Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
52. To build an indifference curve we can first find the utility of a portfolio with 100% in the risk-free asset, then
A. find the utility of a portfolio with 0% in the risk-free asset.
B. change the expected return of the portfolio and equate the utility to the standard deviation. C. find another utility level with 0% risk.
D. change the standard deviation of the portfolio and find the expected return the investor would require to maintain the same utility level.
E. change the risk-free rate and find the utility level that results in the same standard deviation.
53. The Capital Market Line
I) is a special case of the Capital Allocation Line.
II) represents the opportunity set of a passive investment strategy. III) has the one-month T-Bill rate as its intercept.
IV) uses a broad index of common stocks as its risky portfolio. A. I, III, and IV B. II, III, and IV C. III and IV D. I, II, and III E. I, II, III, and IV
54. An investor invests 40 percent of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 60 percent in a T-bill that pays 4 percent. His portfolio's expected return and standard deviation are __________ and __________, respectively. A. 0.114; 0.112 B. 0.087; 0.063 C. 0.096; 0.126 D. 0.087; 0.144 E. 0.106; 0.137
6-16
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
55. An investor invests 70 percent of his wealth in a risky asset with an expected rate of return of 0.11 and a variance of 0.12 and 30 percent in a T-bill that pays 3 percent. His portfolio's expected return and standard deviation are __________ and __________, respectively. A. 0.086; 0.242 B. 0.087; 0.267 C. 0.295; 0.123 D. 0.087; 0.182 E. 0.106; 0.137
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03.
56. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.08? A. 85% and 15% B. 75% and 25% C. 62.5% and 37.5% D. 57% and 43%
E. Cannot be determined.
57. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08? A. 30% and 70% B. 50% and 50% C. 60% and 40% D. 40% and 60%
E. Cannot be determined.
6-17
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
58. The slope of the Capital Allocation Line formed with the risky asset and the risk-free asset is equal to A. 0.47 B. 0.80 C. 2.14 D. 0.40
E. Cannot be determined.
You invest $1000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04.
59. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11? A. 53.8% and 46.2% B. 75% and 25% C. 62.5% and 37.5% D. 46.2% and 53.8% E. Cannot be determined.
60. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.20? A. 30% and 70% B. 50% and 50% C. 60% and 40% D. 40% and 60%
E. Cannot be determined.
61. The slope of the Capital Allocation Line formed with the risky asset and the risk-free asset is equal to A. 0.325. B. 0.675. C. 0.912. D. 0.407.
E. Cannot be determined.
6-18
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045.
62. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.13? A. 130.77% and ?30.77% B. ?30.77% and 130.77% C. 67.67% and 33.33% D. 57.75% and 42.25% E. Cannot be determined.
63. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08? A. 301% and 69.9% B. 50.5% and 49.50% C. 60.0% and 40.0% D. 61.9% and 38.1% E. Cannot be determined.
64. A portfolio that has an expected outcome of $114 is formed by A. Investing $100 in the risky asset.
B. Investing $80 in the risky asset and $20 in the risk-free asset.
C. Borrowing $46 at the risk-free rate and investing the total amount ($146) in the risky asset. D. Investing $43 in the risky asset and $57 in the riskless asset. E. Such a portfolio cannot be formed.
65. The slope of the Capital Allocation Line formed with the risky asset and the risk-free asset is equal to A. 0.4667. B. 0.8000. C. 0.3095. D. 0.41667.
E. Cannot be determined.
6-19
Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
Short Answer Questions
66. Discuss the differences between investors who are risk averse, risk neutral, and risk loving.
67. In the utility function: U = E(r) ? [?0.005As2], what is the significance of \
68. What is a fair game? Explain how the term relates to a risk-averse investor's attitude toward speculation and risk and how the utility function reflects this attitude.
69. Draw graphs that represent indifference curves for the following investors: Harry, who is a risk-averse investor; Eddie, who is a risk-neutral investor; and Ozzie, who is a risk-loving investor. Discuss the nature of each curve and the reasons for its shape.
6-20