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12) Use the information in the table to calculate the expected return and standard deviation of an
equally-weighted portfolio.
8.6 The Risk-and-Return Trade-off
1) Use the following table:
States of the
Economy
Probability of the
State
3-Month
T-Bill
Large-Company
Stock
Small-Company
Stock
Boom
0.3
4%
10%
30%
Steady
0.5
4%
5%
20%
Recession
0.2
4%
0%
10%
Estimate the difference between the standard deviations for large- and small-company stocks.
Which is larger and by how much?
A) Small company stocks by 49.00%
B) Small company stocks by 36.75%
C) Large company stocks by 12.25%
D) Small company stocks by 3.50%
2) Use the following table:
States of the
Economy
Probability of the
State
3-Month
T-Bill
Large-Company
Stock
Small-Company
Stock
Boom
0.3
4
10
30
Steady
0.5
4
5
20
Recession
0.2
4
0
10
How large is the difference between the standard deviation of a small-company stock and a 3-
month T-bill?
A) 7.0%
B) 5.5%
C) 4.0%
D) 3.5%
3) Stock A B C D
Expected Return 5% 5% 7% 6%
Standard Deviation 10% 12% 12% 11%
Which of the following statements is TRUE?
A) A is a better investment than B.
B) B is a better investment than C.
C) C is a better investment than D.
D) D is a better investment than C.
4) Which of the statements below is NOT correct?
A) If two investments have the same expected return, the investment with the lower risk is
preferred.
B) If two investments have the same expected return, the investment with the greater risk is
preferred.
C) If two investments have the same expected risk, the investment with the higher expected
return is preferred.
D) If one investment has a higher expected return and a greater level of risk than another, it is not
clear which investment is the preferred choice.
5) If two investments have the same expected return, a rational investor will choose the
investment with the greater risk in an effort to get a much larger return.
6) If two investments have the same level of risk, a rational investor will choose the investment
with the higher expected rate of return.
7) What are the two investment rules identified in the text? Evaluate the validity of the following
statement and justify your reasoning. "Investors do not like risk and will always choose the
investment with the least risk."
1) Diversification is
A) not putting all of your eggs in one basket.
B) spreading wealth over a variety of investment opportunities.
C) a common investment strategy.
D) All of the above
2) An investor's total investment set may be referred to as ________.
A) the stock market
B) diversification
C) a financial portfolio
D) None of the above
3) When considering expected returns, what is TRUE about the states of the world?
A) They must have probabilities that sum to 100%.
B) They represent all possible outcomes.
C) They are sometimes simplified into outcomes such as boom, bust, and normal.
D) Statements A through C are all true.
4) Richard has two investment opportunities. He can invest in The Sunglasses Company or The
Umbrella Company. What is the expected return and standard deviation of each company?
State of the
Economy
Probability of the
State
Expected Return Sunglasses
Company
Expected Return
Umbrella Company
Sunny
.50
25%
0%
Rainy
.50
0%
25%
A) The expected return for each company is 12.50% and the standard deviation for each
company is 0.00%.
B) The expected return for each company is 12.50% and the standard deviation for each
company is 12.50%.
C) The expected return for each company is 12.50% and the standard deviation for each
company is 156.25%.
D) The expected return for each company is 12.50% and the standard deviation for each
company is 25.00%.
5) Richard has two investment opportunities. He can invest in The Sunglasses Company or The
Umbrella Company. If he diversifies his investment by putting 50% of his money into each
company, what is the expected return and standard deviation of his portfolio?
State of the
Economy
Probability of the
State
Expected Return Sunglasses
Company
Expected Return
Umbrella Company
Sunny
.50
25%
0%
Rainy
.50
0%
25%
A) The expected return for the portfolio is 12.50% and the standard deviation 0.00%.
B) The expected return for the portfolio is 25.00% and the standard deviation 0.00%.
C) The expected return for the portfolio is 12.50% and the standard deviation 12.50%.
D) The expected return for the portfolio is 25.00% and the standard deviation 25.00%.
6) Correlation, a standardized measure of how stocks perform relative to one another in different
states of the economy, has a range from ________.
A) 0.0 to +10.0
B) 0.0 to +1.0
C) -1.0 to +1.0
D) There is no range; correlation is a calculated number that can take on any value.
7) The correlation coefficient, a measurement of the co-movement between two variables, has
what range?
A) From 0.0 to +10.0
B) From 0.0 to +1.0
C) From -1.0 to +10.0
D) From +1.0 to -1.0
8) For purposes of maximum portfolio diversification, which of the following would provide the
greatest diversification?
A) Security A with a correlation coefficient of -0.0
B) Security B with a correlation coefficient of 0.0
C) Security C with a correlation coefficient of -0.50
D) Security D with a correlation coefficient of 0.50
9) The primary benefit of diversification is ________.
A) an increase in expected return
B) an equal reduction in risk and return
C) a reduction in risk
D) Diversification has no real benefit; it is a shell game promoted by investment advisors who
are the only real winners.
10) You wish to diversify your single-security portfolio in a way that will maximize your
reduction in risk. Which of the following securities should you add to your portfolio?
A) Treasury bills that have a correlation coefficient of 0.0 with your current security
B) Alpha Company stock that has a correlation coefficient of -0.25 with your current security
C) Beta Company stock that has a correlation coefficient of 0.50 with your current security
D) Delta Company bonds that have a correlation coefficient of 0.36 with your current security
11) Which of the following securities could NOT have any benefits for diversification with your
investment portfolio?
A) Treasury bills with a correlation coefficient of 0.0 with your portfolio
B) Alpha Company stock that has a correlation coefficient of -0.25 with your portfolio
C) Beta Company stock that has a correlation coefficient of 0.50 with your portfolio
D) All of these choices would reduce risk for your portfolio and therefore show at least some
benefit to diversification.
12) Which of the following statements is FALSE?
A) The maximum benefits to diversification between securities occur when they are perfectly
positively correlated.
B) The maximum benefits to diversification between securities occur when they are perfectly
negatively correlated.
C) There is some benefit to diversification when the correlation between securities is 0.0.
D) There is some benefit to diversification when the correlation between securities is greater than
0.0 but less than 1.0.
13) For most stocks, the correlation coefficient with other stocks is ________.
A) positive
B) negative
C) zero
D) The distribution of correlation coefficients between stocks is uniform from -1.0 to +1.0.
14) The type of risk that can be diversified away is called ________.
A) unsystematic risk
B) systematic risk
C) nondiversifiable risk
D) system-wide risk
15) Unsystematic risk ________.
A) is also known as nondiversifiable risk
B) can be diversified away
C) is system-wide risk
D) is equal to 2 times the systematic risk
16) Assuming that stocks represent most industries, the number of stocks necessary to eliminate
nearly all unsystematic risk varies from ________.
A) 5 to 10
B) 10 to 20
C) 20 to 30
D) 30 to 50
17) ________ is risk that cannot be diversified away.
A) Unsystematic risk
B) Systematic risk
C) Firm-specific risk
D) Diversifiable risk
18) The terms ________ and ________ mean the same thing.
A) nondiversifiable risk; unsystematic risk
B) diversifiable risk; systematic risk
C) diversifiable risk; unsystematic risk
D) total risk; unique risk
19) The truly wonderful thing about diversification is that 100% of risk can be diversified away,
given a large enough portfolio.
20) While the covariance between stocks can take on a negative value, a correlation coefficient
must be positive, or at a minimum, zero.
21) The more positive the degree of correlation between two assets, the greater the risk reduction
when the assets are combined.
22) Optimal risk reduction takes place when combining assets whose correlation coefficient is
0.0.
23) When considering expected returns, the states of the world must sum to 1 (or 100%).
24) Define diversification. What are the benefits to diversification? Will diversification always
lead to greater expected portfolio returns?
