Chapter 6 Risk Aversion and Capital Allocation to Risky Assets
Multiple Choice Questions
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.
Answer: C Difficulty: Moderate
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
Answer: C Difficulty: Moderate 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.
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
Answer: C Difficulty: Easy 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.
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.
Answer: C Difficulty: Moderate 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).
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.)
An investor's own indifference curves might intersect.
I)
Indifference curves have negative slopes.
II) In a set of indifference curves, the highest offers the greatest utility.
III) 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
Answer: D Difficulty: Moderate 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.
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.
Answer: D Difficulty: Moderate Rationale: The more risk averse the investor, the less risk that is tolerated, given a
rate of return.
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
Answer: D Difficulty: Moderate
Use the following to answer questions 8-9:
Assume an investor with the following utility function: U = E(r) - 3/2(s2).
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
Answer: C Difficulty: Moderate Rationale: U = 0.10 - 3/2(0.10)2 = 8.5%; highest utility of choices.
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.
Answer: C Difficulty: Difficult Rationale: U(c) = 9.02%; highest utility of possibilities.
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
Answer: D Difficulty: Difficult 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%.
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.
Answer: A Difficulty: Difficult 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.
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
Answer: C Difficulty: Difficult
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:
13. 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
Answer: C Difficulty: Difficult Rationale: U(c) = 0.21 - 4/2(0.16)2 = 15.88 (highest utility of choices).
14. 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
Answer: D Difficulty: Difficult Rationale: If you are risk neutral, your only concern is with return, not risk.
15. 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.
Answer: B Difficulty: Moderate 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.
16. 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.
Answer: D Difficulty: Easy 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.
17. 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 measure.
D) B and C.
E) none of the above.
Answer: D Difficulty: Easy 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.
18. 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.
Answer: D Difficulty: Moderate 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.
19.
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.
Answer: B Difficulty: Easy Rationale: The presence of risk means that more than one outcome is possible.
20. 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.
Answer: E Difficulty: Easy
Rationale: Utility is enhanced by higher expected returns and diminished by higher risk.
21. 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.
Answer: A Difficulty: Moderate
22. According to the mean-variance criterion, which of the statements below is correct?
A) Investment B dominates Investment A.
B) Investment B dominates Investment C.
C) Investment D dominates all of the other investments.
D) Investment D dominates only Investment B.
E) Investment C dominates investment A.
Answer: B Rationale: This question tests the student's understanding of how to apply the mean-variance criterion.
23. Steve is more risk-averse than Edie. On a graph that shows Steve and Edie's indifference curves, which of the following
is true? Assume that the graph shows expected return on the vertical axis and standard deviation on the horizontal axis.
I)
Steve and Edie's indifference curves might intersect.
II) Steve's indifference curves will have flatter slopes than Edie's.
III) Steve's indifference curves will have steeper slopes than Edie's.
IV) Steve and Edie's indifference curves will not intersect.
V) Steve's indifference curves will be downward sloping and Edie's will be upward sloping.
A) I and V
B) I and III
C) III and IV
D) I and II
E) II and IV
Answer: B Difficulty: Moderate Rationale: This question tests whether the student understands the graphical
properties of indifference curves and how they relate to the degree of risk tolerance.
24. The Capital Allocation Line can be described as the
A) investment opportunity set formed with a risky asset and a risk-free asset.
B) investment opportunity set formed with two risky assets.
C) line on which lie all portfolios that offer the same utility to a particular investor.
D) line on which lie all portfolios with the same expected rate of return and different standard deviations.
E) none of the above.
Answer: A Difficulty: Moderate Rationale: The CAL has an intercept equal to the risk-free rate. It is a straight line
through the point representing the risk-free asset and the risky portfolio, in expected-return/standard deviation space.
25. Which of the following statements regarding the Capital Allocation Line (CAL) is false?
A) The CAL shows risk-return combinations.
B) The slope of the CAL equals the increase in the expected return of a risky portfolio per unit of additional standard
deviation.
C) The slope of the CAL is also called the reward-to-variability ratio.
D) The CAL is also called the efficient frontier of risky assets in the absence of a risk-free asset.
E) Both A and D are true.
Answer: D Difficulty: Moderate Rationale: The CAL consists of combinations of a risky asset and a risk-free asset
whose slope is the reward-to-variability ratio; thus, all statements except d are true.
26. Given the capital allocation line, an investor's optimal portfolio is the portfolio that
A) maximizes her expected profit.
B) maximizes her risk.
C) minimizes both her risk and return.
D) maximizes her expected utility.
E) none of the above.
Answer: D Difficulty: Moderate Rationale: By maximizing expected utility, the investor is obtaining the best riskreturn relationships possible and acceptable for her.
27.
An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of
0.04 and 70 percent in a T-bill that pays 6 percent. His portfolio's expected return and standard deviation are
and
, respectively.
A) 0.114; 0.12
B) 0.087;0.06
C) 0.295; 0.12
D) 0.087; 0.12
E) none of the above
Answer: B Difficulty: Moderate Rationale: E(rP) = 0.3(15%) + 0.7(6%) = 8.7%; sP = 0.3(0.04)1/2 = 6%.
Use the following to answer questions 28-31: You invest $100 in a risky asset with an expected rate of return of 0.12 and a
standard deviation of 0.15 and a T-bill with a rate of return of 0.05.
28. 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 0.09?
A) 85% and 15%
B) 75% and 25%
C) 67% and 33%
D) 57% and 43%
E) cannot be determined
Answer: D Difficulty: Moderate Rationale: 9% = w1(12%) + (1 - w1)(5%); 9% = 12%w1 + 5% - 5%w1; 4% = 7%w1;
w1 = 0.57; 1 - w1 = 0.43; 0.57(12%) + 0.43(5%) = 8.99%.
29. 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 0.06?
A) 30% and 70%
B) 50% and 50%
C) 60% and 40%
D) 40% and 60%
E) cannot be determined
Answer: C Difficulty: Moderate Rationale: 0.06 = x(0.15); x = 40% in risky asset.
30. A portfolio that has an expected outcome of $115 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 $43 at the risk-free rate and investing the total amount ($143) in the risky asset.
D) investing $43 in the risky asset and $57 in the riskless asset.
E) Such a portfolio cannot be formed.
Answer: C Difficulty: Difficult Rationale: For $100, (115-100)/100=15%; .15 = w1(.12) + (1 - w1)(.05);
.15 = .12w1 + .05 - .05w1; 0.10 = 0.07w1; w1 = 1.43($100) = $143; (1 - w1)$100 = -$43.
31. 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) 2.14.
D) 0.41667.
E) Cannot be determined.
Answer: A Difficulty: Moderate Rationale: (0.12 - 0.05)/0.15 = 0.4667.
32. Consider a T-bill with a rate of return of 5 percent and the following risky securities:
Security A: E(r) = 0.15; Variance = 0.04
Security B: E(r) = 0.10; Variance = 0.0225
Security C: E(r) = 0.12; Variance = 0.01
Security D: E(r) = 0.13; Variance = 0.0625
From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk-averse investor
always choose his portfolio?
A) The set of portfolios formed with the T-bill and security A.
B) The set of portfolios formed with the T-bill and security B.
C) The set of portfolios formed with the T-bill and security C.
D) The set of portfolios formed with the T-bill and security D.
E) Cannot be determined.
Answer: C Difficulty: Difficult Rationale: Security C has the highest reward-to-volatility ratio.
Use the following to answer questions 33-36: You are considering investing $1,000 in a T-bill that pays 0.05 and a risky
portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has
an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
33. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest
in the T-bill and P, respectively?
A) 0.25; 0.75
B) 0.19; 0.81
C) 0.65; 0.35
D) 0.50; 0.50
E) cannot be determined
Answer: B E(rp) = 0.6(14%) + 0.4(10%) = 12.4%; 11% = 5x + 12.4(1 - x); x = 0.189 (T-bills) (1-x) =0.811 (risky asset).
34. If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest
in the T-bill, X, and Y, respectively if you keep X and Y in the same proportions to each other as in portfolio P?
A) 0.25; 0.45; 0.30
B) 0.19; 0.49; 0.32
C) 0.32; 0.41; 0.27
D) 0.50; 0.30; 0.20
E) cannot be determined
Answer: C E(rp) = .100.10 = 5w + 12.4(1 - w); x = 0.32 (weight of T-bills); As composition of X and Y are .6 and .4 of P,
respectively, then for 0.68 weight in P, the respective weights must be 0.41 and 0.27; .6(.68) = 41%; .4(.68) = 27%
35. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% percent of your
money in the risky portfolio and 60% in T-bills?
A) $240; $360
B) $360; $240
C) $100; $240
D) $240; $160
E) Cannot be determined
Answer: D Difficulty: Moderate Rationale: $400(0.6) = $240 in X; $400(0.4) = $160 in Y.
36. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio
that has an expected outcome of $1,200?
A) Cannot be determined
B) $54; $568; $378
C) $568; $54; $378
D) $378; $54; $568
E) $108; $514; $378
Answer: B ($1,200 - $1,000)/$1,000 = 12%; (0.6)14% + (0.4)10% = 12.4%; 12% = w5% + 12.4%(1 - w);w=.054; 1-w=.946;
w = 0.054($1,000) = $54 (T-bills); 1 - w = 1 - 0.054 = 0.946($1,000) = $946; $946 x 0.6 = $568 in X; $946 x 0.4 = $378 in Y.
37. A reward-to-volatility ratio is useful in:
A) measuring the standard deviation of returns.
B) understanding how returns increase relative to risk increases.
C) analyzing returns on variable rate bonds.
D) assessing the effects of inflation.
E) none of the above.
Answer: B Rationale: B is the only choice relevant to the reward-to-volatility ratio (risk and return).
38. The change from a straight to a kinked capital allocation line is a result of:
A) reward-to-volatility ratio increasing.
B) borrowing rate exceeding lending rate.
C) an investor's risk tolerance decreasing.
D) increase in the portfolio proportion of the risk-free asset.
E) none of the above.
Answer: B Rationale: The linear capital allocation line assumes that the investor may borrow and lend at the same
rate (the risk-free rate), which obviously is not true. Relaxing this assumption and incorporating the higher borrowing
rates into the model results in the kinked capital allocation line.
39. The first major step in asset allocation is:
A) assessing risk tolerance.
B) analyzing financial statements.
C) estimating security betas.
D) identifying market anomalies.
E) none of the above.
Answer: A A should be the first consideration in asset allocation. B, C, and D refer to security selection.
40. Based on their relative degrees of risk tolerance
A) investors will hold varying amounts of the risky asset in their portfolios.
B) all investors will have the same portfolio asset allocations.
C) investors will hold varying amounts of the risk-free asset in their portfolios.
D) A and C.
E) none of the above.
Answer: D Rationale: By determining levels of risk tolerance, investors can select the optimum portfolio for their own
needs; these asset allocations will vary between amounts of risk-free and risky assets based on risk tolerance.
41. Asset allocation
A) may involve the decision as to the allocation between a risk-free asset and a risky asset.
B) may involve the decision as to the allocation among different risky assets.
C) may involve considerable security analysis.
D) A and B.
E) A and C.
Answer: D Difficulty: Easy Rationale: A and B are possible steps in asset allocation. C is related to security selection.
42. In the mean-standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is
called
.
A) the Security Market Line
B) the Capital Allocation Line
C) the Indifference Curve
D) the investor's utility line
E) none of the above
Answer: B Difficulty: Moderate Rationale: The Capital Allocation Line (CAL) illustrates the possible combinations
of a risk-free asset and a risky asset available to the investor.
43. Treasury bills are commonly viewed as risk-free assets because
A) their short-term nature makes their values insensitive to interest rate fluctuations.
B) the inflation uncertainty over their time to maturity is negligible.
C) their term to maturity is identical to most investors' desired holding periods.
D) Both A and B are true.
E) Both B and C are true.
Answer: D Rationale: Treasury bills do not exactly match most investor's desired holding periods, but because they
mature in only a few weeks or months they are relatively free of interest rate sensitivity and inflation uncertainty.
Use the following to answer questions 44-47:
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information
below refers to these assets.
44. What is the expected return on Bo's complete portfolio?
A) 10.32%
B) 5.28%
C) 9.62%
D) 8.44%
E) 7.58%
Answer: A Difficulty: Easy Rationale: E(rC) = .8*12.00% + .2*3.6% = 10.32%
45. What is the standard deviation of Bo's complete portfolio?
A) 7.20%
B) 5.40%
C) 6.92%
D) 4.98%
E) 5.76%
Answer: E Difficulty: Easy Rationale: Std. Dev. of C = .8*7.20% = 5.76%
46. What is the equation of Bo's Capital Allocation Line?
A) E(rC) = 7.2 + 3.6 * Standard Deviation of C
B) E(rC) = 3.6 + 1.167 * Standard Deviation of C
C) E(rC) = 3.6 + 12.0 * Standard Deviation of C
D) E(rC) = 0.2 + 1.167 * Standard Deviation of C
E) E(rC) = 3.6 + 0.857 * Standard Deviation of C
Answer: B Rationale: The intercept is the risk-free rate (3.60%) and the slope is (12.00%-3.60%)/7.20% = 1.167.
47. What are the proportions of Stocks A, B, and C, respectively in Bo's complete portfolio?
A) 40%, 25%, 35%
B) 8%, 5%, 7%
C) 32%, 20%, 28%
D) 16%, 10%, 14%
E) 20%, 12.5%, 17.5%
Answer: C Proportion in A = .8 * 40% = 32%; proportion in B = .8 * 25% = 20%; proportion in C = .8 * 35% = 28%.
48. 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.
Answer: D Rationale: This references the procedure described on page 207-208 of the text. The authors describe how
to trace out indifference curves using a spreadsheet.
49. 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
Answer: E Rationale: 'The Capital Market Line is the Capital Allocation Line based on the one-month T-Bill rate and
a broad index of common stocks. It applies to an investor pursuing a passive management strategy.
50.
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) none of the above
Answer: C Difficulty: Moderate Rationale: E(rP) = 0.4(18%) + 0.6(4%) = 9.6%; sP = 0.4(0.10)1/2 = 12.6%.
51.
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) none of the above
Answer: A Difficulty: Moderate Rationale: E(rP) = 0.7(11%) + 0.3(3%) = 8.6%; sP = 0.7(0.12)1/2 = 24.2%.
Use the following to answer questions 52-54: 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.
52. 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
Answer: C Difficulty: Moderate Rationale: 8% = w1(11%) + (1 - w1)(3%); 8% = 11%w1 + 3% - 3%w1; 5% = 8%w1;
w1 = 0.625; 1 - w1 = 0.375; 0.625(11%) + 0.375(3%) = 8.0%.
53. 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.
Answer: C Difficulty: Moderate Rationale: 0.08 = x(0.20); x = 40% in risky asset.
54. 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.
Answer: D Difficulty: Moderate Rationale: (0.11 - 0.03)/0.20 = 0.40.
Use the following to answer questions 55-57: 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.
55. 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) 46.1% and 53.8%
E) Cannot be determined.
Answer: A Difficulty: Moderate Rationale: 11% = w1(17%) + (1 - w1)(4%); 11% = 17%w1 + 4% - 4%w1;
7% = 13%w1; w1 = 0.538; 1 - w1 = 0.461; 0.538(17%) + 0.462(4%) = 11.0%.
56. 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.
Answer: B Difficulty: Moderate Rationale: 0.20 = x(0.40); x = 50% in risky asset.
57. 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.
Answer: A Difficulty: Moderate Rationale: (0.17 - 0.04)/0.40 = 0.325.
Essay Questions
58. Discuss the differences between investors who are risk averse, risk neutral, and risk loving.
Answer: 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 "fun" of confronting risk. The purpose of this question is
to ascertain that the student understands the different attitudes toward risk exhibited by different individuals.
59. In the utility function: U = E(r) - -0.005As2, what is the significance of "A"?
A is simply a scale factor indicating the investor's degree of risk aversion. The higher the value of A, the more risk averse the
investor. Of course, the investment advisor must spend some time with client, either via personal conversation or the
administration of a "risk tolerance quiz" in order to assign the appropriate value of A to a given investor.
The rationale for this question is to ascertain whether the student understands the meaning of the variable, A. This variable, as
such, is not presented in most investments texts and it is important that the student understands how the investment advisor
assigns a value to A.
60. 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.
A fair game is a prospect that has a zero risk premium. Investors who are risk averse reject investment portfolios that are fair
games or worse. They will consider risk-free investments and risky investments with positive risk premiums. The risk-averse
investor “penalizes” the expected rate of return of a risky portfolio by a certain percent to account for the risk involved. The
risk-averse investor's utility function favors expected return and disfavors risk, as measured by variance of returns. In the utility
function U=E(R) - .005A*Variance, the risk-averse investor has a positive “A” value so that the second term reduces the level
of utility as the variance increases.
This question tests whether the student understands the interrelationships between the terms risk, risk premium, speculation,
and fair game, and how these terms are quantified by a utility function.
61. 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.
The graph for Harry should show upward-sloping curves because he needs to be compensated with additional expected return
to maintain a certain level of satisfaction when he takes on more risk. Eddie should have horizontal indifference curves, parallel
to the X axis. Since he is risk-neutral, he only cares about expected return. The higher the expected return, the higher his
utility. Ozzie's curves will be downward sloping. The fact that he likes risk means that he is willing to forego some expected
return to have the opportunity to take on more risk. This question allows the student to review the concepts of attitude toward
risk and utility as they related to the resulting indifference curves.
62. Toby and Hannah are two risk-averse investors. Toby is more risk-averse than Hannah. Draw one indifference curve
for Toby and one indifference curve for Hannah on the same graph. Show how these curves illustrate their relative
levels of risk aversion.
The curves may or may not intersect within the range of the graph. Toby's curve will have a steeper slope than Hannah's. The
levels of risk aversion can be illustrated by examining the curves' slopes over a fixed range. Because Toby's curve is steeper
than Hannah's, for a fixed change in standard deviation on the horizontal axis, he will have a greater change in expected return
on the vertical axis. It takes more compensation in the form of expected return to allow Toby to maintain his level of utility
than it takes for Hannah. This question tests whether the student understands the nature of indifference curves and how the riskreturn tradeoff is related to the level of risk aversion.
63. Discuss the characteristics of indifference curves, and the theoretical value of these curves in the portfolio building
process
Indifference curves represent the trade-off between two variables. In portfolio building, the choice is between risk and return.
The investor is indifferent between all possible portfolios lying on one indifference curve. However, indifference curves are
contour maps, with all curves parallel to each other. The curve plotting in the most northwest position is the curve offering the
greatest utility to the investor. However, this most desirable curve may not be attainable in the market place. The point of
tangency between an indifference curve (representing what is desirable) and the capital allocation line (representing what is
possible). is the optimum portfolio for that investor.
This question is designed to ascertain that the student understands the concepts of utility, what is desirable by the investor, what
is possible in the market place, and how to optimize an investor's portfolio, theoretically.
64.Describe how an investor may combine a risk-free asset and one risky asset in order to obtain the optimal portfolio for that
investor.
The investor may combine a risk-free asset (U. S. T-bills or a money market mutual fund and a risky asset, such as an indexed
mutual fund in the proper portions to obtain the desired risk-return relationship for that investor. The investor must realize that
the risk-return relationship is a linear one, and that in order to earn a higher return, the investor must be willing to assume more
risk. The investor must first determine the amount of risk that he or she can tolerate (in terms of the standard deviation of the
total portfolio, which is the product of the proportion of total assets invested in the risky asset and the standard deviation of the
risky asset). One minus this weight is the proportion of total assets to be invested in the risk-free asset. The portfolio return is
the weighted averages of the returns on the two respective assets. Such an asset allocation plan is probably the easiest, most
efficient, and least expensive for the individual investor to build an optimal portfolio.
This question is designed to insure that the student understands ,how using the simple strategy of combining two mutual funds,
the investor can build an optimal portfolio, based on the investor's risk tolerance.
65. The optimal proportion of the risky asset in the complete portfolio is given by the equation y* = [E(r P)-rf] /
(.01A*Variance of P). For each of the variables on the right side of the equation, discuss the impact the variable's
effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse.
The optimal proportion in y is the one that maximizes the investor's utility. Utility is positively related to the risk premium
[E(rP)-rf]. This makes sense because the more expected return an investor gets, the happier he is. The variable “A” represents
the degree of risk aversion. As risk aversion increases, “A” increases. This causes y* to decrease because we are dividing by
a higher number. It makes sense that a more risk-averse investor would hold a smaller proportion of his complete portfolio in
the risky asset and a higher proportion in the risk-free asset. Finally, the standard deviation of the risky portfolio is inversely
related to y*. As P's risk increases, we are again dividing by a larger number, making y* smaller. This corresponds with the
risk-averse investor's dislike of risk as measured by standard deviation.
This allows the students to explore the nature of the equation that was derived by maximizing the investor's expected utility.
The student can illustrate an understanding of the variables that supersedes the application of the equation in calculating the
optimal proportion in P.
66. You are evaluating two investment alternatives. One is a passive market portfolio with an expected return of 10% and
a standard deviation of 16%. The other is a fund that is actively managed by your broker. This fund has an expected
return of 15% and a standard deviation of 20%. The risk-free rate is currently 7%. Answer the questions below based
on this information.
a. What is the slope of the Capital Market Line?
b. What is the slope of the Capital Allocation Line offered by your broker's fund?
c. Draw the CML and the CAL on one graph.
d. What is the maximum fee your broker could charge and still leave you as well off as if you had invested in the
passive market fund? (Assume that the fee would be a percentage of the investment in the broker's fund, and would
be deducted at the end of the year.)
e. How would it affect the graph if the broker were to charge the full amount of the fee?
a. The slope of the CML is (10-7)/16 = 0.1875.
b. The slope of the CAL is (15-7)/20= 0.40.
c. On the graph, both the CML and the CAL have an intercept equal to the risk-free rate (7%). The CAL, with a slope of
0.40, is steeper than the CML, with a slope of 0.1875.
d. To find the maximum fee the broker can charge, the equation (15-7-fee)/20 = 0.1875 is solved for “fee”. The resulting fee
is 4.25%.
e. If the broker charges the full amount of the fee, the CAL's slope would also be 0.1875, so it would rotate down and be
identical to the CML.
This question tests both the application of CAL/CML calculations and the concepts involved.
Chapter 6 Risk Aversion and Capital Allocation to Risky Assets
Multiple Choice Questions
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.
Risk-averse investors only accept risky investments that offer risk premiums over the risk-free rate.
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
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.
5. 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.
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).
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. none of the above
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 riskreturn trade-offs might intersect.
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 feeling about loss
Investment advisors would be least likely to assess the level of return the investor prefers. The investors investing experience,
financial security, feelings about loss, and disposition toward risky or conservative choices will impact risk tolerance.
Assume an investor with the following utility function: U = E(r) - 3/2(s2).
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. none of the above.
U(c) = 9.02%; highest utility of possibilities.
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. none of the above
0.06 = 0.15 - A/2(0.15)2; 0.06 - 0.15 = -A/2(0.0225); -0.09 = -0.01125A;
A = 8; So U = 0.15 - 8/2(0.15)2 = 6%; same as U(Rf) = 6%.
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 C is the only choice with the same risk-return tradeoff.
Investment
1
2
3
4
Expected Return E(r)
0.12
0.15
0.21
0.24
Standard Deviation
0.3
0.5
0.16
0.21
U = E(r) - (A/2)s2, where A = 4.0.
14. 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
U(c) = 0.21 - 4/2(0.16)2 = 15.88 (highest utility of choices).
18. 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 measure.
D. B and C.
E. none of the above.
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.
19. 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.
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.
22. 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.
The certainty equivalent rate of a portfolio is the rate that a risk-free investment would need to offer with certainty to be
considered equally attractive as the risky portfolio.
23. According to the mean-variance criterion, which of the statements below is correct?
Investment
A
B
C
D
E(r)
10%
21%
18%
24%
Standard Deviation
5%
11%
23%
16%
A. Investment B dominates Investment A.
B. Investment B dominates Investment C.
C. Investment D dominates all of the other investments.
D. Investment D dominates only Investment B.
E. Investment C dominates investment A.
This question tests the student's understanding of how to apply the mean-variance criterion.
25. The Capital Allocation Line can be described as the
A. investment opportunity set formed with a risky asset and a risk-free asset.
B. investment opportunity set formed with two risky assets.
C. line on which lie all portfolios that offer the same utility to a particular investor.
D. line on which lie all portfolios with the same expected rate of return and different standard deviations.
E. none of the above.
The CAL has an intercept equal to the risk-free rate. It is a straight line through the point representing the risk-free asset and
the risky portfolio, in expected-return/standard deviation space.
26. Which of the following statements regarding the Capital Allocation Line (CAL) is false?
A. The CAL shows risk-return combinations.
B. The slope of the CAL equals the increase in the expected return of a risky portfolio per unit of additional standard
deviation.
C. The slope of the CAL is also called the reward-to-volatility ratio.
D. The CAL is also called the efficient frontier of risky assets in the absence of a risk-free asset.
E. Both A and D are true.
The CAL consists of combinations of a risky asset and a risk-free asset whose slope is the reward-to-volatility ratio; thus, all
statements except d are true.
28. An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04
and 70 percent in a T-bill that pays 6 percent. His portfolio's expected return and standard deviation are
and
, respectively.
A. 0.114; 0.12
B. 0.087; 0.06
C. 0.295; 0.12
D. 0.087; 0.12
E. none of the above
E(rP) = 0.3(15%) + 0.7(6%) = 8.7%; sP = 0.3(0.04)1/2 = 6%.
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a
rate of return of 0.05.
32. 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 0.09?
A. 85% and 15%
B. 75% and 25%
C. 67% and 33%
D. 57% and 43%
E. cannot be determined
9% = w1(12%) + (1 - w1)(5%); 9% = 12%w1 + 5% - 5%w1; 4% = 7%w1;
w1 = 0.57; 1 - w1 = 0.43; So, 0.57(12%) + 0.43(5%) = 8.99%.
34. A portfolio that has an expected outcome of $115 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 $43 at the risk-free rate and investing the total amount ($143) 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, (115 - 100)/100 = 15%; .15 = w1(.12) + (1 - w1)(.05); .15 = .12w1 + .05 - .05w1; 0.10 = 0.07w1; w1 = 1.43($100) =
$143; (1 - w1)$100 = -$43.
36. Consider a T-bill with a rate of return of 5 percent and the following risky securities:
Security A: E(r) = 0.15; Variance = 0.04
Security B: E(r) = 0.10; Variance = 0.0225
Security C: E(r) = 0.12; Variance = 0.01
Security D: E(r) = 0.13; Variance = 0.0625
From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk-averse investor always
choose his portfolio?
A. The set of portfolios formed with the T-bill and security A.
B. The set of portfolios formed with the T-bill and security B.
C. The set of portfolios formed with the T-bill and security C.
D. The set of portfolios formed with the T-bill and security D.
E. Cannot be determined.
Security C has the highest reward-to-volatility ratio.
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X
and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of
0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.
37. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest
in the T-bill and P, respectively?
A. 0.25; 0.75
B. 0.19; 0.81
C. 0.65; 0.35
D. 0.50; 0.50
E. cannot be determined
E(rp) = 0.6(14%) + 0.4(10%) = 12.4%; 11% = 5x + 12.4(1 - x); x = 0.189 (T-bills) and (1-x) =0.811 (risky asset).
38. If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest
in the T-bill, X, and Y, respectively if you keep X and Y in the same proportions to each other as in portfolio P?
A. 0.25; 0.45; 0.30
B. 0.19; 0.49; 0.32
C. 0.32; 0.41; 0.27
D. 0.50; 0.30; 0.20
E. cannot be determined
E(rp) = .10 = 5w + 12.4(1 - w); x = 0.32 (weight of T-bills); As composition of X and Y are .6 and .4 of P, respectively, then
for 0.68 weight in P, the respective weights must be 0.41 and 0.27; .6(.68) = 41%; .4(.68) = 27%
40. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio
that has an expected outcome of $1,200?
A. Cannot be determined
B. $54; $568; $378
C. $568; $54; $378
D. $378; $54; $568
E. $108; $514; $378
($1,200 - $1,000)/$1,000 = 12%; (0.6)14% + (0.4)10% = 12.4%; 12% = w5% + 12.4%(1 - w); w = .054; 1 - w = .946;
w = 0.054($1,000) = $54 (T-bills); 1 - w = 1 - 0.054 = 0.946($1,000) = $946 (in P); $946 x 0.6 = $568 in X; $946 x 0.4 = $378 in Y.
42. The change from a straight to a kinked capital allocation line is a result of:
A. reward-to-volatility ratio increasing.
B. borrowing rate exceeding lending rate.
C. an investor's risk tolerance decreasing.
D. increase in the portfolio proportion of the risk-free asset.
E. none of the above.
The linear capital allocation line assumes that the investor may borrow and lend at the same rate (the risk-free rate), which
obviously is not true. Relaxing this assumption and incorporating the higher borrowing rates into the model results in the
kinked capital allocation line.
43. The first major step in asset allocation is:
A. assessing risk tolerance.
B. analyzing financial statements.
C. estimating security betas.
D. identifying market anomalies.
E. none of the above.
A should be the first consideration in asset allocation. B, C, and D refer to security selection.
44. Based on their relative degrees of risk tolerance
A. investors will hold varying amounts of the risky asset in their portfolios.
B. all investors will have the same portfolio asset allocations.
C. investors will hold varying amounts of the risk-free asset in their portfolios.
D. A and C.
E. none of the above.
By determining levels of risk tolerance, investors can select the optimum portfolio for their own needs; these asset allocations
will vary between amounts of risk-free and risky assets based on risk tolerance.
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information
below refers to these assets.
E(Rp)
12.00%
Standard Deviation of P
7.20%
T-Bill rate
3.60%
Proportion of Complete Portfolio in P
80%
Proportion of Complete Portfolio in T-Bills
20%
Composition of P
Stock A
40.00%
Stock B
25.00%
Stock C
35.00%
Total
100.00%
48. What is the expected return on Bo's complete portfolio?
A. 10.32%
B. 5.28%
C. 9.62%
D. 8.44%
E. 7.58%
E(rC) = .8 * 12.00% + .2 * 3.6% = 10.32%
49. What is the standard deviation of Bo's complete portfolio?
A. 7.20%
B. 5.40%
C. 6.92%
D. 4.98%
E. 5.76%
Std. Dev. of C = .8 * 7.20% = 5.76%
50. What is the equation of Bo's Capital Allocation Line?
A. E(rC) = 7.2 + 3.6 * Standard Deviation of C
B. E(rC) = 3.6 + 1.167 * Standard Deviation of C
C. E(rC) = 3.6 + 12.0 * Standard Deviation of C
D. E(rC) = 0.2 + 1.167 * Standard Deviation of C
E. E(rC) = 3.6 + 0.857 * Standard Deviation of C
The intercept is the risk-free rate (3.60%) and the slope is (12.00%-3.60%)/7.20% = 1.167.
51. What are the proportions of Stocks A, B, and C, respectively in Bo's complete portfolio?
A. 40%, 25%, 35%
B. 8%, 5%, 7%
C. 32%, 20%, 28%
D. 16%, 10%, 14%
E. 20%, 12.5%, 17.5%
Proportion in A = .8 * 40% = 32%; proportion in B = .8 * 25% = 20%; proportion in C = .8 * 35% = 28%.
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
‘The Capital Market Line is the Capital Allocation Line based on the one-month T-Bill rate and a broad index of common
stocks. It applies to an investor pursuing a passive management strategy.
Chp 7 Optimal Risky Portfolio
Multiple Choice Questions
1. Market risk is also referred to as
A) systematic risk, diversifiable risk.
B) systematic risk, nondiversifiable risk.
C) unique risk, nondiversifiable risk.
D) unique risk, diversifiable risk.
E) none of the above.
Answer: B Rationale: Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be
eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to
the risk that can be eliminated from the portfolio by diversification.
2. The risk that can be diversified away is
A) firm specific risk.
B) beta.
C) systematic risk.
D) market risk.
E) none of the above.
Answer: A Difficulty: Easy Rationale: See explanations for 1 and 2 above.
3. The variance of a portfolio of risky securities
A) is a weighted sum of the securities' variances.
B) is the sum of the securities' variances.
C) is the weighted sum of the securities' variances and covariances.
D) is the sum of the securities' covariances.
E) none of the above.
Answer: C Rationale: The variance of a portfolio of risky securities is a weighted sum taking into account both the
variance of the individual securities and the covariances between securities.
4.
The expected return of a portfolio of risky securities
A) is a weighted average of the securities' returns.
B) is the sum of the securities' returns.
C) is the weighted sum of the securities' variances and covariances.
D) A and C.
E) none of the above.
Answer: A Difficulty: Easy
5. Other things equal, diversification is most effective when
A) securities' returns are uncorrelated.
B) securities' returns are positively correlated.
C) securities' returns are high.
D) securities' returns are negatively correlated.
E) B and C.
Answer: D Difficulty: Moderate Rationale: Negative correlation among securities results in the greatest reduction
of portfolio risk, which is the goal of diversification.
6. The efficient frontier of risky assets is
A) the portion of the investment opportunity set that lies above the global minimum variance portfolio.
B) the portion of the investment opportunity set that represents the highest standard deviations.
C) the portion of the investment opportunity set which includes the portfolios with the lowest standard deviation.
D) the set of portfolios that have zero standard deviation.
E) both A and B are true.
Answer: A Difficulty: Moderate
Rationale: Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of
risk. Only those portfolios above the global minimum variance portfolio meet this criterion.
7. The Capital Allocation Line provided by a risk-free security and N risky securities is
A) the line that connects the risk-free rate and the global minimum-variance portfolio of the risky securities.
B) the line that connects the risk-free rate and the portfolio of the risky securities that has the highest expected
return on the efficient frontier.
C) the line tangent to the efficient frontier of risky securities drawn from the risk-free rate.
D) the horizontal line drawn from the risk-free rate.
E) none of the above.
Answer: C Difficulty: Moderate
Rationale: The Capital Allocation Line represents the most efficient combinations of the risk-free asset and risky
securities. Only C meets that definition.
8. Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The
global minimum variance portfolio has a standard deviation that is always
A) greater than zero.
B) equal to zero.
C) equal to the sum of the securities' standard deviations.
D) equal to -1.
E) none of the above.
Answer: B Rationale: If two securities were perfectly negatively correlated, the weights for the minimum variance portfolio
for those securities could be calculated, and the standard deviation of the resulting portfolio would be zero.
9. Which of the following statements is (are) true regarding the variance of a portfolio of two risky securities?
A) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
B) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
C) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.
D) A and B.
E) A and C.
Answer: C Difficulty: Moderate
Rationale: The lower the correlation between the returns of the securities, the more portfolio risk is reduced.
10. Efficient portfolios of N risky securities are portfolios that
A) are formed with the securities that have the highest rates of return regardless of their standard deviations.
B) have the highest rates of return for a given level of risk.
C) are selected from those securities with the lowest standard deviations regardless of their returns.
D) have the highest risk and rates of return and the highest standard deviations.
E) have the lowest standard deviations and the lowest rates of return.
Answer: B Difficulty: Moderate Rationale: Portfolios that are efficient are those that provide the highest expected
return for a given level of risk.
11. Which of the following statement(s) is (are) true regarding the selection of a portfolio from those that lie on the
Capital Allocation Line?
A) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than
more risk-averse investors.
B) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than
less risk-averse investors.
C) Investors choose the portfolio that maximizes their expected utility.
D) A and C.
E) B and C.
Answer: Rationale: All rational investors select the portfolio that maximizes their expected utility; for investors who are
relatively more risk-averse, doing so means investing less in the optimal risky portfolio and more in the risk-free asset.
Use the following to answer questions 12-18:
Consider the following probability distribution for stocks A and B:
12. The expected rates of return of stocks A and B are
and
, respectively.
A) 13.2%; 9%
B) 14%; 10%
C) 13.2%; 7.7%
D) 7.7%; 13.2%
E) none of the above
Answer: C Rationale: E(RA) = 0.1(10%) + 0.2(13%) + 0.2(12%) + 0.3(14%) + 0.2(15%) = 13.2%; E(RB) = 0.1(8%) +
0.2(7%) + 0.2(6%) + 0.3(9%) + 0.2(8%) = 7.7%.
13. The standard deviations of stocks A and B are
and
, respectively.
A) 1.5%; 1.9%
B) 2.5%; 1.1%
C) 3.2%; 2.0%
D) 1.5%; 1.1%
E) none of the above
Answer: D sA = [0.1(10% - 13.2%)2 + 0.2(13% - 13.2%)2 + 0.2(12% - 13.2%)2 + 0.3(14% - 13.2%)2 + 0.2(15% - 13.2%)2]1/2 = 1.5%;
sB = [0.1(8% - 7.7%)2 + 0.2(7% - 7.7%)2 + 0.2(6% - 7.7%)2 + 0.3(9% - 7.7%)2 + 0.2(8% - 7.7%)2 = 1.1%.
14. The coefficient of correlation between A and B is
A) 0.47.
B) 0.60.
C) 0.58
D) 1.20.
E) none of the above.
Answer: A Rationale: covA,B = 0.1(10% - 13.2%)(8% - 7.7%) + 0.2(13% - 13.2%)(7% - 7.7%) + 0.2(12% - 13.2%)(6% 7.7%) + 0.3(14% - 13.2%)(9% - 7.7%) + 0.2(15% - 13.2%)(8% - 7.7%) = 0.76; rA,B = 0.76/[(1.1)(1.5)] = 0.47.
15. If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and
standard deviation?
A) 9.9%; 3%
B) 9.9%; 1.1%
C) 11%; 1.1%
D) 11%; 3%
E) none of the above
Answer: B E(RP) = 0.4(13.2%) + 0.6(7.7%) = 9.9%; sP = [(0.4)2(1.5)2 + (0.6)2(1.1)2 + 2(0.4)(0.6)(1.5)(1.1)(0.46)]1/2 = 1.1%.
16. Let G be the global minimum variance portfolio. The weights of A and B in G are
and
,
respectively.
A) 0.40; 0.60
B) 0.66; 0.34
C) 0.34; 0.66
D) 0.76; 0.24
E) 0.24; 0.76
Answer: E wA = [(1.1)2 - (1.5)(1.1)(0.46)]/[(1.5)2 + (1.1)2 - (2)(1.5)(1.1)(0.46) = 0.23;
wB = 1 - 0.23 = 0.77.Note that the above solution assumes the solutions obtained in question 13 and 14.
17. The expected rate of return and standard deviation of the global minimum variance portfolio, G, are
and
, respectively.
A) 10.07%; 1.05%
B) 9.04%; 2.03%
C) 10.07%; 3.01%
D) 9.04%; 1.05%
E) none of the above
Answer: D E(RG) = 0.23(13.2%) + 0.77(7.7%) = 8.97% .9%; sG = [(0.23)2(1.5)2 + (0.77)2(1.1)2 +(2)(0.23)(0.77)(1.5)(1.1)(0.46)] 1/2 = 1.05%
18. Which of the following portfolio(s) is (are) on the efficient frontier?
A) The portfolio with 20 percent in A and 80 percent in B.
B) The portfolio with 15 percent in A and 85 percent in B.
C) The portfolio with 26 percent in A and 74 percent in B.
D) The portfolio with 10 percent in A and 90 percent in B.
E) A and B are both on the efficient frontier.
Answer: C The Portfolio's E(Rp), sp, Reward/volatility ratios are 20A/80B: 8.8%, 1.05%, 8.38; 15A/85B: 8.53%, 1.06%,
8.07; 26A/74B: 9.13%, 1.05%, 8.70; 10A/90B: 8.25%, 1.07%, 7.73. The portfolio with 26% in A and 74% in B dominates
all of the other portfolios by the mean-variance criterion.
Use the following to answer questions 19-21:
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard
deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
19. The weights of A and B in the global minimum variance portfolio are
and
, respectively.
A) 0.24; 0.76
B) 0.50; 0.50
C) 0.57; 0.43
D) 0.43; 0.57
E) 0.76; 0.24
Answer: D Difficulty: Moderate Rationale: wA = 12 /(16 + 12) = 0.4286; wB = 1 - 0.4286 = 0.5714.
20. The risk-free portfolio that can be formed with the two securities will earn
rate of return.
A) 8.5%
B) 9.0%
C) 8.9%
D) 9.9%
E) none of the above
Answer: C Difficulty: Difficult Rationale: E(RP) = 0.43(10%) + 0.57(8%) = 8.86%.
21. Which of the following portfolio(s) is (are) most efficient?
A) 45 percent in A and 55 percent in B.
B) 65 percent in A and 35 percent in B.
C) 35 percent in A and 65 percent in B.
D) A and B are both efficient.
E) A and C are both efficient.
Answer: D Rationale: The Portfolio E(Rp), sp, and Reward/volatility ratios are 45A/55B: 8.9%, 0.6%, 14.83;
65A/35B: 9.3%, 6.2%, 1.5; 35A/65B: 8.7%, 2.2%, 3.95. Both A and B are efficient according to the mean-variance
criterion. A has a much higher Reward/volatility ratio.
22. An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital
Allocation Line must:
A) lend some of her money at the risk-free rate and invest the remainder in the optimal risky portfolio.
B) borrow some money at the risk-free rate and invest in the optimal risky portfolio.
C) invest only in risky securities.
D) such a portfolio cannot be formed.
E) B and C
Answer: E Rationale: The only way that an investor can create portfolios to the right of the Capital Allocation Line
is to create a borrowing portfolio (buy stocks on margin). In this case, the investor will not hold any of the risk-free
security, but will hold only risky securities.
23. Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
A) Only portfolio W cannot lie on the efficient frontier.
B) Only portfolio X cannot lie on the efficient frontier.
C) Only portfolio Y cannot lie on the efficient frontier.
D) Only portfolio Z cannot lie on the efficient frontier.
E) Cannot tell from the information given.
Answer: A Rationale: When plotting the above portfolios, only W lies below the efficient frontier as described by
Markowitz. It has a higher standard deviation than Z with a lower expected return.
24. Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
A) Only portfolio A cannot lie on the efficient frontier.
B) Only portfolio B cannot lie on the efficient frontier.
C) Only portfolio C cannot lie on the efficient frontier.
D) Only portfolio D cannot lie on the efficient frontier.
E) Cannot tell from the information given.
Answer: D When plotting the above portfolios, only W lies below the efficient frontier as described by Markowitz. It has a
higher standard deviation than Z with a lower expected return.
25. Portfolio theory as described by Markowitz is most concerned with:
A) the elimination of systematic risk.
B) the effect of diversification on portfolio risk.
C) the identification of unsystematic risk.
D) active portfolio management to enhance returns.
E) none of the above.
Answer: B Markowitz was concerned with reducing portfolio risk by combining risky securities with differing return patterns.
26. The measure of risk in a Markowitz efficient frontier is:
A) specific risk.
B) standard deviation of returns.
C) reinvestment risk.
D) beta.
E) none of the above.
Answer: B Markowitz was interested in eliminating diversifiable risk (and thus lessening total risk) and thus was interested
in decreasing the standard deviation of the returns of the portfolio.
27. A statistic that measures how the returns of two risky assets move together is:
A) variance.
B) standard deviation.
C) covariance.
D) correlation.
E) C and D.
Answer: E Covariance measures whether security returns move together or in opposition; however, only the sign, not the
magnitude, of covariance may be interpreted. Correlation, which is covariance standardized by the product of the standard
deviations of the two securities, may assume values only between +1 and -1; thus, both the sign and the magnitude may be
interpreted regarding the movement of one security's return relative to that of another security.
28. The unsystematic risk of a specific security
A) is likely to be higher in an increasing market.
B) results from factors unique to the firm.
C) depends on market volatility.
D) cannot be diversified away.
E) none of the above.
Answer: B Rationale: Unsystematic (or diversifiable or firm-specific) risk refers to factors unique to the firm. Such
risk may be diversified away; however, market risk will remain.
29. Which statement about portfolio diversification is correct?
A) Proper diversification can reduce or eliminate systematic risk.
B) The risk-reducing benefits of diversification do not occur meaningfully until at least 50-60 individual securities
have been purchased.
C) Because diversification reduces a portfolio's total risk, it necessarily reduces the portfolio's expected return.
D) Typically, as more securities are added to a portfolio, total risk would be expected to decrease at a decreasing
rate.
E) None of the above statements is correct.
Answer: D Rationale: Diversification can eliminate only nonsystematic risk; relatively few securities are required to reduce
this risk, thus diminishing returns result quickly. Diversification does not necessarily reduce returns.
30. The individual investor's optimal portfolio is designated by:
A) The point of tangency with the indifference curve and the capital allocation line.
B) The point of highest reward to variability ratio in the opportunity set.
C) The point of tangency with the opportunity set and the capital allocation line.
D) The point of the highest reward to variability ratio in the indifference curve.
E) None of the above.
Answer: A Rationale: The indifference curve represents what is acceptable to the investor; the capital allocation line
represents what is available in the market. The point of tangency represents where the investor can obtain the greatest utility
from what is available.
31. For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks?
A) +1.00.
B) +0.50.
C) 0.00.
D) -1.00.
E) none of the above.
Answer: D Rationale: The correlation coefficient of -1.00 provides the greatest diversification benefits.
32. In a two-security minimum variance portfolio where the correlation between securities is greater than -1.0
A) the security with the higher standard deviation will be weighted more heavily.
B) the security with the higher standard deviation will be weighted less heavily.
C) the two securities will be equally weighted.
D) the risk will be zero.
E) the return will be zero.
Answer: B Rationale: The security with the higher standard deviation will be weighted less heavily to produce minimum
variance. The return will not be zero; the risk will not be zero unless the correlation coefficient is -1.
33. Which of the following is not a source of systematic risk?
A) the business cycle.
B) interest rates.
C) personnel changes
D) the inflation rate.
E) exchange rates.
Answer: C Rationale: Personnel changes are a firm-specific event that is a component of non-systematic risk. The others
are all sources of systematic risk.
34. The global minimum variance portfolio formed from two risky securities will be riskless when the correlation
coefficient between the two securities is
A) 0.0
B) 1.0
C) 0.5
D) -1.0
E) negative
Answer: D Rationale: The global minimum variance portfolio will have a standard deviation of zero whenever the two
securities are perfectly negatively correlated.
35. Security X has expected return of 12% and standard deviation of 20%. Security Y has expected return of 15% and
standard deviation of 27%. If the two securities have a correlation coefficient of 0.7, what is their covariance?
A) 0.038
B) 0.070
C) 0.018
D) 0.013
E) 0.054
Answer: A
Rationale: Cov(rX, rY) = (.7)(.20)(.27) = .0378
36. When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio,
A) the portfolio standard deviation will be greater than the weighted average of the individual security standard deviations.
B) the portfolio standard deviation will be less than the weighted average of the individual security standard deviations.
C) the portfolio standard deviation will be equal to the weighted average of the individual security standard deviations.
D) the portfolio standard deviation will always be equal to the securities' covariance.
E) none of the above is true.
Answer: B Whenever two securities are less than perfectly positively correlated, the standard deviation of the portfolio of the
two assets will be less than the weighted average of the two securities' standard deviations. There is some benefit to
diversification in this case.
37. The line representing all combinations of portfolio expected returns and standard deviations that can be constructed
from two available assets is called the
A) risk/reward tradeoff line
B) Capital Allocation Line
C) efficient frontier
D) portfolio opportunity set
E) Security Market Line
Answer: D Rationale: The portfolio opportunity set is the line describing all combinations of expected returns and standard
deviations that can be achieved by a portfolio of risky assets.
38. Given an optimal risky portfolio with expected return of 14% and standard deviation of 22% and a risk free rate of
6%, what is the slope of the best feasible CAL?
A) 0.64
B) 0.14
C) 0.08
D) 0.33
E) 0.36
Answer: E
Rationale: Slope = (14-6)/22 = .3636
39. The risk that can be diversified away in a portfolio is referred to as
.
I)
diversifiable risk
II) unique risk
III) systematic risk
IV) firm-specific risk
A) I, III, and IV
B) II, III, and IV
C) III and IV
D) I, II, and IV
E) I, II, III, and IV
Answer: D Rationale: All of these terms are used interchangeably to refer to the risk that can be removed from a portfolio
through diversification.
40. As the number of securities in a portfolio is increased, what happens to the average portfolio standard deviation?
A) It increases at an increasing rate.
B) It increases at a decreasing rate.
C) It decreases at an increasing rate.
D) It decreases at a decreasing rate.
E) It first decreases, then starts to increase as more securities are added.
Answer: D Rationale: Statman's study showed that the risk of the portfolio would decrease as random stocks were added. At
first the risk decreases quickly, but then the rate of decrease slows substantially, as shown in Figure 7.2. The minimum
portfolio risk in the study was 19.2%.
41. In words, the covariance considers the probability of each scenario happening and the interaction between
A) securities' returns relative to their variances.
B) securities' returns relative to their mean returns.
C) securities' returns relative to other securities' returns.
D) the level of return a security has in that scenario and the overall portfolio return.
E) the variance of the security's return in that scenario and the overall portfolio variance.
Answer: B As written in equation 7.4, the covariance of the returns between two securities is the sum over all scenarios of the
product of three things. The first item is the probability that the scenario will happen. The second and third terms represent
the deviations of the securities' returns in that scenario from their own expected returns.
42. The standard deviation of a two-asset portfolio is a linear function of the assets' weights when
A) the assets have a correlation coefficient less than zero.
B) the assets have a correlation coefficient equal to zero.
C) the assets have a correlation coefficient greater than zero.
D) the assets have a correlation coefficient equal to one.
E) the assets have a correlation coefficient less than one.
Answer: D Rationale: When there is a perfect positive correlation (or a perfect negative correlation), the equation for the
portfolio variance simplifies to a perfect square. The result is that the portfolio's standard deviation is linear relative to the
assets' weights in the portfolio.
43. A two-asset portfolio with a standard deviation of zero can be formed when
A) the assets have a correlation coefficient less than zero.
B) the assets have a correlation coefficient equal to zero.
C) the assets have a correlation coefficient greater than zero.
D) the assets have a correlation coefficient equal to one.
E) the assets have a correlation coefficient equal to negative one.
Answer: E Rationale: When there is a perfect negative correlation, the equation for the portfolio variance simplifies to a perfect
square. The result is that the portfolio’s standard deviation equals |wAσA – wBσB|, which can be set equal to zero. The solution
wA = σB/(σA + σB) and wB = 1 – wA will yield a zero-standard deviation portfolio.
44. When borrowing and lending at a risk-free rate are allowed, which Capital Allocation Line (CAL) should the investor
choose to combine with the efficient frontier?
I)
with the highest reward-to-variability ratio.
II) that will maximize his utility.
III) with the steepest slope.
IV) with the lowest slope.
A) I and III
B) I and IV
C) II and IV
D) I only
E) I, II, and III
Answer: E The optimal CAL is the one that is tangent to the efficient frontier. This CAL offers the highest reward-to-variability ratio,
which is the slope of the CAL. It will also allow the investor to reach his highest feasible level of utility.
45. Which Excel tool can be used to find the points along an efficient frontier?
A)
B)
C)
D)
E)
Regression
Solver
Scenarios
Goal Seek
Data Analysis
Answer: B Rationale: Even if the student isn't familiar with Excel's Solver tool, he should recognize it from the discussion in the text.
46. The separation property refers to the conclusion that
A) the determination of the best risky portfolio is objective and the choice of the best complete portfolio is subjective.
B) the choice of the best complete portfolio is objective and the determination of the best risky portfolio is objective.
C) the choice of inputs to be used to determine the efficient frontier is objective and the choice of the best CAL is
subjective.
D) the determination of the best CAL is objective and the choice of the inputs to be used to determine the efficient
frontier is subjective.
E) investors are separate beings and will therefore have different preferences regarding the risk-return tradeoff.
Answer: A Rationale: The determination of the optimal risky portfolio is purely technical and can be done by a manager. The
complete portfolio, which consists of the optimal risky portfolio and the risk-free asset, must be chosen by each investor based
on preferences.
Use the following to answer questions 47-50:
Consider the following probability distribution for stocks A and B:
47. The expected rates of return of stocks A and B are
and
, respectively.
A) 13.2%; 9%.
B) 13%; 8.4%
C) 13.2%; 7.7%
D) 7.7%; 13.2%
E) none of the above
Answer: B E(RA) = 0.15(8%) + 0.2(13%) + 0.15(12%) + 0.3(14%) + 0.2(16%) = 13%; E(RB)
= 0.15(8%) + 0.2(7%) + 0.15(6%) + 0.3(9%) + 0.2(11%) = 8.4%.
48. The standard deviations of stocks A and B are
and
, respectively.
A) 1.56%; 1.99%
B) 2.45%; 1.68%
C) 3.22%; 2.01%
D) 1.54%; 1.11%
E) none of the above
Answer: B sA = [0.15(8% - 13%)2 + 0.2(13% - 13%)2 + 0.15(12% - 13%)2 + 0.3(14% - 13%)2 + 0.2(16% - 13%)2] 1/2 = 2.449%; sB =
[0.15(8% - 8.4%)2 + 0.2(7% - 8.4%)2 + 0.15(6% - 8.4%)2 + 0.3(9% - 8.4%)2 + 0.2(11% - 8.4%)2 ] 1/2= 1.676%.
49. The coefficient of correlation between A and B is
A) 0.474.
B) 0.612.
C) 0.583.
D) 1.206.
E) none of the above.
Answer: C covA,B = 0.15(8% - 13%)(8% - 8.4%) + 0.2(13% - 13%)(7% - 8.4%) + 0.15(12% - 13%)(6% - 8.4%) + 0.3(14%
- 13%)(9% - 8.4%) + 0.2(16% - 13%)(11% - 8.4%) = 2.40; rA,B = 2.40/[(2.45)(1.68)] = 0.583.
50. If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and
standard deviation?
A) 9.9%; 3%
B) 9.9%; 1.1%
C) 10%; 1.7%
D) 10%; 3%
E) none of the above
Answer: C Rationale: E(RP) = 0.35(13%) + 0.65(8.4%) = 10.01%; sP = [(0.35)2(2.45%)2 + (0.65)2(1.68)2 +
2(0.35)(0.65)(2.45)(1.68)(0.583)]1/2 = 1.7%.
Use the following to answer questions 51-52:
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard
deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
51. The weights of A and B in the global minimum variance portfolio are
and
, respectively.
A) 0.24; 0.76
B) 0.50; 0.50
C) 0.57; 0.43
D) 0.45; 0.55
E) 0.76; 0.24
Answer: D Difficulty: Moderate Rationale: wA = 14 /(17 + 14) = 0.45; wB = 1 - 0.45 = 0.55.
52. The risk-free portfolio that can be formed with the two securities will earn
rate of return.
A) 9.5%
B) 10.4%
C) 10.9%
D) 9.9%
E) none of the above
Answer: B Difficulty: Difficult Rationale: E(RP) = 0.45(12%) + 0.55(9%) = 10.35%.
53. Security X has expected return of 14% and standard deviation of 22%. Security Y has expected return of 16% and
standard deviation of 28%. If the two securities have a correlation coefficient of 0.8, what is their covariance?
A) 0.038
B) 0.049
C) 0.018
D) 0.013
E) 0.054
Answer: B Difficulty: Moderate Rationale: Cov(rX, rY) = (.8)(.22)(.28) = .04928
54. Security X has expected return of 9% and standard deviation of 18%. Security Y has expected return of 12% and
standard deviation of 21%. If the two securities have a correlation coefficient of -0.4, what is their covariance?
A) 0.0388
B) 0.0706
C) 0.0184
D) -0.0133
E) -0.1512
Answer: E Difficulty: Moderate Rationale: Cov(rX, rY) = (-.4)(.18)(.21) = -.01512
55. Given an optimal risky portfolio with expected return of 16% and standard deviation of 20% and a risk free rate of
4%, what is the slope of the best feasible CAL?
A) 0.60
B) 0.14
C) 0.08
D) 0.36
E) 0.31
Answer: A Difficulty: Moderate Rationale: Slope = (16-4)/20 = .6
56. Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of
3%, what is the slope of the best feasible CAL?
A) 0.64
B) 0.14
C) 0.08
D) 0.35
E) 0.36
Answer: D Difficulty: Moderate Rationale: Slope = (12-3)/26 = .346
Use the following to answer questions 57-60: Consider the following probability distribution for stocks C and D:
57. The expected rates of return of stocks C and D are
A) 4.4%; 9.5%.
B) 9.5%; 4.4%
C) 6.3%; 8.7%
D) 8.7%; 6.2%
E) none of the above
and
, respectively.
Answer: A E(RC) = 0.30(7%) + 0.5(11%) + 0.20(-16%) = 4.4%; E(RD) = 0.30(-9%) + 0.5(14%) + 0.20(26%) = 9.5%.
58. The standard deviations of stocks C and D are
and
, respectively.
A) 7.62%; 11.24%
B) 11.24%; 7.62%
C) 9.34%; 12.93%
D) 12.93%; 9.34%
E) none of the above
Answer: C Rationale: sC = [0.30(7% - 4.4%)2 + 0.5(11% - 4.4%)2 + 0.20(-16% - 4.4%)2 ] 1/2 = 9.34%;
sD = [0.30(-9% - 9.5%)2 + 0.50(14% - 9.5%)2 +0.20(26% - 9.5%)2] 1/2 = 12.93%.
59. The coefficient of correlation between C and D is
A) 0.665.
B) 0.554.
C) -0.554.
D) -0.665.
E) none of the above.
Answer: C 𝑐𝑜𝑣𝐶,𝐷 = 0.30(7% - 4.4%)(-9% - 9.5%) + 0.50(11% - 4.4%)(14% - 9.5%) + 0.20(-16% - 4.4%)(26% - 9.5%) = 2.40;
𝑟A,B = -66.90/[(9.34)(12.93)] = -0.554
60. If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected rate of return and standard deviation?
A)9.891%; 8.63% B)9.945%; 11.12% C)10.425%; 8.63% D) 10.275%; 11.12% E) none of the above
Answer: C E(RP) = 0.25(4.4%) + 0.75(9.5%) = 10.425%; sP = [(0.25)2(9.34%)2 + (0.75)2(12.93)2 + 2(0.25)(0.75)(9.34)(12.93)(-0.554)]1/2 = 8.63%.
Use the following to answer questions 61-62:
Consider two perfectly negatively correlated risky securities K and L. K has an expected rate of return of 13% and a standard
deviation of 19%. L has an expected rate of return of 10% and a standard deviation of 16%.
61. The weights of K and L in the global minimum variance portfolio are
and
, respectively.
A) 0.24; 0.76
B) 0.50; 0.50
C) 0.54; 0.46
D) 0.45; 0.55
E) 0.76; 0.24
Answer: C
Rationale: wA = 19 /(19 + 16) = 0.54; wB = 1 - 0.54 = 0.46.
62. The risk-free portfolio that can be formed with the two securities will earn
rate of return.
A) 9.5% B) 10.4%
C) 10.9%
D) 9.9%
E) none of the above
Answer: B
Rationale: E(RP) = 0.54(13%) + 0.46(10%) = 11.62%.
63. Security M has expected return of 17% and standard deviation of 32%. Security S has expected return of 13% and
standard deviation of 19%. If the two securities have a correlation coefficient of 0.78, what is their covariance?
A) 0.038
B) 0.049
C) 0.047
D) 0.045
E) 0.054
Answer: C
Rationale: Cov(rX, rY) = (.78)(.32)(.19) = .0474
64. Security X has expected return of 7% and standard deviation of 12%. Security Y has expected return of 11% and
standard deviation of 20%. If the two securities have a correlation coefficient of -0.45, what is their covariance?
A) 0.0388
B) -0.0108
C) 0.0184
D) -0.0133
E) -0.1512
Answer: B
Rationale: Cov(rX, rY) = (-.45)(.12)(.20) = -.0108
65. Given an optimal risky portfolio with expected return of 13% and standard deviation of 26% and a risk free rate of
5%, what is the slope of the best feasible CAL?
A) 0.60
B)
0.14
C) 0.08
D) 0.36
E) 0.31
Answer: E
Rationale: Slope = (13-5)/26 = .31
66. Given an optimal risky portfolio with expected return of 12% and standard deviation of 23% and a risk free rate of
3%, what is the slope of the best feasible CAL?
A) 0.64
B) 0.39
C) 0.08
D) 0.35
E) 0.36
Answer: B
Rationale: Slope = (12-3)/23 = .391
Essay Questions
67. Theoretically, the standard deviation of a portfolio can be reduced to what level? Explain. Realistically, is it possible
to reduce the standard deviation to this level? Explain.
Theoretically, if one could find two securities with perfectly negatively correlated returns (correlation coefficient = -1), one
could solve for the weights of these securities that would produce the minimum variance portfolio of these two securities. The
standard deviation of the resulting portfolio would be equal to zero. However, in reality, securities with perfect negative
correlations do not exist. The rationale for this question is to ascertain whether or not the student understands the concept of
the minimum variance portfolio, the theoretical zero risk portfolio, and the probability of obtaining a zero risk portfolio.
68. Discuss how the investor can use the separation theorem and utility theory to produce an efficient portfolio suitable
for the investor's level of risk tolerance.
One can identify the optimum risky portfolio as the portfolio at the point of tangency between a ray extending from the riskfree rate and the efficient frontier of risky securities. Below the point of tangency on this ray from the risk-free rate, the efficient
portfolios consist of both the optimum risky portfolio and risk-free investments (T-bills); above the point of tangency, the
efficient portfolios consist of the optimum risky portfolio purchased on margin. If the investor's indifference curve, which
reflects that investor's preferences regarding risk and return, is superimposed on the ray from the risk-free rate, the resulting
point of tangency represents the appropriate combination of the optimum risky portfolio and either risk-free assets or margin
buying for that investor. Thus, the separation theorem separates the investing and financing decisions. That is, all investors
will invest in the same optimal risky portfolio, and adjust the risk level of the portfolio by either lending (investing in U. S.
Treasuries, i.e., lending to the U. S. government) or borrowing (buying risky securities on margin). The purpose of this question
is to ascertain whether the student understands the basic principles of utility theory, the optimal risky portfolio, and the
separation theorem, as these concepts relate to constructing the ideal portfolio for a particular investor.
69. State Markowitz's mean-variance criterion. Give some numerical examples of how the criterion would be applied.
The mean-variance criterion states that asset A dominates asset B if and only if E(RA) is greater than or equal to E(RB) and the
standard deviation of A's returns is less than or equal to the standard deviation of B's returns, with at least one strict inequality
holding. Students can give examples of securities dominating others on the basis of expected return or standard deviation, and
can also give examples of comparisons where neither security is inefficient. The mean-variance criterion is the basis of the
chapter material. It is essential that students have a firm grasp of this material.
70. Draw a graph of a typical efficient frontier. Explain why the efficient frontier is shaped the way it is.
The efficient frontier has a curved appearance, as shown throughout the chapter. Figure 7-5 shows several correlation values and the
corresponding shapes of the frontier. The typical shape results from the fact that assets' returns are not perfectly (positively or negatively)
correlated. This question relates to the fundamentals of assets' relationships and their impact on the efficient frontier. Sometimes students
get used to seeing the efficient frontier as it is depicted in subsequent graphs and forget its origin.
Chapter 7 Optimal Risky Portfolios Multiple Choice Questions
1. Market risk is also referred to as
A. systematic risk, diversifiable risk.
B. systematic risk, nondiversifiable risk.
C. unique risk, nondiversifiable risk.
D. unique risk, diversifiable risk.
E. none of the above.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio.
Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be eliminated from
the portfolio by diversification.
4. Diversifiable risk is also referred to as
A. systematic risk, unique risk.
B. systematic risk, market risk.
C. unique risk, market risk.
D. unique risk, firm-specific risk.
E. none of the above.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio.
Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be eliminated from
the portfolio by diversification.
6. Firm-specific risk is also referred to as
A. systematic risk, diversifiable risk.
B. systematic risk, market risk.
C. diversifiable risk, market risk.
D. diversifiable risk, unique risk.
E. none of the above.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio.
Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be eliminated from
the portfolio by diversification.
10. The variance of a portfolio of risky securities
A. is a weighted sum of the securities' variances.
B. is the sum of the securities' variances.
C. is the weighted sum of the securities' variances and covariances.
D. is the sum of the securities' covariances.
E. none of the above.
The variance of a portfolio of risky securities is a weighted sum taking into account both the variance of the individual
securities and the covariances between securities.
13. Other things equal, diversification is most effective when
A. securities' returns are uncorrelated.
B. securities' returns are positively correlated.
C. securities' returns are high.
D. securities' returns are negatively correlated.
E. B and C.
Negative correlation among securities results in the greatest reduction of portfolio risk, which is the goal of diversification.
14. The efficient frontier of risky assets is
A. the portion of the investment opportunity set that lies above the global minimum variance portfolio.
B. the portion of the investment opportunity set that represents the highest standard deviations.
C. the portion of the investment opportunity set which includes the portfolios with the lowest standard deviation.
D. the set of portfolios that have zero standard deviation.
E. both A and B are true.
Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of risk. Only those
portfolios above the global minimum variance portfolio meet this criterion.
15. The Capital Allocation Line provided by a risk-free security and N risky securities is
A. the line that connects the risk-free rate and the global minimum-variance portfolio of the risky securities.
B. the line that connects the risk-free rate and the portfolio of the risky securities that has the highest expected return on the
efficient frontier.
C. the line tangent to the efficient frontier of risky securities drawn from the risk-free rate.
D. the horizontal line drawn from the risk-free rate.
E. none of the above.
The Capital Allocation Line represents the most efficient combinations of the risk-free asset and risky securities. Only C
meets that definition.
16. Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global
minimum variance portfolio has a standard deviation that is always
A. greater than zero.
B. equal to zero.
C. equal to the sum of the securities' standard deviations.
D. equal to -1.
E. none of the above.
If two securities were perfectly negatively correlated, the weights for the minimum variance portfolio for those securities
could be calculated, and the standard deviation of the resulting portfolio would be zero.
17. Which of the following statements is (are) true regarding the variance of a portfolio of two risky securities?
A. The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
B. There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
C. The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.
D. A and B.
E. A and C.
The lower the correlation between the returns of the securities, the more portfolio risk is reduced.
19. Efficient portfolios of N risky securities are portfolios that
A. are formed with the securities that have the highest rates of return regardless of their standard deviations.
B. have the highest rates of return for a given level of risk.
C. are selected from those securities with the lowest standard deviations regardless of their returns.
D. have the highest risk and rates of return and the highest standard deviations.
E. have the lowest standard deviations and the lowest rates of return.
Portfolios that are efficient are those that provide the highest expected return for a given level of risk.
20. Which of the following statement(s) is (are) true regarding the selection of a portfolio from those that lie on the Capital
Allocation Line?
A. Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more riskaverse investors.
B. More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less riskaverse investors.
C. Investors choose the portfolio that maximizes their expected utility.
D. A and C.
E. B and C.
All rational investors select the portfolio that maximizes their expected utility; for investors who are relatively more riskaverse, doing so means investing less in the optimal risky portfolio and more in the risk-free asset.
Consider the following probability distribution for stocks A and B:
State Probability Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
26. If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard
deviation?
A. 9.9%; 3%
B. 9.9%; 1.1%
C. 11%; 1.1%
D. 11%; 3%
E. none of the above
E(RP) = 0.4(13.2%) + 0.6(7.7%) = 9.9%; sP = [(0.4)2(1.5)2 + (0.6)2(1.1)2 + 2(0.4)(0.6)(1.5)(1.1)(0.46)]1/2 = 1.1%.
27. Let G be the global minimum variance portfolio. The weights of A and B in G are
and
,
respectively.
A. 0.40; 0.60
B. 0.66; 0.34
C. 0.34; 0.66
D. 0.76; 0.24
E. 0.24; 0.76
wA = [(1.1)2 - (1.5)(1.1)(0.46)]/[(1.5)2 + (1.1)2 - (2)(1.5)(1.1)(0.46) = 0.23;
wB = 1 - 0.23 = 0.77. Note that the above solution assumes the solutions obtained in question 13 and 14.
28. The expected rate of return and standard deviation of the global minimum variance portfolio, G, are _ and _, respectively.
A. 10.07%; 1.05%
B. 9.04%; 2.03%
C. 10.07%; 3.01%
D. 9.04%; 1.05%
E. none of the above
E(RG) = 0.23(13.2%) + 0.77(7.7%) = 8.97% . 9%; sG = [(0.23)2(1.5)2 + (0.77)2(1.1)2 + (2)(0.23)(0.77)(1.5)(1.1)(0.46)] 1/2 = 1.05%.
29. Which of the following portfolio(s) is (are) on the efficient frontier?
A. The portfolio with 20 percent in A and 80 percent in B.
B. The portfolio with 15 percent in A and 85 percent in B.
C. The portfolio with 26 percent in A and 74 percent in B.
D. The portfolio with 10 percent in A and 90 percent in B.
E. A and B are both on the efficient frontier.
The Portfolio's E(Rp), sp, Reward/volatility ratios are 20A/80B: 8.8%, 1.05%, 8.38; 15A/85B: 8.53%, 1.06%, 8.07; 26A/74B:
9.13%, 1.05%, 8.70; 10A/90B: 8.25%, 1.07%, 7.73. The portfolio with 26% in A and 74% in B dominates all of the other
portfolios by the mean-variance criterion.
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard
deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
30. The weights of A and B in the global minimum variance portfolio are
and
, respectively.
A. 0.24; 0.76
B. 0.50; 0.50
C. 0.57; 0.43
D. 0.43; 0.57
E. 0.76; 0.24
wA = 12 /(16 + 12) = 0.4286; wB = 1 - 0.4286 = 0.5714.
32. Which of the following portfolio(s) is (are) most efficient?
A. 45 percent in A and 55 percent in B.
B. 65 percent in A and 35 percent in B.
C. 35 percent in A and 65 percent in B.
D. A and B are both efficient.
E. A and C are both efficient.
The Portfolio E(Rp), sp, and Reward/volatility ratios are 45A/55B: 8.9%, 0.6%, 14.83; 65A/35B: 9.3%, 6.2%, 1.5; 35A/65B:
8.7%, 2.2%, 3.95. Both A and B are efficient according to the mean-variance criterion. A has a much higher
Reward/volatility ratio.
33. An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital Allocation
Line must:
A. lend some of her money at the risk-free rate and invest the remainder in the optimal risky portfolio.
B. borrow some money at the risk-free rate and invest in the optimal risky portfolio.
C. invest only in risky securities.
D. such a portfolio cannot be formed.
E. B and C
The only way that an investor can create portfolios to the right of the Capital Allocation Line is to create a borrowing
portfolio (buy stocks on margin). In this case, the investor will not hold any of the risk-free security, but will hold only risky
securities.
36. Portfolio theory as described by Markowitz is most concerned with:
A. the elimination of systematic risk.
B. the effect of diversification on portfolio risk.
C. the identification of unsystematic risk.
D. active portfolio management to enhance returns.
E. none of the above.
Markowitz was concerned with reducing portfolio risk by combining risky securities with differing return patterns.
37. The measure of risk in a Markowitz efficient frontier is:
A. specific risk.
B. standard deviation of returns.
C. reinvestment risk.
D. beta.
E. none of the above.
Markowitz was interested in eliminating diversifiable risk (and thus lessening total risk) and thus was interested in decreasing
the standard deviation of the returns of the portfolio.
39. The unsystematic risk of a specific security
A. is likely to be higher in an increasing market.
B. results from factors unique to the firm.
C. depends on market volatility.
D. cannot be diversified away.
E. none of the above.
Unsystematic (or diversifiable or firm-specific) risk refers to factors unique to the firm. Such risk may be diversified away;
however, market risk will remain.
41. The individual investor's optimal portfolio is designated by:
A. The point of tangency with the indifference curve and the capital allocation line.
B. The point of highest reward to variability ratio in the opportunity set.
C. The point of tangency with the opportunity set and the capital allocation line.
D. The point of the highest reward to variability ratio in the indifference curve.
E. None of the above.
The indifference curve represents what is acceptable to the investor; the capital allocation line represents what is available in
the market. The point of tangency represents where the investor can obtain the greatest utility from what is available.
43. In a two-security minimum variance portfolio where the correlation between securities is greater than -1.0
A. the security with the higher standard deviation will be weighted more heavily.
B. the security with the higher standard deviation will be weighted less heavily.
C. the two securities will be equally weighted.
D. the risk will be zero.
E. the return will be zero.
The security with the higher standard deviation will be weighted less heavily to produce minimum variance. The return will
not be zero; the risk will not be zero unless the correlation coefficient is -1.
49. Given an optimal risky portfolio with expected return of 14% and standard deviation of 22% and a risk free rate of 6%,
what is the slope of the best feasible CAL?
A. 0.64
B. 0.14
C. 0.08
D. 0.33
E. 0.36
Slope = (14 - 6)/22 = .3636
54. The standard deviation of a two-asset portfolio is a linear function of the assets' weights when
A. the assets have a correlation coefficient less than zero.
B. the assets have a correlation coefficient equal to zero.
C. the assets have a correlation coefficient greater than zero.
D. the assets have a correlation coefficient equal to one.
E. the assets have a correlation coefficient less than one.
When there is a perfect positive correlation (or a perfect negative correlation), the equation for the portfolio variance
simplifies to a perfect square. The result is that the portfolio's standard deviation is linear relative to the assets' weights in the
portfolio.
58. The separation property refers to the conclusion that
A. the determination of the best risky portfolio is objective and the choice of the best complete portfolio is subjective.
B. the choice of the best complete portfolio is objective and the determination of the best risky portfolio is objective.
C. the choice of inputs to be used to determine the efficient frontier is objective and the choice of the best CAL is subjective.
D. the determination of the best CAL is objective and the choice of the inputs to be used to determine the efficient frontier is
subjective.
E. investors are separate beings and will therefore have different preferences regarding the risk-return tradeoff.
The determination of the optimal risky portfolio is purely technical and can be done by a manager. The complete portfolio,
which consists of the optimal risky portfolio and the risk-free asset, must be chosen by each investor based on preferences.
Chp 8 Capital assets pricing model Multiple Choice Questions
1. In the context of the Capital Asset Pricing Model (CAPM) the relevant measure of risk is
A) unique risk.
B) beta.
C) standard deviation of returns.
D) variance of returns.
E) none of the above.
Answer: B
Rationale: Once, a portfolio is diversified, the only risk remaining is systematic risk, which is measured by beta.
2. According to the Capital Asset Pricing Model (CAPM) a well diversified portfolio's rate of return is a function of
A) market risk
B) unsystematic risk
C) unique risk.
D) reinvestment risk.
E) none of the above.
Answer: A Rationale: With a diversified portfolio, the only risk remaining is market, or systematic, risk. This is the
only risk that influences return according to the CAPM.
3. The market portfolio has a beta of
A) 0.
B) 1.
C) -1.
D) 0.5.
E) none of the above
Answer: B Rationale: By definition, the beta of the market portfolio is 1.
4. The risk-free rate and the expected market rate of return are 0.06 and 0.12, respectively. According to the capital
asset pricing model (CAPM), the expected rate of return on security X with a beta of 1.2 is equal to
A) 0.06.
B) 0.144.
C) 0.12.
D) 0.132
E) 0.18
Answer: D Rationale: E(R) = 6% + 1.2(12 - 6) = 13.2%.
5. The risk-free rate and the expected market rate of return are 0.056 and 0.125, respectively. According to the capital
asset pricing model (CAPM), the expected rate of return on a security with a beta of 1.25 is equal to
A) 0.1225
B) 0.144.
C) 0.153.
D) 0.134
E) 0.117
Answer: A Rationale: E(R) = 5.6% + 1.25(12.5 - 5.6) = 14.225%.
6. Which statement is not true regarding the market portfolio?
A) It includes all publicly traded financial assets.
B) It lies on the efficient frontier.
C) All securities in the market portfolio are held in proportion to their market values.
D) It is the tangency point between the capital market line and the indifference curve.
E) All of the above are true.
Answer: D
Rationale: The tangency point between the capital market line and the indifference curve is the optimal portfolio for a
particular investor.
7. Which statement is not true regarding the Capital Market Line (CML)?
A) The CML is the line from the risk-free rate through the market portfolio.
B) The CML is the best attainable capital allocation line.
C) The CML is also called the security market line.
D) The CML always has a positive slope.
E) The risk measure for the CML is standard deviation.
Answer: C
Rationale: Both the Capital Market Line and the Security Market Line depict risk/return relationships. However, the
risk measure for the CML is standard deviation and the risk measure for the SML is beta (thus C is not true; the other
statements are true).
8. The market risk, beta, of a security is equal to
A)
B)
C)
D)
E)
the covariance between the security's return and the market return divided by the variance of the market's returns.
the covariance between the security and market returns divided by the standard deviation of the market's returns.
the variance of the security's returns divided by the covariance between the security and market returns.
the variance of the security's returns divided by the variance of the market's returns.
none of the above.
Answer: A Rationale: Beta is a measure of how a security's return covaries with the market returns, normalized by the market variance.
9. According to the Capital Asset Pricing Model (CAPM), the expected rate of return on any security is equal to
A) Rf + β [E(RM)].
B) Rf + β [E(RM) - Rf].
C) β [E(RM) - Rf].
D) E(RM) + Rf.
E) none of the above.
Answer: B Rationale: The expected rate of return on any security is equal to the risk free rate plus the systematic
risk of the security (beta) times the market risk premium, E(RM - Rf).
10. The Security Market Line (SML) is
A) the line that describes the expected return-beta relationship for well-diversified portfolios only.
B) also called the Capital Allocation Line.
C) the line that is tangent to the efficient frontier of all risky assets.
D) the line that represents the expected return-beta relationship.
E) the line that represents the relationship between an individual security's return and the market's return.
Answer: D Rationale: The SML is a measure of expected return per unit of risk, where risk is defined as beta (systematic risk).
11. According to the Capital Asset Pricing Model (CAPM), fairly priced securities
A) have positive betas.
B) have zero alphas.
C) have negative betas.
D) have positive alphas.
E) none of the above.
Answer: B Rationale: A zero alpha results when the security is in equilibrium (fairly priced for the level of risk).
12. According to the Capital Asset Pricing Model (CAPM), under priced securities
A) have positive betas.
B) have zero alphas.
C) have negative betas.
D) have positive alphas.
E) none of the above.
Answer: D Difficulty: Moderate
13. According to the Capital Asset Pricing Model (CAPM), over priced securities
A) have positive betas.
B) have zero alphas.
C) have negative betas.
D) have positive alphas.
E) none of the above.
Answer: C Rationale: A zero alpha results when the security is in equilibrium (fairly priced for the level of risk).
14. According to the Capital Asset Pricing Model (CAPM),
A) a security with a positive alpha is considered overpriced.
B) a security with a zero alpha is considered to be a good buy.
C) a security with a negative alpha is considered to be a good buy.
D) a security with a positive alpha is considered to be underpriced.
E) none of the above.
Answer: D Rationale: A security with a positive alpha is one that is expected to yield an abnormal positive rate of
return, based on the perceived risk of the security, and thus is underpriced.
15. According to the Capital Asset Pricing Model (CAPM), which one of the following statements is false?
A) The expected rate of return on a security decreases in direct proportion to a decrease in the risk-free rate.
B) The expected rate of return on a security increases as its beta increases.
C) A fairly priced security has an alpha of zero.
D) In equilibrium, all securities lie on the security market line.
E) All of the above statements are true.
Answer: A Difficulty: Moderate
Rationale: Statements B, C, and D are true, but statement A is false.
16. In a well diversified portfolio
A) market risk is negligible.
B) systematic risk is negligible.
C) unsystematic risk is negligible.
D) nondiversifiable risk is negligible.
E) none of the above.
Answer: C Rationale: Market, or systematic, or nondiversifiable, risk is present in a diversified portfolio; the
unsystematic risk has been eliminated.
17. Empirical results regarding betas estimated from historical data indicate that
A) betas are constant over time.
B) betas of all securities are always greater than one.
C) betas are always near zero.
D) betas appear to regress toward one over time.
E) betas are always positive.
Answer: D Rationale: Betas vary over time, betas may be negative or less than one, betas are not always near zero;
however, betas do appear to regress toward one over time.
18. Your personal opinion is that a security has an expected rate of return of 0.11. It has a beta of 1.5. The risk-free rate
is 0.05 and the market expected rate of return is 0.09. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: C Rationale: 11% = 5% + 1.5(9% - 5%) = 11.0%; therefore, the security is fairly priced.
19. The risk-free rate is 7 percent. The expected market rate of return is 15 percent. If you expect a stock with a beta of
1.3 to offer a rate of return of 12 percent, you should
A) buy the stock because it is overpriced.
B) sell short the stock because it is overpriced.
C) sell the stock short because it is underpriced.
D) buy the stock because it is underpriced.
E) none of the above, as the stock is fairly priced.
Answer: B Rationale: 12% < 7% + 1.3(15% - 7%) = 17.40%; therefore, stock is overpriced and should be shorted.
20. You invest $600 in a security with a beta of 1.2 and $400 in another security with a beta of 0.90. The beta of the
resulting portfolio is
A) 1.40
B) 1.00
C) 0.36
D) 1.08
E) 0.80
Answer: D Rationale: 0.6(1.2) + 0.4(0.90) = 1.08.
21. A security has an expected rate of return of 0.10 and a beta of 1.1. The market expected rate of return is 0.08 and the
risk-free rate is 0.05. The alpha of the stock is
A) 1.7%.
B) -1.7%.
C) 8.3%.
D) 5.5%.
E) none of the above.
Answer: A Rationale: 10% - [5% +1.1(8% - 5%)] = 1.7%.
22. Your opinion is that CSCO has an expected rate of return of 0.13. It has a beta of 1.3. The risk-free rate is 0.04 and
the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: B Difficulty: Moderate
Rationale: 11.5% - 4% + 1.3(11.5% - 4%) = -2.25%; therefore, the security is overpriced.
23. Your opinion is that CSCO has an expected rate of return of 0.1375. It has a beta of 1.3. The risk-free rate is 0.04
and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: C Rationale: 13.75% - 4% + 1.3(11.5% - 4%) = 0.0%; therefore, the security is fairly priced.
24. Your opinion is that CSCO has an expected rate of return of 0.15. It has a beta of 1.3. The risk-free rate is 0.04 and
the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: A Rationale: 15% - 4% + 1.3(11.5% - 4%) = 1.25%; therefore, the security is under priced.
25. Your opinion is that Boeing has an expected rate of return of 0.112. It has a beta of 0.92. The risk-free rate is 0.04
and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: A Rationale: 11.2% - 4% + 0.92(10% - 4%) = 1.68%; therefore, the security is under priced.
26. Your opinion is that Boeing has an expected rate of return of 0.0952. It has a beta of 0.92. The risk-free rate is 0.04
and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: C Rationale: 9.52% - 4% + 0.92(10% - 4%) = 0.0%; therefore, the security is fairly priced.
27. Your opinion is that Boeing has an expected rate of return of 0.08. It has a beta of 0.92. The risk-free rate is 0.04
and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: C Rationale: 8.0% - 4% + 0.92(10% - 4%) = -1.52%; therefore, the security is overpriced.
28. The risk-free rate is 4 percent. The expected market rate of return is 11 percent. If you expect CAT with a beta of
1.0 to offer a rate of return of 10 percent, you should
A) buy stock X because it is overpriced.
B) sell short stock X because it is overpriced.
C) sell stock short X because it is underpriced.
D) buy stock X because it is underpriced.
E) none of the above, as the stock is fairly priced.
Answer: B Rationale: 10% < 4% + 1.0(11% - 4%) = 11.0%; therefore, stock is overpriced and should be shorted.
29. The risk-free rate is 4 percent. The expected market rate of return is 11 percent. If you expect CAT with a beta of
1.0 to offer a rate of return of 11 percent, you should
A) buy stock X because it is overpriced.
B) sell short stock X because it is overpriced.
C) sell stock short X because it is underpriced.
D) buy stock X because it is underpriced.
E) none of the above, as the stock is fairly priced.
Answer: E Difficulty: Moderate
Rationale: 11% = 4% + 1.0(11% - 4%) = 11.0%; therefore, stock is fairly priced.
30. The risk-free rate is 4 percent. The expected market rate of return is 11 percent. If you expect CAT with a beta of
1.0 to offer a rate of return of 13 percent, you should
A) buy stock X because it is overpriced.
B) sell short stock X because it is overpriced.
C) sell stock short X because it is underpriced.
D) buy stock X because it is underpriced.
E) none of the above, as the stock is fairly priced.
Answer: D Rationale: 13% > 4% + 1.0(11% - 4%) = 11.0%; therefore, stock is under priced.
31. You invest 55% of your money in security A with a beta of 1.4 and the rest of your money in security B with a beta
of 0.9. The beta of the resulting portfolio is
A) 1.466
B) 1.157
C) 0.968
D) 1.082
E) 1.175
Answer: E Rationale: 0.55(1.4) + 0.45(0.90) = 1.175.
32. Given the following two stocks A and B
33.
34.
35.
36.
If the expected market rate of return is 0.09 and the risk-free rate is 0.05, which security would be considered the
better buy and why?
A) A because it offers an expected excess return of 1.2%.
B) B because it offers an expected excess return of 1.8%.
C) A because it offers an expected excess return of 2.2%.
D) B because it offers an expected return of 14%.
E) B because it has a higher beta.
Answer: C Rationale: A's excess return is expected to be 12% - [5% + 1.2(9% - 5%)] = 2.2%. B's excess return is
expected to be 14% - [5% + 1.8(9% - 5%)] = 1.8%.
Capital Asset Pricing Theory asserts that portfolio returns are best explained by:
A) economic factors.
B) specific risk.
C) systematic risk.
D) diversification.
E) none of the above.
Answer: C Rationale: The risk remaining in diversified portfolios is systematic risk; thus, portfolio returns are
commensurate with systematic risk.
According to the CAPM, the risk premium an investor expects to receive on any stock or portfolio increases:
A) directly with alpha.
B) inversely with alpha.
C) directly with beta.
D) inversely with beta.
E) in proportion to its standard deviation.
Answer: C Rationale: The market rewards systematic risk, which is measured by beta, and thus, the risk premium on
a stock or portfolio varies directly with beta.
What is the expected return of a zero-beta security?
A) The market rate of return.
B) Zero rate of return.
C) A negative rate of return.
D) The risk-free rate.
E) None of the above.
Answer: D Rationale: E(RS) = rf + 0(RM - rf) = rf.
Standard deviation and beta both measure risk, but they are different in that
A) beta measures both systematic and unsystematic risk.
B) beta measures only systematic risk while standard deviation is a measure of total risk.
C) beta measures only unsystematic risk while standard deviation is a measure of total risk.
D) beta measures both systematic and unsystematic risk while standard deviation measures only systematic risk.
E) beta measures total risk while standard deviation measures only nonsystematic risk.
Answer: B Rationale: B is the only true statement.
37. The expected return-beta relationship
A) is the most familiar expression of the CAPM to practitioners.
B) refers to the way in which the covariance between the returns on a stock and returns on the market measures the
contribution of the stock to the variance of the market portfolio, which is beta.
C) assumes that investors hold well-diversified portfolios.
D) all of the above are true.
E) none of the above is true.
Answer: D Rationale: Statements A, B and C all describe the expected return-beta relationship.
38. The security market line (SML)
A) can be portrayed graphically as the expected return-beta relationship.
B) can be portrayed graphically as the expected return-standard deviation of market returns relationship.
C) provides a benchmark for evaluation of investment performance.
D) A and C.
E) B and C.
Answer: D Rationale: The SML is a measure of expected return-beta (the CML is a measure of expected returnstandard deviation of market returns). The SML provides the expected return-beta relationship for "fairly priced"
securities; thus if a portfolio manager selects securities that are underpriced and produces a portfolio with a positive
alpha, this portfolio manager would receive a positive evaluation.
39. Research by Jeremy Stein of MIT resolves the dispute over whether beta is a sufficient pricing factor by suggesting
that managers should use beta to estimate
A) long-term returns but not short-term returns.
B) short-term returns but not long-term returns.
C) both long- and short-term returns.
D) book-to-market ratios.
E) None of the above was suggested by Stein.
Answer: A Difficulty: Difficult
40. Studies of liquidity spreads in security markets have shown that
A) liquid stocks earn higher returns than illiquid stocks.
B) illiquid stocks earn higher returns than liquid stocks.
C) both liquid and illiquid stocks earn the same returns.
D) illiquid stocks are good investments for frequent, short-term traders.
E) None of the above is true.
Answer: B Difficulty: Difficult
41.
An underpriced security will plot
A) on the Security Market Line.
B) below the Security Market Line.
C) above the Security Market Line.
D) either above or below the Security Market Line depending on its covariance with the market.
E) either above or below the Security Market Line depending on its standard deviation.
Answer: C Rationale: An underpriced security will have a higher expected return than the SML would predict;
therefore it will plot above the SML.
42. The risk premium on the market portfolio will be proportional to
A) the average degree of risk aversion of the investor population.
B) the risk of the market portfolio as measured by its variance.
C) the risk of the market portfolio as measured by its beta.
D) both A and B are true.
E) both A and C are true.
Answer: D Rationale: The risk premium on the market portfolio is proportional to the average degree of risk
aversion of the investor population and the risk of the market portfolio measured by its variance.
43. In equilibrium, the marginal price of risk for a risky security must be
A) equal to the marginal price of risk for the market portfolio.
B) greater than the marginal price of risk for the market portfolio.
C) less than the marginal price of risk for the market portfolio.
D) adjusted by its degree of nonsystematic risk.
E) none of the above is true.
Answer: A Difficulty: Moderate
Rationale: In equilibrium, the marginal price of risk for a risky security must be equal to the marginal price of risk for
the market. If not, investors will buy or sell the security until they are equal.
44. The capital asset pricing model assumes
A) all investors are price takers.
B) all investors have the same holding period.
C) investors pay taxes on capital gains.
D) both A and B are true.
E) A, B and C are all true.
Answer: D Rationale: The CAPM assumes that investors are price-takers with the same single holding period and that there
are no taxes or transaction costs.
45. If investors do not know their investment horizons for certain
A) the CAPM is no longer valid.
B) the CAPM underlying assumptions are not violated.
C) the implications of the CAPM are not violated as long as investors' liquidity needs are not priced.
D) the implications of the CAPM are no longer useful.
E) none of the above is true.
Answer: C Rationale: This is discussed in the chapter's section about extensions to the CAPM. It examines what the
consequences are when the assumptions are removed.
46. The value of the market portfolio equals
A) the sum of the values of all equity securities.
B) the sum of the values of all equity and fixed income securities.
C) the sum the values of all equity, fixed income, and derivative securities.
D) the sum of the values of all equity, fixed income, and derivative securities plus the value of all mutual funds.
E) the entire wealth of the economy.
Answer: E Rationale: The market portfolio includes all assets in existence.
47. The amount that an investor allocates to the market portfolio is negatively related to
I)
II)
III)
IV)
A)
B)
C)
D)
E)
the expected return on the market portfolio.
the investor's risk aversion coefficient.
the risk-free rate of return.
the variance of the market portfolio
I and II
II and III
II and IV
II, III, and IV
I, III, and IV
I)
II)
III)
IV)
A)
B)
C)
D)
E)
It is similar to the separation property.
It implies that a passive investment strategy can be efficient.
It implies that efficient portfolios can be formed only through active strategies.
It means that professional managers have superior security selection strategies.
I and IV
I, II, and IV
I and II
III and IV
II and IV
Answer: D The optimal proportion is given by y = (E(RM)-rf)/(.01xAσ2M). This amount will decrease as rf, A, and σ2M decrease.
48. One of the assumptions of the CAPM is that investors exhibit myopic behavior. What does this mean?
A) They plan for one identical holding period.
B) They are price-takers who can't affect market prices through their trades.
C) They are mean-variance optimizers.
D) They have the same economic view of the world.
E) They pay no taxes or transactions costs.
Answer: A Rationale: Myopic behavior is shortsighted, with no concern for medium-term or long-term implications.
49. The CAPM applies to
A) portfolios of securities only.
B) individual securities only.
C) efficient portfolios of securities only.
D) efficient portfolios and efficient individual securities only.
E) all portfolios and individual securities.
Answer: E Rationale: The CAPM is an equilibrium model for all assets. Each asset's risk premium is a function of its beta
coefficient and the risk premium on the market portfolio.
50. Which of the following statements about the mutual fund theorem is true?
Answer: C The mutual fund theorem is similar to the separation property. The technical task of creating mutual funds can be
delegated to professional managers; then individuals combine the mutual funds with risk-free assets according to their
preferences. The passive strategy of investing in a market index fund is efficient.
51. The expected return -- beta relationship of the CAPM is graphically represented by
A) the security market line.
B) the capital market line.
C) the capital allocation line.
D) the efficient frontier with a risk-free asset.
E) the efficient frontier without a risk-free asset.
Answer: A Rationale: The security market line shows expected return on the vertical axis and beta on the horizontal
axis. It has an intercept of rf and a slope of E(RM) - rf.
52. A “fairly priced” asset lies
A) above the security market line.
B) on the security market line.
C) on the capital market line.
D) above the capital market line.
E) below the security market line.
Answer: B Rationale: Securities that lie on the SML earn exactly the expected return generated by the CAPM.
Their prices are proportional to their beta coefficients and they have alphas equal to zero.
53. For the CAPM that examines illiquidity premiums, if there is correlation among assets due to common systematic
risk factors, the illiquidity premium on asset i is a function of
A) the market's volatility.
B) asset i's volatility.
C) the trading costs of security i.
D) the risk-free rate.
E) the money supply.
Answer: C Rationale: The formula for this extension to the CAPM relaxes the assumption that trading is costless.
54. Your opinion is that security A has an expected rate of return of 0.145. It has a beta of 1.5. The risk-free rate is 0.04
and the market expected rate of return is 0.11. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: C Rationale: 14.5% = 4% + 1.5(11% - 4%) = 14.5%; therefore, the security is fairly priced.
55. Your opinion is that security C has an expected rate of return of 0.106. It has a beta of 1.1. The risk-free rate is 0.04
and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security is
A) underpriced.
B) overpriced.
C) fairly priced.
D) cannot be determined from data provided.
E) none of the above.
Answer: A Rationale: 4% + 1.1(10% - 4%) = 10.6%; therefore, the security is fairly priced.
56. The risk-free rate is 4 percent. The expected market rate of return is 12 percent. If you expect stock X with a beta of
1.0 to offer a rate of return of 10 percent, you should
A) buy stock X because it is overpriced.
B) sell short stock X because it is overpriced.
C) sell stock short X because it is underpriced.
D) buy stock X because it is underpriced.
E) none of the above, as the stock is fairly priced.
Answer: B Rationale: 10% < 4% + 1.0(12% - 4%) = 12.0%; therefore, stock is overpriced and should be shorted.
57. The risk-free rate is 5 percent. The expected market rate of return is 11 percent. If you expect stock X with a beta of
2.1 to offer a rate of return of 15 percent, you should
A) buy stock X because it is overpriced.
B) sell short stock X because it is overpriced.
C) sell stock short X because it is underpriced.
D) buy stock X because it is underpriced.
E) none of the above, as the stock is fairly priced.
Answer: B Difficulty: Moderate
Rationale: 15% < 5% + 2.1(11% - 5%) = 17.6%; therefore, stock is overpriced and should be shorted.
58. You invest 50% of your money in security A with a beta of 1.6 and the rest of your money in security B with a beta
of 0.7. The beta of the resulting portfolio is
A) 1.40
B) 1.15
C) 0.36
D) 1.08
E) 0.80
Answer: B Rationale: 0.5(1.6) + 0.5(0.70) = 1.15.
59. You invest $200 in security A with a beta of 1.4 and $800 in security B with a beta of 0.3. The beta of the resulting
portfolio is A. 1.40
A) 1.00
B) 0.52
C) 1.08
D) 0.80
Answer: C Rationale: 0.2(1.4) + 0.8(0.3) = 0.52.
60. Security A has an expected rate of return of 0.10 and a beta of 1.3. The market expected rate of return is 0.10 and the
risk-free rate is 0.04. The alpha of the stock is
A) 1.7%.
B) -1.8%.
C) 8.3%.
D) 5.5%.
E) none of the above.
Answer: B Rationale: 10% - [4% +1.3(10% - 4%)] = -1.8%.
61. A security has an expected rate of return of 0.15 and a beta of 1.25. The market expected rate of return is 0.10 and
the risk-free rate is 0.04. The alpha of the stock is
A) 1.7%.
B) -1.7%.
C) 8.3%.
D) 3.5%.
E) none of the above.
Answer: D Rationale: 15% - [4% +1.25(10% - 4%)] = 3.5%.
62. A security has an expected rate of return of 0.13 and a beta of 2.1. The market expected rate of return is 0.09 and the
risk-free rate is 0.045. The alpha of the stock is
A) -0.95%.
B) -1.7%.
C) 8.3%.
D) 5.5%.
E) none of the above.
Answer: A Rationale: 13% - [4.5% +2.1(9% - 4.5%)] = -0.95%.
63. Assume that a security is fairly priced and has an expected rate of return of 0.13. The market expected rate of return
is 0.13 and the risk-free rate is 0.04. The beta of the stock is
?
A) 1.25
B) 1.7
C) 1
D) 0.95
E) none of the above.
Answer: C Rationale: 13% = [4% +β(13% - 4%)]; 9% = β(9%); β = 1.
64. Assume that a security is fairly priced and has an expected rate of return of 0.17. The market expected rate of return
is 0.11 and the risk-free rate is 0.04. The beta of the stock is
?
A) 1.25
B) 1.86
C) 1
D) 0.95
E) none of the above.
Answer: B Difficulty: Moderate
Rationale: 17% = [4% +β(11% - 4%)]; 13% = β(7%); β = 1.86.
Essay Questions
65. Discuss the differences between the capital market line and the security market line.
The capital market line measures the excess return (return of the portfolio over the risk-free return) per unit of total risk, as
measured by standard deviation. The CML applies to efficient portfolios only. The security market line measures the excess
returns of a portfolio or a security per unit of systematic risk (beta). The SML applies to individual securities and to all portfolios
(whether efficiently diversified or not). Thus, the SML has much general applications than the CML and is more broadly used.
The SML is frequently used to evaluate the performance of portfolio managers. The rational of this question is to determine
whether the students understand the basic differences between these two common risk/return relationships resulting from the
capital asset pricing model.
66. Discuss the assumptions of the capital asset pricing model, and how these assumptions relate to the "real world"
investment decision process. The assumptions are:
(a) The market is composed of many small investors, who are price-takers; i. e., perfect competition. In reality this assumption
was fairly realistic until recent years when institutional investors increasingly began to influence the market with their large
transactions, especially those transactions via program trading. Since the 1987 market crash, circuit breakers on program
trading have been enacted and market volatility has decreased somewhat.
(b) All investors have the same holding period. Obviously, different investors have different goals, and thus have different
holding periods.
(c) Investments are limited to those that are publicly traded. In addition, it is assumed that investors may borrow or lend any
amount at a fixed, risk-free rate. Obviously, investors may purchase assets that are not publicly traded; however, the dollar
volume of publicly traded assets is considerable. The assumption that investors can borrow or lend any amount at a fixed,
risk-free rate obviously is false. However, the model can be modified to incorporate different borrowing and lending rates.
(d) Investors pay no taxes on returns and incur no transaction costs. Obviously, investors do pay taxes and do incur transaction
costs. The tax differentials across different types of investment income and across different income levels have been
lessened as a result of the income tax simplification of 1986. Obviously, investors should consider after-tax, not beforetax, returns; however, the no-tax assumption of the model is not a serious departure from reality. In addition, any investment
vehicle should stand on its own merits, not its tax status (again, less of a problem with the tax simplification of 1986).
Compared to other investment alternatives, such as real estate, transaction costs for securities are relatively low, unless the
investor is an active trader. The active trader should be sure that he or she is not trading himself/herself out of a profit
situation and into a loss situation and making profits for the broker. In general, these assumptions are not serious violations
of "real world" scenarios.
(e) All investors are mean-variance efficient. This assumption implies that all investors make decisions based on maximizing
returns available at an acceptable risk level; most investors probably make decisions in this manner. However, some
investors are pure wealth maximizers (regardless of the risk level); and other investors are so risk averse that avoiding risk
is their only goal.
(f) All investors have homogeneous expectations, meaning that given the same data all investors would process the data in the
same manner, resulting in the same risk/return assessments for all investment alternatives. Obviously, we do not have
homogenous expectations; one only has to read the differing recommendations of various analysts to realize that we have
heterogeneous expectations. However, modeling heterogeneous expectations would require multiple, specific models; the
homogenous expectations assumption allows the development of a generalized model, the CAPM.
This question was designed to determine the student's understanding of the implications of the assumptions of the CAPM and
requires the student to integrate much of the information introduced in the course to date and to integrate basic knowledge from
economics principles courses.
67. Discuss the mutual fund theorem.
The mutual fund theorem is based on the concept that investors may obtain an efficient portfolio by holding the market
(investing in an S&P 500 index fund, for example). The investor may adjust his or her holdings to the appropriate risk level by
combining this investment with investment in risk-free instruments. Thus, the investor is separating the investment decision
from the financing decision (separation theorem). Using this approach the investor may have an efficient passive investment
strategy. This question tests the student's understanding of one of the fundamental results of the CAPM.
68. Discuss how the CAPM might be used in capital budgeting decisions and utility rate decisions.
The CAPM can be used to establish a hurdle rate for capital budgeting projects, based on the projects' beta coefficients.
For utility rate cases, the CAPM can be used to determine the fair rate of return for the utilities' stockholders. Utility rates can
then be set to target these returns. ( the general nature of the CAPM and the diversity of its applications)
69. List and discuss two of the assumptions of the CAPM.
Assumptions are 1) there are many investors, none of whom can have an impact on market prices, 2) investors are single-period
planners with myopic behavior, 3) investments are limited to a universe of publicly traded financial assets and risk-free
borrowing and lending, 4) there are no taxes or transactions costs, 5) all investors are rational mean-variance optimizers who
use the Markowitz model for portfolio selection, and 6) all investors share the same economic view of the world. Students may
discuss these items as presented in the chapter or expand the discussion.
The question gives the student some flexibility in choosing which assumptions to discuss.
Chapter 9 Arbitrage Pricing Theory and Multifactor Models of Risk and Return Multiple Choice Questions
1.
a relationship between expected return and risk.
A) APT stipulates
B) CAPM stipulates
C) Both CAPM and APT stipulate
D) Neither CAPM nor APT stipulate
E) No pricing model has found
Answer: C Rationale: Both models attempt to explain asset pricing based on risk/return relationships.
2. Which pricing model provides no guidance concerning the determination of the risk premium on factor portfolios?
A) The CAPM
B) The multifactor APT
C) Both the CAPM and the multifactor APT
D) Neither the CAPM nor the multifactor APT
E) None of the above is a true statement.
Answer: B The multifactor APT provides no guidance as to the determination of the risk premium on the various factors. The
CAPM assumes that the excess market return over the risk-free rate is the market premium in the single factor CAPM.
3. An arbitrage opportunity exists if an investor can construct a
investment portfolio that will yield a sure profit.
A) positive
B) negative
C) zero
D) all of the above
E) none of the above
Answer: C If the investor can construct a portfolio without the use of the investor's own funds and the portfolio yields a positive
profit, arbitrage opportunities exist.
4. The APT was developed in 1976 by
.
A) Lintner
B) Modigliani and Miller
C) Ross
D) Sharpe
E) none of the above
Answer: C Rationale: Ross developed this model in 1976.
5. A
portfolio is a well-diversified portfolio constructed to have a beta of 1 on one of the factors and a beta of 0
on any other factor.
A) factor
B) market
C) index
D) A and B
E) A, B, and C
Answer: A Rationale: A factor model portfolio has a beta of 1 one factor, with zero betas on other factors.
6. The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called
.
A) arbitrage
B) capital asset pricing
C) factoring
D) fundamental analysis
E) none of the above
Answer: A Rationale: Arbitrage is earning of positive profits with a zero (risk-free) investment.
7. In developing the APT, Ross assumed that uncertainty in asset returns was a result of
A) a common macroeconomic factor.
B) firm-specific factors.
C) pricing error.
D) neither A nor B
E) both A and B
Answer: E Rationale: Total risk (uncertainty) is assumed to be composed of both macroeconomic and firm-specific factors.
8. The provides an unequivocal statement on the expected return-beta relationship for all assets, whereas the
implies
that this relationship holds for all but perhaps a small number of securities.
A) APT, CAPM
B) APT, OPM
C) CAPM, APT
D) CAPM, OPM
E) none of the above
Answer: C The CAPM is an asset-pricing model based on the risk/return relationship of all assets. The APT implies that
this relationship holds for all well-diversified portfolios, and for all but perhaps a few individual securities.
9. Consider a single factor APT. Portfolio A has a beta of 1.0 and an expected return of 16%. Portfolio B has a beta of 0.8
and an expected return of 12%. The risk-free rate of return is 6%. If you wanted to take advantage of an arbitrage
opportunity, you should take a short position in portfolio
and a long position in portfolio
.
A) A, A
B) A, B
C) B, A
D) B, B
E) A, the riskless asset
Answer: C A: 16% = 1.0F + 6%; F = 10%; B: 12% = 0.8F + 6%: F = 7.5%; thus, short B and take a long position in A.
10. Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%. Portfolio B has a beta
of 0.4 and an expected return of 15%. The risk-free rate of return is 10%. If you wanted to take advantage of an
arbitrage opportunity, you should take a short position in portfolio
and a long position in portfolio
.
A) A, A
B) A, B
C) B, A
D) B, B
E) none of the above
Answer: C A: 13% = 10%+0.2F; F = 15%; B: 15% = 10% + 0.4F; F = 12.5%; therefore, short B and take a long position in A
11. Consider the one-factor APT. The variance of returns on the factor portfolio is 6%. The beta of a well-diversified
portfolio on the factor is 1.1. The variance of returns on the well-diversified portfolio is approximately
.
A) 3.6%
B) 6.0%
C) 7.3%
D) 10.1%
E) none of the above
Answer: C Rationale: s2P = (1.1)2(6%) = 7.26%.
12. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 18%. The standard
deviation on the factor portfolio is 16%. The beta of the well-diversified portfolio is approximately
.
A) 0.80
B) 1.13
C) 1.25
D) 1.56
E) none of the above
Answer: B Rationale: (18%)2 = (16%)2 b2; b = 1.125.
13. Consider the single-factor APT. Stocks A and B have expected returns of 15% and 18%, respectively. The risk-free
rate of return is 6%. Stock B has a beta of 1.0. If arbitrage opportunities are ruled out, stock A has a beta of
.
A) 0.67
B) 1.00
C) 1.30
D) 1.69
E) none of the above
Answer: E Rationale: A: 15% = 6% + bF; B: 8% = 6% + 1.0F; F = 12%; thus, beta of A = 9/12 = 0.75.
14. Consider the multifactor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1
and a beta of .8 on factor 2. The risk premium on the factor 1 portfolio is 3%. The risk-free rate of return is 6%.
What is the risk-premium on factor 2 if no arbitrage opportunities exit?
A) 2%
B) 3%
C) 4%
D) 7.75%
E) none of the above
Answer: D Rationale: 16.4% = 1.4(3%) + .8x + 6%; x = 7.75.
15. Consider the multifactor model APT with two factors. Portfolio A has a beta of 0.75 on factor 1 and a beta of 1.25 on
factor 2. The risk premiums on the factor 1 and factor 2 portfolios are 1% and 7%, respectively. The risk-free rate of
return is 7%. The expected return on portfolio A is
if no arbitrage opportunities exist.
A) 13.5%
B) 15.0%
C) 16.5%
D) 23.0%
E) none of the above
Answer: C Rationale: 7% + 0.75(1%) + 1.25(7%) = 16.5%.
16. Consider the multifactor APT with two factors. The risk premiums on the factor 1 and factor 2 portfolios are 5% and
6%, respectively. Stock A has a beta of 1.2 on factor 1, and a beta of 0.7 on factor 2. The expected return on stock A
is 17%. If no arbitrage opportunities exist, the risk-free rate of return is
.
A) 6.0%
B) 6.5%
C) 6.8%
D) 7.4%
E) none of the above
Answer: C Rationale: 17% = x% + 1.2(5%) + 0.7(6%); x = 6.8%.
17. Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor and portfolio B has a beta of 2.0 on the
factor. The expected returns on portfolios A and B are 11% and 17%, respectively. Assume that the risk-free rate is
6% and that arbitrage opportunities exist. Suppose you invested $100,000 in the risk-free asset, $100,000 in portfolio
B, and sold short $200,000 of portfolio A. Your expected profit from this strategy would be
.
A) -$1,000
B) $0
C) $1,000
D) $2,000
E) none of the above
Answer: C Rationale: $100,000(0.06) = $6,000 (risk-free position); $100,000(0.17) = $17,000 (portfolio B); $200,000(0.11) = -$22,000 (short position, portfolio A); 1,000 profit.
18. Consider the one-factor APT. Assume that two portfolios, A and B, are well diversified. The betas of portfolios A
and B are 1.0 and 1.5, respectively. The expected returns on portfolios A and B are 19% and 24%, respectively.
Assuming no arbitrage opportunities exist, the risk-free rate of return must be
.
A) 4.0%
B) 9.0%
C) 14.0%
D) 16.5%
E) none of the above
Answer: B Rationale: A: 19% = rf + 1(F); B:24% = rf + 1.5(F); 5% = .5(F); F = 10%; 24% = rf + 1.5(10); ff = 9%.
19. Consider the multifactor APT. The risk premiums on the factor 1 and factor 2 portfolios are 5% and 3%,
respectively. The risk-free rate of return is 10%. Stock A has an expected return of 19% and a beta on factor 1 of
0.8. Stock A has a beta on factor 2 of
.
A) 1.33
B) 1.50
C) 1.67
D) 2.00
E) none of the above
Answer: C Rationale: 19% = 10% + 5%(0.8) + 3%(x); x = 1.67.
20. Consider the single factor APT. Portfolios A and B have expected returns of 14% and 18%, respectively. The riskfree rate of return is 7%. Portfolio A has a beta of 0.7. If arbitrage opportunities are ruled out, portfolio B must have
a beta of
.
A) 0.45
B) 1.00
C) 1.10
D) 1.22
E) none of the above
Answer: C Rationale: A: 14% = 7% + 0.7F; F = 10; B: 18% = 7% + 10b; b = 1.10.
Use the following to answer questions 21-24:
There are three stocks, A, B, and C. You can either invest in these stocks or short sell them. There are three possible states
of nature for economic growth in the upcoming year; economic growth may be strong, moderate, or weak. The returns for
the upcoming year on stocks A, B, and C for each of these states of nature are given below:
State of Nature
Stock
Strong Growth
Moderate Growth
Weak Growth
A
39%
17%
-5%
B
30%
15%
0%
C
6%
14%
22%
21.
If you invested in an equally weighted portfolio of stocks A and B, your portfolio return would be __ if economic
growth were moderate.
A) 3.0%
B) 14.5%
C) 15.5%
D) 16.0%
E) none of the above
Answer: D Rationale: E(Rp) = 0.5(17%) + 0.5(15%) = 16%.
22. If you invested in an equally weighted portfolio of stocks A and C, your portfolio return would be __ if economic
growth was strong.
A) 17.0%
B) 22.5%
C) 30.0%
D) 30.5%
E) none of the above
Answer: B Rationale: 0.5(39%) + 0.5(6%) = 22.5%.
23. If you invested in an equally weighted portfolio of stocks B and C, your portfolio return would be
if economic
growth was weak.
A) -2.5%
B) 0.5%
C) 3.0%
D) 11.0%
E) none of the above
Answer: D Rationale: 0.5(0%) + 0.5(22%) = 11%.
24. If you wanted to take advantage of a risk-free arbitrage opportunity, you should take a short position in
and a long position in an equally weighted portfolio of
.
A) A, B and C
B) B, A and C
C) C, A and B
D) A and B, C
E) none of the above, none of the above
Answer: C E(RA) = (39% + 17% - 5%)/3 = 17%; E(RB) = (30% + 15% + 0%)/3 = 15%;
E(RC) = (22% + 14% + 6%)/3 = 14%; E(RP) = -0.5(14%) + 0.5[(17% + 15%)/2]; -7.0% + 8.0% = 1.0%.
Use the following to answer questions 25-26: Consider the multifactor APT. There are two independent economic factors, F1
and F2. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios:
Portfolio
A
B
 on F1
1.0
2.0
 on F2
2.0
0.0
Expected Return
19%
12%
25. Assuming no arbitrage opportunities exist, the risk premium on the factor F1 portfolio should be
.
A) 3%
B) 4% C) 5% D) 6% E) none of the above
Answer: A
Rationale: 2A: 38% = 12% + 2.0(RP1) + 4.0(RP2); B: 12% = 6% + 2.0(RP1) + 0.0(RP2);
26% = 6% + 4.0(RP2); RP2 = 5; A: 19% = 6% + RP1 + 2.0(5); RP1 = 3%.
26. Assuming no arbitrage opportunities exist, the risk premium on the factor F2 portfolio should be
.
A) 3%
B) 4%
C) 5%
D) 6%
E) none of the above
Answer: C Rationale: See solution to previous problem.
27. A zero-investment portfolio with a positive expected return arises when
.
A) an investor has downside risk only
B) the law of prices is not violated
C) the opportunity set is not tangent to the capital allocation line
D) a risk-free arbitrage opportunity exists
E) none of the above
Answer: D
Rationale: When an investor can create a zero-investment portfolio (by using none of the investor's own funds) with a
possibility of a positive profit, a risk-free arbitrage opportunity exists.
28. An investor will take as large a position as possible when an equilibrium price relationship is violated. This is an
example of
.
A) a dominance argument
B) the mean-variance efficiency frontier
C) a risk-free arbitrage
D) the capital asset pricing model
E) none of the above
Answer: C Rationale: When the equilibrium price is violated, the investor will buy the lower priced asset and
simultaneously place an order to sell the higher priced asset. Such transactions result in risk-free arbitrage. The
larger the positions, the greater the risk-free arbitrage profits.
29. The APT differs from the CAPM because the APT
.
A) places more emphasis on market risk
B) minimizes the importance of diversification
C) recognizes multiple unsystematic risk factors
D) recognizes multiple systematic risk factors
E) none of the above
Answer: D Rationale: The CAPM assumes that market returns represent systematic risk. The APT recognizes that
other macroeconomic factors may be systematic risk factors.
30. The feature of the APT that offers the greatest potential advantage over the CAPM is the
.
A) use of several factors instead of a single market index to explain the risk-return relationship
B) identification of anticipated changes in production, inflation and term structure as key factors in explaining the
risk-return relationship
C) superior measurement of the risk-free rate of return over historical time periods
D) variability of coefficients of sensitivity to the APT factors for a given asset over time
E) none of the above
Answer: A Rationale: The advantage of the APT is the use of multiple factors, rather than a single market index, to
explain the risk-return relationship. However, APT does not identify the specific factors.
31. In terms of the risk/return relationship
A) only factor risk commands a risk premium in market equilibrium.
B) only systematic risk is related to expected returns.
C) only nonsystematic risk is related to expected returns.
D) A and B.
E) A and C.
Answer: D Rationale: Nonfactor risk may be diversified away; thus, only factor risk commands a risk premium in
market equilibrium. Nonsystematic risk across firms cancels out in well-diversified portfolios; thus, only systematic
risk is related to expected returns.
32. The following factors might affect stock returns:
A) the business cycle.
B) interest rate fluctuations.
C) inflation rates.
D) all of the above.
E) none of the above.
Answer: D Rationale: A, B, and C all are likely to affect stock returns.
33. Advantage(s) of the APT is(are)
A) that the model provides specific guidance concerning the determination of the risk premiums on the factor portfolios.
B) that the model does not require a specific benchmark market portfolio.
C) that risk need not be considered.
D) A and B.
E) B and C.
Answer: B The APT provides no guidance concerning the determination of the risk premiums on the factor portfolios. Risk
must be considered in both the CAPM and APT. A major advantage of APT over the CAPM is that a specific benchmark
market portfolio is not required.
34. Portfolio A has expected return of 10% and standard deviation of 19%. Portfolio B has expected return of 12% and
standard deviation of 17%. Rational investors will
A) Borrow at the risk free rate and buy A.
B) Sell A short and buy B.
C) Sell B short and buy A.
D) Borrow at the risk free rate and buy B.
E) Lend at the risk free rate and buy B.
Answer: B Rationale: Rational investors will arbitrage by selling A and buying B.
35. An important difference between CAPM and APT is
A) CAPM depends on risk-return dominance; APT depends on a no arbitrage condition.
B) CAPM assumes many small changes are required to bring the market back to equilibrium; APT assumes a few
large changes are required to bring the market back to equilibrium.
C) implications for prices derived from CAPM arguments are stronger than prices derived from APT arguments.
D) all of the above are true.
E) both A and B are true.
Answer: E Rationale: Under the risk-return dominance argument of CAPM, when an equilibrium price is violated many investors
will make small portfolio changes, depending on their risk tolerance, until equilibrium is restored. Under the no-arbitrage argument
of APT, each investor will take as large a position as possible so only a few investors must act to restore equilibrium. Implications
derived from APT are much stronger than those derived from CAPM, making C an incorrect statement.
36. A professional who searches for mispriced securities in specific areas such as merger-target stocks, rather than one
who seeks strict (risk-free) arbitrage opportunities is engaged in
A) pure arbitrage.
B) risk arbitrage.
C) option arbitrage.
D) equilibrium arbitrage.
E) none of the above.
Answer: B Risk arbitrage involves searching for mispricings based on speculative information that may or may not materialize.
37. In the context of the Arbitrage Pricing Theory, as a well-diversified portfolio becomes larger its nonsystematic risk
approaches
A) one.
B) infinity.
C) zero.
D) negative one.
E) none of the above.
Answer: C As the number of securities, n, increases, the nonsystematic risk of a well-diversified portfolio approaches zero.
38. A well-diversified portfolio is defined as
A) one that is diversified over a large enough number of securities that the nonsystematic variance is essentially
zero.
B) one that contains securities from at least three different industry sectors.
C) a portfolio whose factor beta equals 1.0.
D) a portfolio that is equally weighted.
E) all of the above.
Answer: A Rationale: A well-diversified portfolio is one that contains a large number of securities, each having a
small (but not necessarily equal) weight, so that nonsystematic variance is negligible.
39. The APT requires a benchmark portfolio
A) that is equal to the true market portfolio.
B) that contains all securities in proportion to their market values.
C) that need not be well-diversified.
D) that is well-diversified and lies on the SML.
E) that is unobservable.
Answer: D Rationale: Any well-diversified portfolio lying on the SML can serve as the benchmark portfolio for the
APT. The true (and unobservable) market portfolio is only a requirement for the CAPM.
40. Imposing the no-arbitrage condition on a single-factor security market implies which of the following statements?
the expected return-beta relationship is maintained for all but a small number of well-diversified portfolios.
I)
the expected return-beta relationship is maintained for all well-diversified portfolios.
II) the expected return-beta relationship is maintained for all but a small number of individual securities.
III) the expected return-beta relationship is maintained for all individual securities.
A)
B)
C)
D)
E)
I and III are correct.
I and IV are correct.
II and III are correct.
II and IV are correct.
Only I is correct.
Answer: C Rationale: The expected return-beta relationship must hold for all well-diversified portfolios and for all
but a few individual securities; otherwise arbitrage opportunities will be available.
41. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium on the
first factor portfolio is 4% and the risk premium on the second factor portfolio is 3%. If portfolio A has a beta of 1.2
on the first factor and .8 on the second factor, what is its expected return?
A) 7.0%
B) 8.0%
C) 9.2%
D) 13.0%
E) 13.2%
Answer: E Rationale: .06 + 1.2 (.04) + .8 (.03) = .132
42. The term, “arbitrage” refers to
A) buying low and selling high.
B) short selling high and buying low.
C) earning risk-free economic profits.
D) negotiating for favorable brokerage fees.
E) hedging your portfolio through the use of options.
Answer: C Rationale: Arbitrage is exploiting security mispricings by the simultaneous purchase and sale to gain
economic profits without taking any risk. A capital market in equilibrium rules out arbitrage opportunities.
43. To take advantage of an arbitrage opportunity, an investor would
construct a zero investment portfolio that will yield a sure profit.
I)
construct a zero beta investment portfolio that will yield a sure profit.
II) make simultaneous trades in two markets without any net investment.
III) short sell the asset in the low-priced market and buy it in the high-priced market.
A) I and IV
B) I and III
C) II and III
D) I, III, and IV
E) II, III, and IV
Answer: B Rationale: Only I and III are correct. II is incorrect because the beta of the portfolio does not need to be
zero. IV is incorrect because the opposite is true.
44. The factor F in the APT model represents
A) firm-specific risk.
B) the sensitivity of the firm to that factor.
C) a factor that affects all security returns.
D) the deviation from its expected value of a factor that affects all security returns.
E) a random amount of return attributable to firm events.
Answer: D Rationale: F measures the unanticipated portion of a factor that is common to all security returns.
45. In the APT model, what is the nonsystematic standard deviation of an equally-weighted portfolio that has an average
value of (ei) equal to 25% and 50 securities?
A) 12.5%
B)
625%
C) 0.5%
D)
3.54%
E) 14.59%
1 2
1
2
Answer: D Rationale:  2 (e )   (e )  25   12 .5,  (e )  12 .5  3.54 %
p

n

i
50
p
46. Which of the following is true about the security market line (SML) derived from the APT?
A) The SML has a downward slope.
B) The SML for the APT shows expected return in relation to portfolio standard deviation.
C) The SML for the APT has an intercept equal to the expected return on the market portfolio.
D) The benchmark portfolio for the SML may be any well-diversified portfolio.
E) The SML is not relevant for the APT.
Answer: D The benchmark portfolio does not need to be the (unobservable) market portfolio under the APT, but can
be any well-diversified portfolio. The intercept still equals the risk-free rate.
47. If arbitrage opportunities are to be ruled out, each well-diversified portfolio's expected excess return must be
A) inversely proportional to the risk-free rate.
B) inversely proportional to its standard deviation.
C) proportional to its weight in the market portfolio.
D) proportional to its standard deviation.
E) proportional to its beta coefficient.
Answer: E For each well-diversified portfolio (P and Q, for example), it must be true that [E(rp)-rf]/βp = [E(rQ)-rf]/ βQ.
48. Suppose you are working with two factor portfolios, Portfolio 1 and Portfolio 2. The portfolios have expected returns
of 15% and 6%, respectively. Based on this information, what would be the expected return on well-diversified
portfolio A, if A has a beta of 0.80 on the first factor and 0.50 on the second factor? The risk-free rate is 3%.
A) 15.2%
B) 14.1%
C) 13.3%
D) 10.7%
E) 8.4%
Answer: B Rationale: E(RA) = 3 +0.8*(15-3) + 0.5*(6-3) = 14.1
49. Which of the following is (are) true regarding the APT?
I)
The Security Market Line does not apply to the APT.
II) More than one factor can be important in determining returns.
III) Almost all individual securities satisfy the APT relationship.
IV) It doesn't rely on the market portfolio that contains all assets.
50.
51.
52.
53.
54.
A) II, III, and IV
B) II and IV
C) II and III
D) I, II, and IV
E) I, II, III, and IV
Answer: A Rationale: All except the first item are true. There is a Security Market Line associated with the APT.
In a factor model, the return on a stock in a particular period will be related to
A) factor risk.
B) non-factor risk.
C) standard deviation of returns.
D) both A and B are true.
E) none of the above are true.
Answer: D Rationale: Factor models explain firm returns based on both factor risk and non-factor risk.
Which of the following factors did Chen, Roll and Ross not include in their multifactor model?
A) Change in industrial production
B) Change in expected inflation
C) Change in unanticipated inflation
D) Excess return of long-term government bonds over T-bills
E) All of the above factors were included in their model.
Answer: E Chen, Roll and Ross included the four listed factors as well as the excess return of long-term corporate
bonds over long-term government bonds in their model.
Which of the following factors were used by Fama and French in their multi-factor model?
A) Return on the market index
B) Excess return of small stocks over large stocks.
C) Excess return of high book-to-market stocks over low book-to-market stocks.
D) All of the above factors were included in their model.
E) None of the above factors was included in their model.
Answer: D Rationale: Fama and French included all three of the factors listed.
Which of the following factors did Merton not suggest as a likely source of uncertainty that might affect security
returns?
A) uncertainties in labor income.
B) prices of important consumption goods.
C) book-to-market ratios.
D) changes in future investment opportunities.
E) All of the above are sources of uncertainty affecting security returns.
Answer: C Merton did not suggest book-to-market ratios as an ICAPM pricing factor; the other three were
suggested.
Black argues that past risk premiums on firm-characteristic variables, such as those described by Fama and French,
are problematic because.
A) they may result from data snooping.
B) they are sources of systematic risk.
C) they can be explained by security characteristic lines.
D) they are more appropriate for a single-factor model.
E) they are macroeconomic factors.
Answer: A Difficulty: Moderate
55. Multifactor models seek to improve the performance of the single-index model by
A) modeling the systematic component of firm returns in greater detail.
B) incorporating firm-specific components into the pricing model.
C) allowing for multiple economic factors to have differential effects
D) all of the above are true.
E) none of the above are true.
Answer: D Difficulty: Easy
56. Multifactor models such as the one constructed by Chen, Roll, and Ross, can better describe assets' returns by
A) expanding beyond one factor to represent sources of systematic risk.
B) using variables that are easier to forecast ex ante.
C) calculating beta coefficients by an alternative method.
D) using only stocks with relatively stable returns.
E) ignoring firm-specific risk.
Answer: A The study used five different factors to explain security returns, allowing for several sources of risk to affect the
returns.
57. Consider the multifactor model APT with three factors. Portfolio A has a beta of 0.8 on factor 1, a beta of 1.1 on
factor 2, and a beta of 1.25 on factor 3. The risk premiums on the factor 1, factor 2, and factor 3 are 3%, 5% and 2%,
respectively. The risk-free rate of return is 3%. The expected return on portfolio A is
if no arbitrage
opportunities exist.
A) 13.5%
B) 13.4%
C) 16.5%
D) 23.0%
E) none of the above
Answer: B Rationale: 3% + 0.8(3%) + 1.1(5%) + 1.25(2%) = 13.4%.
58. Consider the multifactor APT. The risk premiums on the factor 1 and factor 2 portfolios are 6% and 4%,
respectively. The risk-free rate of return is 4%. Stock A has an expected return of 16% and a beta on factor 1 of 1.3.
Stock A has a beta on factor 2 of
.
A) 1.33
B) 1.05
C) 1.67
D) 2.00
E) none of the above
Answer: B Rationale: 16% = 4% + 6%(1.3) + 4%(x); x = 1.05.
59. Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 5%, the risk premium on the
first factor portfolio is 4% and the risk premium on the second factor portfolio is 6%. If portfolio A has a beta of 0.6
on the first factor and 1.8 on the second factor, what is its expected return?
A) 7.0%
B) 8.0%
C) 18.2%
D) 13.0%
E) 13.2%
Answer: C Rationale: .05 + .6 (.04) + 1.8 (.06) = .182
60. Consider a single factor APT. Portfolio A has a beta of 2.0 and an expected return of 22%. Portfolio B has a beta of
1.5 and an expected return of 17%. The risk-free rate of return is 4%. If you wanted to take advantage of an
arbitrage opportunity, you should take a short position in portfolio
and a long position in portfolio
.
A) A, A
B) A, B
C) B, A
D) B, B
E) A, the riskless asset
Answer: C A: 22% = 2.0F + 4%; F = 9%; B: 17% = 1.5F + 4%: F = 8.67%; thus, short B and take a long position in
A.
61. Consider the single factor APT. Portfolio A has a beta of 0.5 and an expected return of 12%. Portfolio B has a beta
of 0.4 and an expected return of 13%. The risk-free rate of return is 5%. If you wanted to take advantage of an
arbitrage opportunity, you should take a short position in portfolio
and a long position in portfolio
.
A) A, A
B) A, B
C) B, A
D) B, B
E) none of the above
Answer: B: A: 12% = 5% + 0.5F; F = 14%; B: 13% = 5% + 0.4F; F = 20%; therefore, short A and take a long position in B.
62. Consider the one-factor APT. The variance of returns on the factor portfolio is 9%. The beta of a well-diversified
portfolio on the factor is 1.25. The variance of returns on the well-diversified portfolio is approximately
.
A) 3.6%
B) 6.0%
C) 7.3%
D) 14.1%
E) none of the above
Answer: D Rationale: s2P = (1.25)2(9%) = 14.06%.
63. Consider the one-factor APT. The standard deviation of returns on a well-diversified portfolio is 22%. The standard
deviation on the factor portfolio is 14%. The beta of the well-diversified portfolio is approximately
.
A) 0.80
B) 1.13
C) 1.25
D) 1.57
E) none of the above
Answer: D Rationale: (22%)2 = (14%)2b2; b = 1.57.
64. Consider the single-factor APT. Stocks A and B have expected returns of 12% and 14%, respectively. The risk-free
rate of return is 5%. Stock B has a beta of 1.2. If arbitrage opportunities are ruled out, stock A has a beta of
.
A) 0.67
B) 0.93
C) 1.30
D) 1.69
E) none of the above
Answer: B Rationale: A: 12% = 5% + bF; B: 14% = 5% + 1.2F; F = 7.5%; Thus, beta of A = 7/7.5 = 0.93.
65. Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on factor 1
and a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%.
What is the risk-premium on factor 2 if no arbitrage opportunities exit?
A) 9.26%
B) 3%
C) 4%
D) 7.75%
E) none of the above
Answer: A Rationale: 17.6% = 1.45(3.2%) + .86x + 5%; x = 9.26.
Short Answer Questions
66. Discuss the advantages of arbitrage pricing theory (APT) over the capital asset pricing model (CAPM) relative to
diversified portfolios.
Answer: The APT does not require that the benchmark portfolio in the SML relationship be the true market portfolio. Any
well-diversified portfolio lying on the SML may serve as a benchmark portfolio. Thus, the APT has more flexibility than the
CAPM, as problems associated with an unobservable market portfolio are not a concern with APT. In addition, the APT
provides further justification for the use of the index model for practical implementation of the SML relationship. That is, if
the index portfolio is not a precise proxy for the true market portfolio, which is a cause of considerable concern in the context
of the CAPM, if an index portfolio is sufficiently diversified, the SML relationship holds, according to APT.This question is
designed to determine if the student understands the basic advantages of APT over the CAPM.
67. Discuss the advantages of the multifactor APT over the single factor APT and the CAPM. What is one shortcoming
of the multifactor APT and how does this shortcoming compare to CAPM implications?
Answer: The single factor APT and the CAPM assume that there is only one systematic risk factor affecting stock returns.
However, obviously several factors may affect stock returns. Some of these factors are: business cycles, interest rate
fluctuations, inflation rates, oil prices, etc. A multifactor model can accommodate these multiple sources of risk.
One shortcoming of the multifactor APT is that the model provides no guidance concerning the risk premiums on the factor
portfolios. The CAPM implies that the risk premium on the market is determined by the market's variance and the average
degree of risk aversion across investors.
68. Discuss arbitrage opportunities in the context of violations of the law of one price.
Answer: The law of one price is violated when an asset is trading at different prices in two markets. If the price differential
exceeds the transactions costs, a simultaneous trade in the two markets can produce a sure profit with a zero investment. That
is, the investor can sell short the asset in the high-priced market and buy the asset in the low-priced market. The investor has
been able to assume these positions with a zero investment (using the proceeds of the short transaction to finance the long
position). However, it should be remembered that individual investors do not have access to the proceeds of a short transaction
until the position has been covered.
69. Discuss the similarities and the differences between the CAPM and the APT with regard to the following factors:
capital market equilibrium, assumptions about risk aversion, risk-return dominance, and the number of investors
required to restore equilibrium.
Answer: Both the CAPM and the APT are market equilibrium models, which examine the factors that affect securities' prices.
In equilibrium, there are no overpriced or underpriced securities. In both models, mispriced securities can be identified and
purchased or sold as appropriate to earn excess profits. The CAPM is based on the idea that there are large numbers of investors
who are focused on risk-return dominance. Under the CAPM, when a mispricing occurs, many individual investors make small
changes in their portfolios, guided by their degrees of risk aversion. The aggregate effect of their actions brings the market
back into equilibrium. Under the APT, each investor wants an infinite arbitrage position in the mispriced asset. Therefore, it
would not take many investors to identify the arbitrage opportunity and act to bring the market back to equilibrium. The student
can compare the two models by focusing on the specific items.
70. Security A has a beta of 1.0 and an expected return of 12%. Security B has a beta of 0.75 and an expected return of
11%. The risk-free rate is 6%. Explain the arbitrage opportunity that exists; explain how an investor can take
advantage of it. Give specific details about how to form the portfolio, what to buy and what to sell.
Answer: An arbitrage opportunity exists because it is possible to form a portfolio of security A and the risk-free asset that has
a beta of 0.75 and a different expected return than security B. The investor can accomplish this by choosing .75 as the weight
in A and .25 in the risk-free asset. This portfolio would have E(rp) = 0.75(12%) + 0.25(6%) = 10.5%, which is less than B's
11% expected return. The investor should buy B and finance the purchase by short selling A and borrowing at the risk-free
asset. This question is similar to Concept Check question 3 on page 348.
71. Name three variables that Chen, Roll, and Ross used to measure the impact of macroeconomic factors on security
returns. Briefly explain the reasoning behind their model.
Answer: The factors they considered were IP (the % change in industrial production), EI (the % change in expected inflation),
UI (the % change in unanticipated inflation), CG (excess return of long-term corporate bonds over long-term government
bonds), and GB (excess return of long-term government bonds over T-bills). The rational for their model is that many different
economic factors can combine to affect securities' returns. Also, by including factors that are related to the business cycle, the
estimation of beta coefficients should be improved. Each beta will represent only the impact of the corresponding variable on
returns. The student has some flexibility in remembering which variables were used in the study. A general understanding of
macroeconomic variables will be helpful in answering the question. The question provides an opportunity to measure the
student's understanding of the types of risk that are relevant and how they can be explicitly considered in the model.
Essay Questions Chapter 8 Index Models
66. Discuss the advantages of the single-index model over the Markowitz model in terms of numbers of variable estimates
required and in terms of understanding risk relationships.
For a 50 security portfolio, the Markowitz model requires the following parameter estimates:
n = 50 estimates of expected returns; n = 50 estimates of variances;
(n2 - n)/2 = 1,225 estimates of covariances; 1,325 estimates.
For a 50 security portfolio, the single-index model requires the following parameter estimates:
n = 50 estimates of expected excess returns, E(R); n = 50 estimates of sensitivity coefficients, βi;
n = 50 estimates of the firm-specific variances, σ2(ei);
1 estimate for the variance of the common macroeconomic factor, σ2M; or (3n + 1) estimates.
In addition, the single-index model provides further insight by recognizing that different firms have different sensitivities to
macroeconomic events. The model also summarizes the distinction between macroeconomic and firm-specific risk factors.
This question is designed to ascertain that the student understands the significant simplifications and improvements offered
by the single-index model over the Markowitz model.
67. Discuss the security characteristic line (SCL).
The security characteristic line (SCL) is the result of estimating the regression equation of the single-index model. The
SCL is a plot of the typical excess returns on a security over the risk-free rate as a function of the excess return on the market.
The slope of the SCL is the beta of the security, and they-intercept, alpha, is the excess return on the security when the excess
market return is zero. This question is designed to ascertain that the student understands how the SCL is obtained, as this
relationship is the one that is most frequently used by published information services for the estimation of the regression
parameters, alpha and beta.
68. Discuss the "adjusted betas" published by Merrill Lynch in Security Risk Evaluation.
Over time, security betas move toward 1, as the average beta of all securities is 1 and variables regress toward the mean.
Thus, if a historic beta has been greater than 1, the chances are that in the future, this beta will be less than the historic beta.
The opposite relationship will be observed if the historic beta has been less than one. Merrill Lynch uses the following
relationship to calculate "adjusted betas". Adjusted beta = 2/3 (sample beta) + 1/3 (1).
This question is important, as many published sources quote an "adjusted beta" with no explanation as to how such a number
was obtained. The regression toward the mean is a valid statistical concept and it is important that the student understands
that this concept represents the theory behind the possibly undocumented "adjusted betas".
Chapter 10 Index Models Multiple Choice Questions
1. As diversification increases, the total variance of a portfolio approaches
.
A) 0
B) 1
C) the variance of the market portfolio
D) infinity
E) none of the above
Answer: C As more and more securities are added to the portfolio, unsystematic risk decreases and most of the
remaining risk is systematic, as measured by the variance of the market portfolio.
2. The index model was first suggested by
.
A) Graham
B) Markowitz
C) Miller
D) Sharpe
E) none of the above
Answer: D Rationale: William Sharpe, building on the work of Harry Markowitz, developed the index model.
3. A single-index model uses
as a proxy for the systematic risk factor.
A) a market index, such as the S&P 500
B) the current account deficit
C) the growth rate in GNP
D) the unemployment rate
E) none of the above
Answer: A
The single-index model uses a market index, such as the S&P 500, as a proxy for the market, and thus for systematic risk.
4. The Security Risk Evaluation book published by Merrill Lynch relies on the
most recent monthly
observations to calculate regression parameters.
A) 12
B) 36
C) 60
D) 120
E) none of the above
Answer: C Rationale: Most published betas and other regression parameters, including those published by Merrill
Lynch, are based on five years of monthly return data.
5. The Security Risk Evaluation book published by Merrill Lynch uses the
as a proxy for the market
portfolio.
A) Dow Jones Industrial Average
B) Dow Jones Transportation Average
C) S&P 500 Index
D) Wilshire 5000
E) none of the above
Answer: C Rationale: The Merrill Lynch data (and much of the other published data sets) are based on the S&P 500
index as a market proxy.
6. According to the index model, covariances among security pairs are
A) due to the influence of a single common factor represented by the market index return
B) extremely difficult to calculate
C) related to industry-specific events
D) usually positive
E) A and D
Answer: E Most securities move together most of the time, and move with a market index, or market proxy.
7. The intercept calculated by Merrill Lynch in the regression equations is equal to
A) α in the CAPM
B) α + rf(1 + β)
C) α + rf(1 - β)
D) 1 - α
E) none of the above
Answer: C Difficulty: Moderate
Rationale: The intercept that Merrill Lynch calls alpha is really, using the parameters of the CAPM, an estimate of a
+ rf (1 - b). The apparent justification for this procedure is that, on a monthly basis, rf (1 - b) is small and is apt to be
swamped by the volatility of actual stock returns.
8. Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the
regression line is an estimate of
.
A) the α of the asset
B) the β of the asset
C) the σ of the asset
D) the δ of the asset
E) none of the above
Answer: B The slope of the regression line, b, measures the volatility of the stock versus the volatility of the market.
9. In a factor model, the return on a stock in a particular period will be related to
_.
A) firm-specific events
B) macroeconomic events
C) the error term
D) both A and B
E) neither A nor B
Answer: D The return on a stock is related to both firm-specific and macroeconomic events.
10. Rosenberg and Guy found that
helped to predict a firm's beta.
A) the firm's financial characteristics
B) the firm's industry group
C) firm size
D) both A and B
E) A, B and C all helped to predict betas.
Answer: E Rosenberg and Guy found that after controlling for the firm's financial characteristics, the firm's industry
group was a significant predictor of the firm's beta.
11. If the index model is valid,
would be helpful in determining the covariance between assets K and L.
A) βk
B) βL
C) σM
D) all of the above
E) none of the above
Answer: D If the index model is valid A, B, and C are determinants of the covariance between K and L.
12. Rosenberg and Guy found that
helped to predict firms' betas.
A) debt/asset ratios
B) market capitalization
C) variance of earnings
D) all of the above
E) none of the above
Answer: D Rationale: Rosenberg and Guy found that A, B, and C were determinants of firms' betas.
13. If a firm's beta was calculated as 0.6 in a regression equation, Merrill Lynch would state the adjusted beta at a number
A) less than 0.6 but greater than zero.
B) between 0.6 and 1.0.
C) between 1.0 and 1.6.
D) greater than 1.6.
E) zero or less.
Answer: B Rationale: Betas, on average, equal one; thus, betas over time regress toward the mean, or 1. Therefore,
if historic betas are less than 1, adjusted betas are between 1 and the calculated beta.
14. The beta of Exxon stock has been estimated as 1.2 by Merrill Lynch using regression analysis on a sample of
historical returns. The Merrill Lynch adjusted beta of Exxon stock would be
.
A) 1.20
B) 1.32
C) 1.13
D) 1.0
E) none of the above
Answer: C Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.2) + 1/3 = 1.13.
15. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 100 stocks
in order to construct a mean-variance efficient portfolio constrained by 100 investments. They will need to calculate
expected returns and
variances of returns.
A) 100, 100
B) 100, 4950
C) 4950, 100
D) 4950, 4950
E) none of the above
Answer: A The expected returns of each of the 100 securities must be calculated. In addition, the 100 variances
around these returns must be calculated.
16. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 100 stocks
in order to construct a mean-variance efficient portfolio constrained by 100 investments. They will need to calculate
covariances.
A) 45
B) 100
C) 4,950
D) 10,000
E) none of the above
Answer: C (n2 - n)/2 = (10,000 - 100)/2 = 4,950 covariances must be calculated.
17. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 200 stocks in
order to construct a mean-variance efficient portfolio constrained by 200 investments. They will need to calculate
estimates of expected returns and
estimates of sensitivity coefficients to the macroeconomic factor.
A) 200; 19,900
B) 200; 200
C) 19,900; 200
D) 19,900; 19.900
E) none of the above
Answer: B For a single-index model, n(200), expected returns and n(200) sensitivity coefficients to the macroeconomic
factor must be estimated.
18. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 500 stocks in
order to construct a mean-variance efficient portfolio constrained by 500 investments. They will need to calculate
estimates of firm-specific variances and
estimates for the variance of the macroeconomic factor.
A) 500; 1
B) 500; 500
C) 124,750; 1
D) 124,750; 500
E) 250,000; 500
Answer: A For the single-index model, n(500) estimates of firm-specific variances must be calculated and 1 estimate for the
variance of the common macroeconomic factor.
19. Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 16%. The risk-free
rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 11% and there are no firm-specific
events affecting the stock performance. The β of the stock is
.
A) 0.67
B) 0.75
C) 1.0
D) 1.33
E) 1.50
Answer: C 11% = 0% + b(11%); b = 1.0.
20. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model
holds. If the ó of your portfolio was 0.20 and ó M was 0.16, the β of the portfolio would be approximately
.
A) 0.64
B) 0.80
C) 1.25
D) 1.56
E) none of the above
Answer: C s2p / s2m = b2; (0.2)2/(0.16)2 = 1.56; b = 1.25.
21. Suppose the following equation best describes the evolution of β over time: βt = 0.25 + 0.75βt-1
If a stock had a β of 0.6 last year, you would forecast the β to be
in the coming year.
A) 0.45
B) 0.60
C) 0.70
D) 0.75
E) none of the above
Answer: C 0.25 + 0.75(0.6) = 0.70.
22. Merrill Lynch estimates the index model for a stock using regression analysis involving total returns. They estimated
the intercept in the regression equation at 6% and the β at 0.5. The risk-free rate of return is 12%. The true β of the
stock is
.
A) 0%
B) 3%
C) 6%
D) 9%
E) none of the above
Answer: A 6% = a + 12% (1 - 0.5); a = 0%.
23. The index model for stock A has been estimated with the following result: RA = 0.01 + 0.9RM + eA
If σM = 0.25 and R2A = 0.25, the standard deviation of return of stock A is
.
A) 0.2025
B) 0.2500
C) 0.4500
D) 0.8100
E) none of the above
Answer: C R2 = b2s2M / s2;0.25 = [(0.81)(0.25)2]/s2; s = 0.4500.
24. The index model for stock B has been estimated with the following result: RB = 0.01 + 1.1RM + eB
If σM = 0.20 and R2B = 0.50, the standard deviation of the return on stock B is
.
A) 0.1111
B) 0.2111
C) 0.3111
D) 0.4111
E) none of the above
Answer: C R2 = b2s2M / s2; 0.5 = [(1.1)2(0.2)2]/s2; s = 0.3111.
25. Suppose you forecast that the market index will earn a return of 15% in the coming year. Treasury bills are yielding
6%. The unadjusted β of Mobil stock is 1.30. A reasonable forecast of the return on Mobil stock for the coming year
is
if you use Merrill Lynch adjusted betas.
A) 15.0%
B) 15.5%
C) 16.0%
D) 16.8%
E) none of the above
Answer: D Adjusted beta = 2/3(1.3) + 1/3 = 1.20; E(rM) = 6% + 1.20(9%) = 16.8%.
26. The index model has been estimated for stocks A and B with the following results:
RA = 0.01 + 0.5RM + eA
RB = 0.02 + 1.3RM + eB
σM = 0.25 σ(eA) = 0.20 σ(eB) = 0.10
The covariance between the returns on stocks A and B is
.
A) 0.0384
B) 0.0406
C) 0.1920
D) 0.0050
E) 0.4000
Answer: B Cov(RA,RB) = bAbBs2M = 0.5(1.3)(0.25)2 = 0.0406.
27. The index model has been estimated for stocks A and B with the following results:
RA = 0.01 + 0.8RM + eA
RB = 0.02 + 1.2RM + eB
σM = 0.20 σ(eA) = 0.20 σ (eB) = 0.10
The standard deviation for stock A is
.
A) 0.0656
B) 0.0676
C) 0.2561
D) 0.2600
E) none of the above
Answer: C Rationale: σA = [(0.8)2(0.2)2 + (0.2)2]1/2 = 0.2561.
28. The index model has been estimated for stock A with the following results:
RA = 0.01 + 0.8RM + eA
σM = 0.20 σ(eA) = 0.10
The standard deviation of the return for stock A is
.
A) 0.0356
B) 0.1886
C) 0.1600
D) 0.6400
E) none of the above
Answer: B σB = [(.8)2(0.2)2 + (0.1)2]1/2 = 0.1886.
29. Security returns
A) are based on both macro events and firm-specific events.
B) are based on firm-specific events only.
C) are usually positively correlated with each other.
D) A and B.
E) A and C.
Answer: E Stock returns are usually highly positively correlated with each other. Stock returns are affected by both
macro economic events and firm-specific events.
30. The single-index model
A) greatly reduces the number of required calculations, relative to those required by the Markowitz model.
B) enhances the understanding of systematic versus nonsystematic risk.
C) greatly increases the number of required calculations, relative to those required by the Markowitz model.
D) A and B.
E) B and C.
Answer: D The single index model both greatly reduces the number of calculations and enhances the understanding
of the relationship between systematic and unsystematic risk on security returns.
31. The Security Characteristic Line (SCL)
A) plots the excess return on a security as a function of the excess return on the market.
B) allows one to estimate the beta of the security.
C) allows one to estimate the alpha of the security.
D) all of the above.
E) none of the above.
Answer: D The security characteristic line, which plots the excess return of the security as a function of the excess
return of the market allows one to estimate both the alpha and the beta of the security.
32. The expected impact of unanticipated macroeconomic events on a security's return during the period is
A) included in the security's expected return.
B) zero.
C) equal to the risk free rate.
D) proportional to the firm's beta.
E) infinite.
Answer: B The expected value of unanticipated macroeconomic events is zero, because by definition it must
average to zero or it would be incorporated into the expected return.
33. Covariances between security returns tend to be
A) positive because of SEC regulations.
B) positive because of Exchange regulations.
C) positive because of economic forces that affect many firms.
D) negative because of SEC regulations
E) negative because of economic forces that affect many firms.
Answer: C Economic forces such as business cycles, interest rates, and technological changes tend to have similar
impacts on many firms.
34. In the single-index model represented by the equation ri = E(ri) + βiF + ei, the term ei represents
A) the impact of unanticipated macroeconomic events on security i's return.
B) the impact of unanticipated firm-specific events on security i's return.
C) the impact of anticipated macroeconomic events on security i's return.
D) the impact of anticipated firm-specific events on security i's return.
E) the impact of changes in the market on security i's return.
Answer: B The textbook discusses a model in which macroeconomic events are used as a single index for security
returns. The ei term represents the impact of unanticipated firm-specific events. The ei term has an expected value of
zero. Only unanticipated events would affect the return.
35. Suppose you are doing a portfolio analysis that includes all of the stocks on the NYSE. Using a single-index model
rather than the Markowitz model
the number of inputs needed from
to
.
A) increases, about 1,400, more than 1.4 million
B) increases, about 10,000, more than 125,000
C) reduces, more than 125,000, about 10,000
D) reduces, more than 4 million, about 9,000
E) increases, about 150, more than 1,500
Answer: D This example is discussed in the textbook. The main point for the students to remember is that the single-index
model drastically reduces the number of inputs required.
36. One “cost” of the single-index model is that it
A) is virtually impossible to apply.
B) prohibits specialization of efforts within the security analysis industry.
C) requires forecasts of the money supply.
D) is legally prohibited by the SEC.
E) allows for only two kinds of risk -- macro risk and micro risk.
Answer: E The single-index model discussed in chapter 10 broke risk into macro and micro portions. In this model other
factors such as industry effects.
37. The Security Characteristic Line (SCL) associated with the single-index model is a plot of
A) the security's returns on the vertical axis and the market index's returns on the horizontal axis.
B) the market index's returns on the vertical axis and the security's returns on the horizontal axis.
C) the security's excess returns on the vertical axis and the market index's excess returns on the horizontal axis.
D) the market index's excess returns on the vertical axis and the security's excess returns on the horizontal axis.
E) the security's returns on the vertical axis and Beta on the horizontal axis.
Answer: C The student needs to remember that it is the excess returns that are plotted and that the security's returns are plotted
as a dependent variable.
38. The idea that there is a limit to the reduction of portfolio risk due to diversification is
A) contradicted by both the CAPM and the single-index model.
B) contradicted by the CAPM.
C) contradicted by the single-index model.
D) supported in theory, but not supported empirically.
E) supported both in theory and by empirical evidence.
Answer: E The benefits of diversification are limited to the level of systematic risk. Figure 8.1 shows this concept graphically
39. In their study about predicting beta coefficients, which of the following did Rosenberg and Guy find to be factors that
influence beta?
industry group
I)
variance of cash flow
II) dividend yield
III) growth in earnings per share
A) I and II
B) I and III
C) I, II, and III
D) I, II, and IV
E) I, II, III, and IV
Answer: E All of the factors mentioned, as well as variance of earnings, firm size, and debt-to-asset ratio, were found to help predict betas
40. If a firm's beta was calculated as 1.6 in a regression equation, Merrill Lynch would state the adjusted beta at a number
A) less than 0.6 but greater than zero.
B) between 0.6 and 1.0.
C) between 1.0 and 1.6.
D) greater than 1.6.
E) zero or less.
Answer: C Betas, on average, equal one; thus, betas over time regress toward the mean, or 1. Therefore, if historic
betas are more than 1, adjusted betas are between 1 and the calculated beta.
41. The beta of a stock has been estimated as 1.8 by Merrill Lynch using regression analysis on a sample of historical
returns. The Merrill Lynch adjusted beta of the stock would be
.
A) 1.20
B) 1.53
C) 1.13
D) 1.0
E) none of the above
Answer: B Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.8) + 1/3 = 1.53.
42. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 40 stocks in
order to construct a mean-variance efficient portfolio constrained by 40 investments. They will need to calculate
expected returns and
variances of returns.
A) 100, 100
B) 40, 40
C) 4950, 100
D) 4950, 4950
E) none of the above
Answer: B The expected returns of each of the 40 securities must be calculated. In addition, the 40 variances around these
returns must be calculated.
43. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 40 stocks in
order to construct a mean-variance efficient portfolio constrained by 40 investments. They will need to calculate
covariances.
A) 45
B) 780
C) 4,950
D) 10,000
E) none of the above
Answer: B (n2 - n)/2 = (1,600 - 40)/2 = 780 covariances must be calculated.
44. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 60 stocks in order
to construct a mean-variance efficient portfolio constrained by 60 investments. They will need to calculate
estimates of expected returns and
estimates of sensitivity coefficients to the macroeconomic factor.
A) 200; 19,900
B) 200; 200
C) 60; 60
D) 19,900; 19.900
E) none of the above
Answer: C For a single-index model, n(60), expected returns and n(60) sensitivity coefficients to the macroeconomic factor
must be estimated.
45. Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 10%. The risk-free
rate of return is 3%. The stock earns a return that exceeds the risk-free rate by 11% and there are no firm-specific
events affecting the stock performance. The β of the stock is
.
A) 0.64
B) 0.75
C) 1.17
D) 1.33
E) 1.50
Answer: A 7% = 0% + b(11%); b = 0.636.
46. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model
holds. If the σ of your portfolio was 0.25 and σM was 0.21, the β of the portfolio would be approximately
.
A) 0.64
B) 1.19
C) 1.25
D) 1.56
E) none of the above
Answer: B s2p / s2m = b2; (0.25)2/(0.21)2 = 1.417; b = 1.19.
47. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model
holds. If the σ of your portfolio was 0.18 and σM was 0.22, the β of the portfolio would be approximately
.
A) 0.64
B) 1.19
C) 0.82
D) 1.56
E) none of the above
Answer: C s2p / s2m = b2; (0.18)2/(0.22)2 = 0.669; b = 0.82.
48. Suppose the following equation best describes the evolution of β over time: ât = 0.4 + 0.6βt-1
If a stock had a β of 0.9 last year, you would forecast the β to be
in the coming year.
A) 0.45
B) 0.60
C) 0.70
D) 0.94
E) none of the above
Answer: D 0.4 + 0.6(0.9) = 0.94.
49. Suppose the following equation best describes the evolution of β over time: β t = 0.3 + 0.2βt-1
If a stock had a β of 0.8 last year, you would forecast the β to be
in the coming year.
A) 0.46
B) 0.60
C) 0.70
D) 0.94
E) none of the above
Answer: A 0.3 + 0.2(0.8) = 0.46.
50. The index model for stock A has been estimated with the following result: RA = 0.01 + 0.94RM + eA
If σM = 0.30 and R2A = 0.28, the standard deviation of return of stock A is
.
A) 0.2025
B) 0.2500
C) 0.4500
D) 0.5329
E) none of the above
Answer: D R2 = b2s2M / s2; 0.28 = [(0.94) 2(0.30) 2] / .28; s = 0.5329.
51. 30. A reasonable forecast of the return on Mobil stock for the coming year is
if you use Merrill Lynch
adjusted betas.
A) 15.0%
B) 15.5%
C) 16.0%
D) 14.6%
E) none of the above
Answer: D Adjusted beta = 2/3(1.5) + 1/3 = 1.33; E(rM) = 4% + 1.33(8%) = 14.6%.
52. The index model has been estimated for stocks A and B with the following results:
RA = 0.01 + 0.8RM + eA
RB = 0.02 + 1.1RM + eB
σM = 0.30 σ (eA) = 0.20 σ (eB) = 0.10
The covariance between the returns on stocks A and B is
.
A) 0.0384
B) 0.0406
C) 0.1920
D) 0.0050
E) 0.0792
Answer: E Cov(RA,RB) = bAbBs2M = 0.8(1.1)(0.30)2 = 0.0792.
53. If a firm's beta was calculated as 1.35 in a regression equation, Merrill Lynch would state the adjusted beta at a
number
A) less than 1.35
B) between 0.0 and 1.0.
C) between 1.0 and 1.35.
D) greater than 1.35.
E) zero or less.
Answer: C Betas, on average, equal one; thus, betas over time regress toward the mean, or 1. Therefore, if historic
betas are less than 1, adjusted betas are between 1 and the calculated beta.
54. The beta of a stock has been estimated as 1.4 by Merrill Lynch using regression analysis on a sample of historical
returns. The Merrill Lynch adjusted beta of the stock would be
.
A) 1.27
B) 1.32
C) 1.13
D) 1.0
E) none of the above
Answer: A Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.4) + 1/3 = 1.27.
55. The beta of a stock has been estimated as 0.85 by Merrill Lynch using regression analysis on a sample of historical
returns. The Merrill Lynch adjusted beta of the stock would be
.
A) 1.01
B) 0.95
C) 1.13
D) 0.90
E) none of the above
Answer: D Rationale: Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(0.85) + 1/3 = 0.90.
56. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 125 stocks
in order to construct a mean-variance efficient portfolio constrained by 125 investments. They will need to calculate
expected returns and
variances of returns.
A) 125, 125
B) 125, 15,625
C) 15,625, 125
D) 15,625, 15,625
E) none of the above
Answer: A Rationale: The expected returns of each of the 125 securities must be calculated. In addition, the 125
variances around these returns must be calculated.
57. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 125 stocks
in order to construct a mean-variance efficient portfolio constrained by 125 investments. They will need to calculate
covariances.
A) 90
B) 125
C) 7,750
D) 15,625
E) none of the above
Answer: C (n2 - n)/2 = (15,625 - 125)/2 = 7,750 covariances must be calculated.
58. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 132 stocks
in order to construct a mean-variance efficient portfolio constrained by 132 investments. They will need to calculate
covariances.
A) 100
B) 132
C) 4,950
D) 8,646
E) none of the above
Answer: D (n2 - n)/2 = (17,424 - 132)/2 = 8,646 covariances must be calculated.
59. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 217 stocks in
order to construct a mean-variance efficient portfolio constrained by 217 investments. They will need to calculate
estimates of expected returns and
estimates of sensitivity coefficients to the macroeconomic
factor.
A) 217; 47,089
B) 217; 217
C) 47,089; 217
D) 47,089; 47,089
E) none of the above
Answer: B For a single-index model, n(217), expected returns and n(217) sensitivity coefficients to the
macroeconomic factor must be estimated.
60. Assume that stock market returns do follow a single-index structure. An investment fund analyzes 500 stocks in
order to construct a mean-variance efficient portfolio constrained by 750 investments. They will need to calculate
estimates of firm-specific variances and
estimates for the variance of the macroeconomic factor.
A) 750; 1
B) 750; 750
C) 124,750; 1
D) 124,750; 750
E) 562,500; 750
Answer: A For the single-index model, n(750) estimates of firm-specific variances must be calculated and 1
estimate for the variance of the common macroeconomic factor.
61. Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 10%. The risk-free
rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 5% and there are no firm-specific
events affecting the stock performance. The β of the stock is
.
A) 0.67
B) 0.75
C) 1.0
D) 1.33
E) 1.50
Answer: C 5% = 0% + b(5%); b = 1.0.
62. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model
holds. If the ó of your portfolio was 0.24 and σM was 0.18, the β of the portfolio would be approximately
.
A) 0.64
B) 1.33
C) 1.25
D) 1.56
E) none of the above
Answer: B s2p / s2m = b2; (0.24)2/(0.18)2 = 1.78; b = 1.33.
63. Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model
holds. If the σ of your portfolio was 0.14 and σM was 0.19, the β of the portfolio would be approximately
.
A) 0.74
B) 0.80
C) 1.25
D) 1.56
E) none of the above
Answer: A s2p / s2m = b2; (0.14)2/(0.19)2 = 0.54; b = 0.74.
64. Suppose the following equation best describes the evolution of β over time: βt = 0.30 + 0.70βt-1
If a stock had a β of 0.82 last year, you would forecast the β to be
in the coming year.
A) 0.91
B) 0.77
C) 0.63
D) 0.87
E) none of the above
Answer: D 0.30 + 0.70(0.82) = 0.874.
65. The index model has been estimated for stocks A and B with the following results:
RA = 0.03 + 0.7RM + eA
RB = 0.01 + 0.9RM + eB
σM = 0.35 σ(eA) = 0.20 σ(eB) = 0.10
The covariance between the returns on stocks A and B is
.
A) 0.0384
B) 0.0406
C) 0.1920
D) 0.0772
E) 0.4000
Answer: D Cov(RA,RB) = bAbBs2M = 0.7(0.9)(0.35)2 = 0.0772.