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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets

6. In a return-standard deviation space, which of the following statements is (are) true for risk-averse investors? (The vertical and horizontal lines are referred to as the expected return-axis and the standard deviation-axis, respectively.) I) An investor's own indifference curves might intersect. II) Indifference curves have negative slopes.

III) In a set of indifference curves, the highest offers the greatest utility. IV) Indifference curves of two investors might intersect. A. I and II only B. II and III only C. I and IV only D. III and IV only E. II and IV only

An investor's indifference curves are parallel (thus they cannot intersect) and have positive slopes. The highest indifference curve (the one in the most northwestern position) offers the greatest utility. Indifference curves of investors with similar risk-return trade-offs might intersect.

AACSB: Analytic Bloom's: Understand Difficulty: Intermediate Topic: Risk Tolerance

7. Elias is a risk-averse investor. David is a less risk-averse investor than Elias. Therefore, A. for the same risk, David requires a higher rate of return than Elias. B. for the same return, Elias tolerates higher risk than David.

C. for the same risk, Elias requires a lower rate of return than David. D. for the same return, David tolerates higher risk than Elias. E. cannot be determined.

The more risk averse the investor, the less risk that is tolerated for a given rate of return.

AACSB: Analytic Bloom's: Understand Difficulty: Intermediate Topic: Risk Aversion

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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets

8. When an investment advisor attempts to determine an investor's risk tolerance, which factor would they be least likely to assess?

A. The investor's prior investing experience B. The investor's degree of financial security

C. The investor's tendency to make risky or conservative choices D. The level of return the investor prefers E. The investor's feelings about loss

Investment advisors would be least likely to assess the level of return the investor prefers. The investor's investing experience, financial security, feelings about loss, and disposition toward risky or conservative choices will impact risk tolerance.

AACSB: Analytic Bloom's: Understand Difficulty: Intermediate Topic: Risk Aversion

Assume an investor with the following utility function: U = E(r) ? 3/2(s2).

9. To maximize her expected utility, she would choose the asset with an expected rate of return of _______ and a standard deviation of ________, respectively. A. 12%; 20% B. 10%; 15% C. 10%; 10% D. 8%; 10% E. 10%; 12%

U = 0.10 ? 3/2(0.10) 2 = 8.5%; highest utility of choices.

AACSB: Analytic Bloom's: Apply

Difficulty: Intermediate Topic: Risk Aversion

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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets

10. To maximize her expected utility, which one of the following investment alternatives would she choose?

A. A portfolio that pays 10 percent with a 60 percent probability or 5 percent with 40 percent probability.

B. A portfolio that pays 10 percent with 40 percent probability or 5 percent with a 60 percent probability.

C. A portfolio that pays 12 percent with 60 percent probability or 5 percent with 40 percent probability.

D. A portfolio that pays 12 percent with 40 percent probability or 5 percent with 60 percent probability.

E. A portfolio that pays 12 percent with 20 percent probability or 2 percent with 80 percent probability.

U(c) = 9.02%; highest utility of possibilities.

AACSB: Analytic Bloom's: Apply

Difficulty: Challenge Topic: Risk Aversion

11. A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6 percent. An investor has the following utility function: U = E(r) ? (A/2)s2. Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset? A. 5 B. 6 C. 7 D. 8 E. 1

0.06 = 0.15 ? A/2(0.15)2; 0.06 ? 0.15 = ?A/2(0.0225); ?0.09 = ?0.01125A; A = 8; U = 0.15 ? 8/2(0.15)2 = 6%; U(Rf) = 6%.

AACSB: Analytic Bloom's: Apply

Difficulty: Challenge Topic: Risk Aversion

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Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets

12. According to the mean-variance criterion, which one of the following investments dominates all others?

A. E(r) = 0.15; Variance = 0.20 B. E(r) = 0.10; Variance = 0.20 C. E(r) = 0.10; Variance = 0.25 D. E(r) = 0.15; Variance = 0.25 E. E(r) = 0.12; Variance = 0.35

(r) = 0.15; Variance = 0.20 gives the highest return with the least risk; return per unit of risk is .75, which dominates the reward-risk ratio for the other choices.

AACSB: Analytic Bloom's: Understand Difficulty: Challenge Topic: Risk Aversion

13. Consider a risky portfolio, A, with an expected rate of return of 0.15 and a standard

deviation of 0.15, that lies on a given indifference curve. Which one of the following portfolios might lie on the same indifference curve? A. E(r) = 0.15; Standard deviation = 0.20 B. E(r) = 0.15; Standard deviation = 0.10 C. E(r) = 0.10; Standard deviation = 0.10 D. E(r) = 0.20; Standard deviation = 0.15 E. E(r) = 0.10; Standard deviation = 0.20

Portfolio A has a reward to risk ratio of 1.0; portfolio E(r) = 0.15; Standard deviation = 0.20 is the only choice with the same risk-return tradeoff.

AACSB: Analytic Bloom's: Apply

Difficulty: Challenge Topic: Risk Aversion

U = E(r) ? (A/2)s2, where A = 4.0.

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