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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
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.
11% = w1(17%) + (1 ? w1)(4%); 11% = 17%w1 + 4% ? 4%w1; 7% = 13%w1; w1 = 0.538; 1 ? w1 = 0.462; 0.538(17%) + 0.462(4%) = 11.0%.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
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.
0.20 = x(0.40); x = 50% in risky asset.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
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. (0.17 ? 0.04)/0.40 = 0.325.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
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
13% = w1(11%) + (1 ? w1)(4.5%); 13% = 11%w1 + 4.5% ? 4.5%w1; 8.5% = 6.5%w1; w1 = 1.3077; 1 ? w1 = ?0.3077; 1.308(11%) + (?0.3077)(4.5%) = 13.00%.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
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
0.08 = x(0.21); x = 38.1% in risky asset.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
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.
For $100, (114 ? 100)/100 = 14%; .14 = w1(.11) + (1 ? w1)(.045); .14 = .11w1 + .045 ? .045w1; 0.095 = 0.065w1; w1 = 1.46($100) = $146; (1 ? w1)$100 = ?$46.
AACSB: Analytic Bloom's: Understand Difficulty: Challenge
Topic: Portfolio Risk Allocation
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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets
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. (0.11 ? 0.045)/0.21 = 0.3095.
AACSB: Analytic Bloom's: Apply
Difficulty: Intermediate
Topic: Portfolio Risk Allocation
Short Answer Questions
66. Discuss the differences between investors who are risk averse, risk neutral, and risk loving.
The investor who is risk averse will take additional risk only if that risk-taking is likely to be rewarded with a risk premium. This investor examines the potential risk-return trade-offs of investment alternatives. The investor who is risk neutral looks only at the expected returns of the investment alternative and does not consider risk; this investor will select the investment alternative with the highest expected rate of return. The risk lover will engage in fair games and gambles; this investor adjusts the expected return upward to take into account the \confronting risk.
Feedback: The purpose of this question is to ascertain that the student understands the different attitudes toward risk exhibited by different individuals.
AACSB: Reflective Thinking Bloom's: Evaluate Difficulty: Basic Topic: Risk Aversion
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