% 14.0% S 4.6% 5.0% T 11.7% 18.5% U 6.2% 7.5% Q) If you are only willing to make an investment with a standard deviation of 7.0%, is it possible for you to earn a return of 7.0%?
2 Problem 2: Consider a market composed of only two risky assets, A and B, with the following properties: a StockA Expected return 25%, SD 20% StockB Expected return 15%, SD 25% a) Suppose their correlation is 0.8. What is the expected return of the following portfolios: one that invests 0% in A, one that invests 10% in A, 20% in A and so on until 100%? Plot the portfolio frontier formed by these portfolios.b) Repeat part (1) under the assumption that the correlation is -0.8.c) Explain in detail what is the intuition behind the difference across the answers you found for part (1) and part (2).
Assume an investor with the coefficient of risk aversion A=5.5. To maximize her expected utility, she would choose the asset with an expected rate of return of _______ and a standard deviation of ________, respectively." a. 21%; 16% b. 24%; 21% c. 12%; 30% d. 15%; 5%
Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. 1. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio? 2. In addition to the funds A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is 10, its variance 0.0625, its correlation with A is 0.1050 and its correlation with B is 0.07. You want to achieve an expected return of 16% on your portfolio, with the minimum possible risk (measured by the standard deviation). Derive analytically (that is, without the help of solver, but trough calculus) the weights of such desired portfolio, and its standard deviation.
The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standarddeviation of 20%. Answer the following questions.a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition ofA to make the investors prefer the optimal risky portfolio than the risk free asset? b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expectedreturn and standard deviation of the investor’s optimal complete portfolio?
The risk-free rate is currently 3.3%, and the market return is 14.8%. Assume you are considering the following investments: Investment Beta A 1.54 B 1.16 C 0.51 D 0.11 E 2.14 . a. Which investment is most risky? Least risky? b. Use the capital asset pricing model (CAPM) to find the required return on each of the investments. c. Find the security market line (SML), using your findings in part b. d. On the basis of your findings in part c, what relationship exists between risk and return? Explain.
23. The certainty equivalent rate of a portfolio is a. the rate that a risk free investment would need to offer with certainty to be considered equally attractive as the risky portfolio. b. the rate that the investor must earn for certain to give up the use of his or her money. c. the minimum rate guarteed by institutions such as banks. d. the rate that equates "A" in the utility function with the average risk aversion coefficient for all risk averse investors. e. represented by the scaling factor "-.005' in the utility function
a. Use the following information: E[rXOM] = 15.6%, standard deviationXOM = 15.9% E[rMS]=29.7%, standard deviationMS = 35.2% Correlation of returns: ρXOM,MS = 0.139, rf=10% If the optimal amount to invest in the first asset (w) is 0.43, what is the variance of the risky portfolio when w=0.43? (write in decimal format using 5 decimal places) b. When choosing the best point of the POS (the curved line connecting two possible assets you can invest in) you need to find the point that: 1.Has the greatest difference between it’s return and the risk free rate, thus leading to the best return 2. You must solve for the optimal y allocation in order to find the best point on the POS 3. The point with the lowest standard deviation 4. The point with the greatest Sharpe ratio