Multiple Choice Questions
C 1. Which of the following statements regarding risk-averse investors is true? A) They only care about the rate of return. B) They accept investments that are fair games. C) They only accept risky investments that offer risk premiums over the
risk-free rate.
D) They are willing to accept lower returns and high risk. E) A and B.
C 2. Which of the following statements is (are) true?
I) Risk-averse investors reject investments that are fair games.
II) Risk-neutral investors judge risky investments only by the expected
returns.
III) Risk-averse investors judge investments only by their riskiness. IV) Risk-loving investors will not engage in fair games.
A) I only B) II only C) I and II only D) II and III only E) II, III, and IV only Rationale: Risk-averse investors consider a risky investment only if the
investment offers a risk premium. Risk-neutral investors look only at expected returns when making an investment decision.
C 3. In the mean-standard deviation graph an indifference curve has a ________
slope.
A) negative B) zero C) positive D) northeast
E) cannot be determined Rationale: The risk-return trade-off is one in which greater risk is taken if
greater returns can be expected, resulting in a positive slope.
C 4. In the mean-standard deviation graph, which one of the following statements
is true regarding the indifference curve of a risk-averse investor?
A) It is the locus of portfolios that have the same expected rates of return and
different standard deviations.
B) It is the locus of portfolios that have the same standard deviations and
different rates of return.
C) It is the locus of portfolios that offer the same utility according to returns
and standard deviations.
D) It connects portfolios that offer increasing utilities according to returns and
standard deviations.
E) none of the above. Rationale: Indifference curves plot trade-off alternatives that provide equal
utility to the individual (in this case, the trade-offs are the risk-return
characteristics of the portfolios).
D 5. 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) none of the above Rationale: An investor's indifference curves are parallel, and thus 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.
D 6. 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. Rationale: The more risk averse the investor, the less risk that is tolerated,
given a rate of return.
D 7. 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 feeling about loss
Use the following to answer questions 8-9:
Assume an investor with the following utility function: U = E(r) - 3/2(s2). C 8. 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) none of the above
Rationale: U = 0.10 - 3/2(0.10)2 = 8.5%; highest utility of choices.
C 9. 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) none of the above. Rationale: U(c) = 9.02%; highest utility of possibilities.
D 10. 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) none of the above Rationale: 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%.
A 11. 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) none of these dominates the other alternatives. Rationale: A 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.
C 12. 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 Rationale: Portfolio A has a reward to risk ratio of 1.0; portfolio C is the only
choice with the same risk-return tradeoff.
Use the following to answer questions 13-15:
C 13. D 14. B 15. D 16.
D 17.
Based on the utility function above, which investment would you select? A) 1 B) 2 C) 3 D) 4
E) cannot tell from the information given
Rationale: U(c) = 0.21 - 4/2(0.16)2 = 15.88 (highest utility of choices). Which investment would you select if you were risk neutral? A) 1 B) 2 C) 3 D) 4
E) cannot tell from the information given
Rationale: If you are risk neutral, your only concern is with return, not risk. The variable (A) in the utility function represents the: A) investor's return requirement. B) investor's aversion to risk.
C) certainty-equivalent rate of the portfolio. D) minimum required utility of the portfolio. E) none of the above.
Rationale: A is an arbitrary scale factor used to measure investor risk tolerance. The higher the value of A, the more risk averse the investor. The exact indifference curves of different investors A) cannot be known with perfect certainty.
B) can be calculated precisely with the use of advanced calculus.
C) although not known with perfect certainty, do allow the advisor to create
more suitable portfolios for the client. D) A and C.
E) none of the above.
Rationale: Indifference curves cannot be calculated precisely, but the theory does allow for the creation of more suitable portfolios for investors of differing levels of risk tolerance.
The riskiness of individual assets
A) should be considered for the asset in isolation.
B) should be considered in the context of the effect on overall portfolio
volatility.
C) combined with the riskiness of other individual assets (in the proportions
these assets constitute of the entire portfolio) should be the relevant risk
D 18.
B 19. E 20. A 21.
B 22.
measure. D) B and C.
E) none of the above.
Rationale: The relevant risk is portfolio risk; thus, the riskiness of an individual security should be considered in the context of the portfolio as a whole. A fair game
A) will not be undertaken by a risk-averse investor. B) is a risky investment with a zero risk premium. C) is a riskless investment. D) Both A and B are true. E) Both A and C are true.
Rationale: A fair game is a risky investment with a payoff exactly equal to its expected value. Since it offers no risk premium, it will not be acceptable to a risk-averse investor.
The presence of risk means that A) investors will lose money.
B) more than one outcome is possible.
C) the standard deviation of the payoff is larger than its expected value. D) final wealth will be greater than initial wealth. E) terminal wealth will be less than initial wealth.
Rationale: The presence of risk means that more than one outcome is possible.
The utility score an investor assigns to a particular portfolio, other things equal, A) will decrease as the rate of return increases.
B) will decrease as the standard deviation increases. C) will decrease as the variance increases. D) will increase as the variance increases. E) will increase as the rate of return increases.
Rationale: Utility is enhanced by higher expected returns and diminished by higher risk.
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
money.
C) the minimum rate guaranteed 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.
According to the mean-variance criterion, which of the statements below is correct?