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Homework answers / question archive / York University ADMD 4501 CHAPTER 7 AN INTRODUCTION TO PORTFOLIO MANAGEMENT TRUE/FALSE QUESTIONS 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 1950’s and early 1960’s, 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.
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.
(c) 1 Between 1990 and 2000, the standard deviation of the returns for the NIKKEI 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
(b) 2 Between 1994 and 2004, the standard deviation of the returns for the S&P 500 and the NYSE 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
(e) 3 Between 1980 and 1990, the standard deviation of the returns for the NIKKEI 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
(c) 4 Between 1975 and 1985, the standard deviation of the returns for the NYSE and the S&P 500 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
(a) 5 Between 1986 and 1996, 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
(d) 6 Between 1980 and 2000, the standard deviation of the returns for the NIKKEI 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
(c) 7 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% |
||
(a) 8 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%
(d) 9 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%
(c) 10 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% |
|
|
|
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% |
||
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
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
a) 8.79%
b) 12.5%
c) 13.75%
d) 7.72%
e) 12%
(a) 13 What is the standard deviation of this portfolio? a) 8.79%
b) 13.75%
c) 12.5%
d) 7.72%
e) 5.64%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 25% E(RB) = 15%
(?A) = 18% (?B) = 11%
WA = 0.75 WB = 0.25
COVA,B = -0.0009
(c) 14 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%
(e) 15 What is the standard deviation of this portfolio? a) 5.45%
b) 18.64%
c) 20.0%
d) 22.5%
e) 13.65%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 9% E(RB) = 11%
(?A) = 4% (?B) = 6%
WA = 0.4 WB = 0.6
COVA,B = 0.0011
(d) 16 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%
(b) 17 What is the standard deviation of this portfolio? a) 3.68%
b) 4.56%
c) 4.99%
d) 5.16%
e) 6.02%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 10% E(RB) = 8%
(?A) = 6% (?B) = 5%
WA = 0.3 WB = 0.7
COVA,B = 0.0008
(a) 18 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) 8.6%
b) 8.1%
c) 9.3%
d) 10.2%
e) 11.6%
(e) 19 What is the standard deviation of this portfolio? a) 5.02%
b) 3.88%
c) 6.21%
d) 4.04%
e) 4.34%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 8% E(RB) = 15%
(?A) = 7% (?B) = 10%
WA = 0.4 WB = 0.6
COVA,B = 0.0006
(b) 20 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) 8.0%
b) 12.2%
c) 7.4%
d) 9.1%
e) 11.6%
(d) 21 What is the standard deviation of this portfolio? a) 3.89%
b) 4.61%
c) 5.02%
d) 6.83%
e) 6.09%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 16% E(RB) = 10%
(?A) = 9% (?B) = 7%
WA = 0.5 WB = 0.5
COVA,B = 0.0009
(c) 22 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) 10.6 %
b) 10.2%
c) 13.0%
d) 11.9%
e) 14.0%
(a) 23 What is the standard deviation of this portfolio? a) 6.08%
b) 5.89%
c) 7.06%
d) 6.54%
e) 7.26%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 7% E(RB) = 9%
(?A) = 6% (?B) = 5%
WA = 0.6 WB = 0.4
COVA,B = 0.0014
(d) 24 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) 5.8%
b) 6.1%
c) 6.9%
d) 7.8%
e) 8.9%
(a) 25 What is the standard deviation of this portfolio? a) 4.87%
b) 3.62%
c) 4.13%
d) 5.76%
e) 6.02%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 10% E(RB) = 14%
(?A) = 7% (?B) = 8%
WA = 0.7 WB = 0.3
COVA,B = 0.0013
(e) 26 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) 6.4%
b) 9.1%
c) 10.2%
d) 10.8%
e) 11.2%
(b) 27 What is the standard deviation of this portfolio? a) 4.51%
b) 5.94%
c) 6.75%
d) 7.09%
e) 8.62%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 18% E(RB) = 13%
(?A) = 7% (?B) = 6%
WA = 0.3 WB = 0.7
COVA,B = 0.0011
(d) 28 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) 10.10%
b) 11.60%
c) 13.88%
d) 14.50%
e) 15.37%
(a) 29 What is the standard deviation of this portfolio? a) 5.16%
b) 5.89%
c) 6.11%
d) 6.57%
e) 7.02%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset (A) Asset (B)
E(RA) = 16% E(RB) = 14%
(?A) = 3% (?B) = 8%
WA = 0.5 WB = 0.5
COVA,B = 0.0014
(e) 30 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) 11%
b) 12%
c) 13%
d) 14%
e) 15%
b) 4.88%
c) 5.24%
d) 5.98%
e) 6.52%
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset 1 Asset 2
E(R1) = 0.28 E(R2) = 0.12
E(?1) = 0.15 E(?2) = 0.11
W1 = 0.42 W2 = 0.58
r1,2 = 0.7
b) 0.1367
c) 0.1169
d) 0.1872
e) 0.20
(c) 33 Calculate the expected standard deviation of the two stock portfolio. a) 0.1367
b) 0.1872
c) 0.1169
d) 0.20
e) 0.3950
USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS
Asset 1 Asset 2
E(R1) = .12 E(R2) = .16
E(?1) = .04 E(?2) = .06
(a) 34 Calculate the expected return and expected standard deviation of a two stock portfolio when r1,2 = - .60 and w1 = .75.
a) .13 and .0024
b) .13 and .0455
c) .12 and .0585
d) .12 and .5585
e) .13 and .6758
(d) 35 Calculate the expected returns and expected standard deviations of a two stock portfolio when r1,2 = .80 and w1 = .60.
a) .144 and .0002
b) .144 and .0018
c) .136 and .0045
d) .136 and .0455
e) .136 and .4554
(d) 36 Consider two securities, A and B. Security A and B have a correlation coefficient
of 0.65. Security A has standard deviation of 12, and security B has standard deviation of 25. Calculate the covariance between these two securities.
a) 300
b) 461.54
c) 261.54
d) 195
e) 200
(a) 37 Calculate the expected return for a three asset portfolio with the following
Asset Exp. Ret. Std. Dev
|
|
Weight |
|
||
|
A |
0.0675 |
|
0.12 |
0.25 |
|
B |
0.1235 |
|
0.1675 |
0.35 |
|
C |
0.1425 |
|
0.1835 |
0.40 |
a) 11.71%
b) 11.12%
c) 15.70%
d) 14.25%
e) 6.75%.
(c) 38 Given the following weights and expected security returns, calculate the expected
return for the portfolio.
Weight Expected Return
.20 .06
.25 .08
.30 .10
.25 .12
a) .085
b) .090
c) .092
d) .097
e) None of the above
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