CHAPTER 6—AN INTRODUCTION TO PORTFOLIO MANAGEMENT
TRUE/FALSE
1. A good portfolio is a collection of individually good assets.
2. Risk is defined as the uncertainty of future outcomes.
3. Prior to the work of Markowitz in the late 1950s and early 1960s, portfolio managers did not have a
well developed, quantitative means of measuring risk.
4. A basic assumption of the Markowitz model is that investors base decisions solely on expected return
and risk.
5. Markowitz assumed that, given an expected return, investors prefer to minimize risk.
6. The correlation coefficient and the covariance are measures of the extent to which two random
variables move together.
7. For a two-stock portfolio containing Stocks i and j, the correlation coefficient of returns (rij) is equal to
the square root of the covariance (covij).
8. If the covariance of two stocks is positive, these stocks tend to move together over time.
9. The expected return and standard deviation of a portfolio of risky assets is equal to the weighted
average of the individual asset’s expected returns and standard deviation.
10. The combination of two assets that are completely negatively correlated provides maximum returns.
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11. Increasing the correlation among assets in a portfolio results in an increase in the standard deviation of
the portfolio.
12. Combining assets that are not perfectly correlated does affect both the expected return of the portfolio
as well as the risk of the portfolio.
13. In a three-asset portfolio the standard deviation of the portfolio is one third of the square root of the
sum of the individual standard deviations.
14. As the number of risky assets in a portfolio increases, the total risk of the portfolio decreases.
15. Assuming that everyone agrees on the efficient frontier (given a set of costs), there would be
consensus that the optimal portfolio on the frontier would be where the ratio of return per unit of risk
was greatest.
16. An investor is risk neutral if she chooses the asset with lower risk given a choice of several assets with
equal returns.
17. A portfolio is efficient if no other asset or portfolios offer higher expected return with the same (or
lower) risk or lower risk with the same (or higher) expected return.
18. A measure that only considers deviations above the mean is semi-variance.
MULTIPLE CHOICE
1. When individuals evaluate their portfolios they should evaluate
a.
All the Canadian and non-Canadian. stocks.
b.
All marketable securities.
c.
All marketable securities and other liquid assets.
d.
All assets.
e.
All assets and liabilities.
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2. The probability of an adverse outcome is a definition of
a.
Statistics.
b.
Variance.
c.
Random.
d.
Risk.
e.
Semi-variance above the mean.
3. The Markowitz model is based on several assumptions regarding investor behaviour. Which of the
following is not such any assumption?
a.
Investors consider each investment alternative as being represented by a probability
distribution of expected returns over some holding period.
b.
Investors maximize one-period expected utility.
c.
Investors estimate the risk of the portfolio on the basis of the variability of expected
returns.
d.
Investors base decisions solely on expected return and risk.
e.
None of the above (that is, all are assumptions of the Markowitz model)
4. Markowitz believes that any asset or portfolio of assets can be described by ____ parameter(s).
a.
One
b.
Two
c.
Three
d.
Four
e.
Five
5. Semi-variance, when applied to portfolio theory, is concerned with
a.
The square root of deviations from the mean.
b.
All deviations below the mean.
c.
All deviations above the mean.
d.
All deviations.
e.
The summation of the squared deviations from the mean.
6. The purpose of calculating the covariance between two stocks is to provide a(n) ____ measure of their
movement together.
a.
Absolute
b.
Relative
c.
Indexed
d.
Loglinear
e.
Squared
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7. In a two-stock portfolio, if the correlation coefficient between two stocks were to decrease over time
everything else remaining constant the portfolio’s risk would
a.
Decrease.
b.
Remain constant.
c.
Increase.
d.
Fluctuate positively and negatively.
e.
Be a negative value.
8. Which of the following statements about the correlation coefficient is false?
a.
The values range between −1 to +1.
b.
A value of +1 implies that the returns for the two stocks move together in a completely
linear manner.
c.
A value of −1 implies that the returns move in a completely opposite direction.
d.
A value of zero means that the returns are independent.
e.
None of the above (that is, all statements are true)
9. You are given a two-asset portfolio with a fixed correlation coefficient. If the weights of the two assets
are varied the expected portfolio return would be ____ and the expected portfolio standard deviation
would be ____.
a.
Nonlinear, elliptical
b.
Nonlinear, circular
c.
Linear, elliptical
d.
Linear, circular
e.
Circular, elliptical
10. In a given a portfolio of stocks, what is the envelope curve containing the set of best possible
combinations known as?
a.
Efficient portfolio.
b.
Utility curve.
c.
Efficient frontier.
d.
Last frontier.
e.
Capital asset pricing model.
11. What will happen to the return, if equal risk is added moving along the envelope curve containing the
best possible combinations?
a.
Decrease at an increasing rate.
b.
Decrease at a decreasing rate.
c.
Increase at an increasing rate.
d.
Increase at a decreasing rate.
e.
Remain constant.
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12. When is a portfolio considered to be efficient?
a.
When no other portfolio offers higher expected returns with the same risk.
b.
When no other portfolio offers lower risk with the same expected return.
c.
When there is no portfolio with a higher return.
d.
Choices a and b.
e.
All of the above.
13. The optimal portfolio is identified at the point of tangency between the efficient frontier and the
a.
highest possible utility curve.
b.
lowest possible utility curve.
c.
middle range utility curve.
d.
steepest utility curve.
e.
flattest utility curve.
14. An individual investor’s utility curves specify the tradeoffs he or she is willing to make between
a.
high risk and low risk assets.
b.
high return and low return assets.
c.
covariance and correlation.
d.
return and risk.
e.
efficient portfolios.
15. As the correlation coefficient between two assets decreases, the shape of the efficient frontier
a.
approaches a horizontal straight line.
b.
bends out.
c.
bends in.
d.
approaches a vertical straight line.
e.
none of the above.
16. A portfolio manager is considering adding another security to his portfolio. The correlations of the five
alternatives available are listed below. Which security would enable the highest level of risk
diversification?
a.
0.0
b.
0.25
c.
−0.25
d.
−0.75
e.
1.0
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17. A positive covariance between two variables indicates that
a.
the two variables move in different directions.
b.
the two variables move in the same direction.
c.
the two variables are low risk.
d.
the two variables are high risk.
e.
the two variables are risk free.
18. A positive relationship between expected return and expected risk is consistent with
a.
investors being risk seekers.
b.
investors being risk avoiders.
c.
investors being risk averse.
d.
all of the above.
e.
none of the above.
19. The slope of the efficient frontier is calculated as follows
a.
E(Rportfolio)/E(portfolio)
b.
E(portfolio)/E(Rportfolio)
c.
E(Rportfolio)/E(portfolio)
d.
E(portfolio)/E(Rportfolio)
e.
None of the above
20. The slope of the utility curves for a strongly risk-averse investor, relative to the slope of the utility
curves for a less risk-averse investor, will
a.
Be steeper.
b.
Be flatter.
c.
Be vertical.
d.
Be horizontal.
e.
None of the above.
21. All of the following are assumptions of the Markowitz model except
a.
Risk is measured based on the variability of returns.
b.
Investors maximize one-period expected utility.
c.
Investors’ utility curves demonstrate properties of diminishing marginal utility of wealth.
d.
Investors base decisions solely on expected return and time.
e.
All of the above.
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22. The most import criteria when adding new investments to a portfolio is the
a.
Expected return of the new investment.
b.
Standard deviation of the new investment.
c.
Correlation of the new investment with the portfolio.
d.
Choices a and b.
e.
All of the above are equally important.
23. A portfolio of two securities that are perfectly positively correlated has
a.
A standard deviation that is the weighted average of the individual securities standard
deviations.
b.
An expected return that is the weighted average of the individual securities expected
returns.
c.
No diversification benefit over holding either of the securities independently.
d.
Choices b and c.
e.
All of the above.
24. Between 1999 and 2009, the standard deviation of the returns for the S&P/TSX and the DJIA indexes
were 0.18 and 0.16, respectively, and the covariance of these index returns was 0.003. What was the
correlation coefficient between the two market indicators?
a.
9.6
b.
0.0187
c.
0.1042
d.
0.0166
e.
0.343
25. Between 2000 and 2010, the standard deviation of the returns for the TSX Venture and the S&P/TSX
indexes were 0.27 and 0.14, respectively, and the covariance of these index returns was 0.03. What
was the correlation coefficient between the two market indicators?
a.
1.26
b.
0.7937
c.
0.2142
d.
0.1111
e.
0.44
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26. Between 1989 and 1999, the standard deviation of the returns for the S&P/TSX and the DJIA indexes
were 0.19 and 0.06, respectively, and the covariance of these index returns was 0.0014. What was the
correlation coefficient between the two market indicators?
a.
8.1428
b.
0.0233
c.
0.0073
d.
0.2514
e.
0.1228
27. Between 1985 and 1995, the standard deviation of the returns for the S&P/TSX and the TSX Venture
indexes were 0.06 and 0.07, respectively, and the covariance of these index returns was 0.0008. What
was the correlation coefficient between the two market indicators?
a.
.1525
b.
.1388
c.
.1458
d.
.1622
e.
.1064
28. Between 1998 and 2008, the standard deviation of the returns for the NYSE and the DJIA indexes
were 0.10 and 0.09, respectively, and the covariance of these index returns was 0.0009. What was the
correlation coefficient between the two market indicators?
a.
.1000
b.
.1100
c.
.1258
d.
.1322
e.
.1164
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29. Between 1989and 2009, the standard deviation of the returns for the S&P/TSX and the DJIA indexes
were 0.08 and 0.10, respectively, and the covariance of these index returns was 0.0007. What was the
correlation coefficient between the two market indicators?
a.
.0906
b.
.0985
c.
.0796
d.
.0875
e.
.0654
30. What is the expected return of the three-stock portfolio described below?
Common Stock
Market Value
Expected Return
Ando Inc.
95,000
12.0%
Bee Co.
32,000
8.75%
Cool Inc.
65,000
17.7%
a.
18.45%
b.
12.82%
c.
13.38%
d.
15.27%
e.
16.67%
31. What is the expected return of the three-stock portfolio described below?
Common Stock
Market Value
Expected Return
Xerox
125,000
8%
Yelcon
250,000
25%
Zwiebal
175,000
16%
a.
18.27%
b.
14.33%
c.
16.33%
d.
12.72%
e.
16.45%
32. What is the expected return of the three-stock portfolio described below?
Common Stock
Market Value
Expected Return
Alko Inc.
25,000
38%
Belmont Co.
100,000
10%
Cardo Inc.
75,000
16%
a.
21.33%
b.
12.50%
c.
32.00%
d.
15.75%
e.
16.80%
33. What is the expected return of the three-stock portfolio described below?
Common Stock
Market Value
Expected Return
Delton Inc.
50,000
10%
Efley Co.
40,000
11%
Grippon Inc.
60,000
16%
a.
14.89%
b.
16.22%
c.
12.66%
d.
13.85%
e.
16.99%
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34. What is the expected return of the three-stock portfolio described below?
Common Stock
Market Value
Expected Return
Lupko Inc.
50,000
13%
Mackey Co.
25,000
9%
Nippon Inc.
75,000
14%
a.
12.04%
b.
12.83%
c.
13.07%
d.
15.89%
e.
17.91%
Exhibit 6-1
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Asset (A)
Asset (B)
E(RA) = 10%
E(RB) = 15%
(A) = 8%
(B) = 9.5%
WA = 0.25
WB = 0.75
CovA,B = 0.006
35. Refer to Exhibit 6-1. What is the expected return of a portfolio of two risky assets if the expected
return E(Ri), standard deviation (i), covariance (COVi,j), and asset weight (Wi) are as shown above?
a.
8.79%
b.
12.5%
c.
13.75%
d.
7.72%
e.
12%
= WAE(RA) + WBE(RB)
= (0.25)(10) + (0.75)(15) = 13.75%
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36. Refer to Exhibit 6-1. What is the standard deviation of this portfolio?
a.
8.79%
b.
13.75%
c.
12.5%
d.
7.72%
e.
5.64%
Exhibit 6-2
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Asset (A)
Asset (B)
E(RA) = 25%
E(RB) = 15%
(A) = 18%
(B) = 11%
WA = 0.75
WB = 0.25
COVA,B = −0.0009
37. Refer to Exhibit 6-2. What is the expected return of a portfolio of two risky assets if the expected
return E(Ri), standard deviation (i), covariance (COVi,j), and asset weight (Wi) are as shown above?
a.
18.64%
b.
20.0%
c.
22.5%
d.
13.65%
e.
11%
38. Refer to Exhibit 6-2. What is the standard deviation of this portfolio?
a.
5.45%
b.
18.64%
c.
20.0%
d.
22.5%
e.
13.65%
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Exhibit 6-3
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Asset (A)
Asset (B)
E(RA) = 9%
E(RB) = 11%
(A) = 4%
(B) = 6%
WA = 0.4
WB = 0.6
COVA,B = 0.0011
39. Refer to Exhibit 6-3. What is the expected return of a portfolio of two risky assets if the expected
return E(Ri), standard deviation (i), covariance (COVi,j), and asset weight (Wi) are as shown above?
a.
8.95%
b.
9.30%
c.
9.95%
d.
10.20%
e.
10.70%
40. Refer to Exhibit 6-3. What is the standard deviation of this portfolio?
a.
3.68%
b.
4.56%
c.
4.99%
d.
5.16%
e.
6.02%
Exhibit 6-4
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Asset (A)
Asset (B)
E(RA) = 10%
E(RB) = 8%
(A) = 6%
(B) = 5%
WA = 0.3
WB = 0.7
COVA,B = 0.0008