Deck 5: The Mathematics of Diversification

Question 1

The work of Harry Markowitz is based on the search for

A) efficient portfolios
B) undervalued securities
C) the highest long-term growth rates
D) minimum risk portfolios

Answer 1

efficient portfolios

Question 2

Securities A and B have expected returns of 12% and 15%, respectively. If you put 30% of your money in Security A and the remainder in B, what is the portfolio expected return?

A) 13.4%
B) 14.1%
C) 14.6%
D) 15.3%

Answer 2

14.1%

Question 3

Securities A and B have expected returns of 12% and 15%, respectively. If you put 40% of your money in Security A and the remainder in B, what is the portfolio expected return?

A) 13.4%
B) 13.8%
C) 14.6%
D) 15.3%

Answer 3

13.8%

Question 4

The variance of a two-security portfolio decreases as the return correlation of the two securities

A) increases
B) decreases
C) changes in either direction
D) cannot be determined

Question 5

A security has a return variance of 25%. The standard deviation of returns is

A) 5%
B) 15%
C) 25%
D) 50%

Question 6

A security has a return variance of 16%. The standard deviation of returns is

A) 4%
B) 16%
C) 40%
D) 50%

Question 7

Covariance is the product of two securities'

A) expected deviations from their means
B) standard deviations
C) betas
D) standard deviations divided by their correlation

Question 8

The covariance of a random variable with itself is

A) its correlation with itself
B) its standard deviation
C) its variance
D) equal to 1.0

Question 9

Covariance is _____ correlation is ______.

A) positive, positive or negative
B) negative, positive or negative
C) positive or negative, positive or zero
D) positive or negative, positive or negative

Question 10

For a six-security portfolio, it is necessary to calculate ___ covariances plus ___ variances.

A) 36, 6
B) 30, 6
C) 15, 6
D) 30, 12

Question 11

COV (A,B) = .335. What is COV (B,A)?

A) - 0.335
B) 0.335
C) (0.335 × 0.335)
D) Cannot be determined

Question 12

One of the first proponents of the single index model was

A) William Sharpe
B) Robert Merton
C) Eugene Fama
D) Merton Miller

Question 13

Without knowing beta, determining portfolio variance with a sixty-security portfolio requires ___ statistics per security.

A) 1
B) 60
C) 3600/2
D) 3600

Question 14

Securities A, B, and C have betas of 1.2, 1.3, and 1.7, respectively. What is the beta of an equally weighted portfolio of all three?

A) 1.15
B) 1.40
C) 1.55
D) 1.60

Question 15

Securities A, B, and C have betas of 1.2, 1.3, and 1.7, respectively. What is the beta of a portfolio composed of 1/2 A and 1/4 each of B and C?

A) 1.15
B) 1.35
C) 1.55
D) 1.60

Question 16

A diversified portfolio has a beta of 1.2; the market variance is 0.25. What is the diversified portfolio's variance?

A) 0.33
B) 0.36
C) 0.41
D) 0.44

Question 17

Security A has a beta of 1.2; security B has a beta of 0.8. If the market variance is 0.30, what is COV (A,B)?

A) .255
B) .288
C) .314
D) .355

Question 18

As portfolio size increases, the variance of the error term generally

A) increases
B) decreases
C) approaches 1.0
D) becomes erratic

Question 19

The least risk portfolio is called the

A) optimum portfolio
B) efficient portfolio
C) minimum variance portfolio
D) market portfolio

Question 20

Industry effects are associated with

A) the single index model
B) the multi-index model
C) the Markowitz model
D) the covariance matrix

Question 21

COV (A,B) is equal to

A) the product of their standard deviations and their correlation
B) the product of their variances and their correlation
C) the product of their standard deviations and their covariances
D) the product of their variances and their covariances

Question 22

The covariance between a constant and a random variable is

A) zero
B) 1.0
C) their correlation
D) the product of their betas

Question 23

The covariance between a security's returns and those of the market index is 0.03. If the security beta is 1.15, what is the market variance?

A) 0.005
B) 0.010
C) 0.021
D) 0.026

Question 24

COV(A,B) = 0.50; the variance of the market is 0.25, and the beta of Security A is 1.00. What is the beta of security B?

A) 1.00
B) 1.25
C) 1.50
D) 2.00

Question 25

There are 1,700 stocks in the Value Line index. How many covariances would have to be calculated in order to use the Markowitz full covariance model?

A) 1,700
B) 5,650
C) 12,350
D) 1,444,150

Question 26

There are 1,700 stocks in the Value Line index. How many betas would have to be calculated in order to find the portfolio variance?

A) 1,700
B) 5,650
C) 12,350
D) 1,444,150

Question 27

Knowing beta, determining the portfolio with a sixty-security fully diversified portfolio requires ______ statistic(s) per security.

A) 1
B) 60
C) 3600/2
D) 3600

Question 28

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the expected return for a portfolio with 80% invested in Stock A and 20% invested in Stock B?

A) 17%
B) 19%
C) 21%
D) 23%

Question 29

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the standard deviation for a portfolio with 80% invested in Stock A and 20% invested in Stock B?

A) 15.8%
B) 18.4%
C) 22.0%
D) 28.0%

Question 30

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the beta for a portfolio with 80% invested in Stock A and 20% invested in Stock B?

A) 0.57
B) 0.77
C) 0.97
D) 1.17

Question 31

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the covariance between Stock A and Stock B?

A) 0.015
B) 0.025
C) 0.035
D) 0.045

Question 32

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the percent invested in Stock A to yield the minimum standard deviation portfolio containing Stock A and Stock B?

A) 25%
B) 50%
C) 75%
D) 90%

Question 33

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the expected return for a portfolio with 50% invested in Stock A and 50% invested in Stock B?

A) 18%
B) 19%
C) 20%
D) 21%

Question 34

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the standard deviation for a portfolio with 50% invested in Stock A and 50% invested in Stock B?

A) 15%
B) 20%
C) 23%
D) 25%

Question 35

Suppose Stock A has an expected return of 15%, a standard deviation of 20%, and a Beta of 0.4 while Stock B has an expected return of 25%, a standard deviation of 30% and a beta of 1.25, and the correlation between the two stocks is 0.25. What is the beta for a portfolio with 50% invested in Stock A and 50% invested in Stock B?

A) 0.425
B) 0.625
C) 0.825
D) 1.125

Question 36

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the expected return for a portfolio with 70% invested in Stock M and 30% invested in Stock N?

A) 11%
B) 13%
C) 15%
D) 17%

Question 37

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the standard deviation for a portfolio with 70% invested in Stock M and 30% invested in Stock N?

A) 12.5%
B) 13.6%
C) 15.7%
D) 18.0%

Question 38

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the covariance between Stock M and Stock N?

A) 0.01052
B) 0.01875
C) 0.03425
D) 0.04775

Question 39

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the percent invested in Stock M to yield the minimum standard deviation portfolio containing Stock M and Stock N?

A) 34%
B) 55%
C) 73%
D) 92%

Question 40

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the expected return for a portfolio with 80% invested in Stock M and 20% invested in Stock N?

A) 12%
B) 14%
C) 16%
D) 18%

Question 41

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the standard deviation for a portfolio with 80% invested in Stock M and 20% invested in Stock N?

A) 13.2%
B) 15.1%
C) 17.3%
D) 21.5%

Question 42

Suppose Stock M has an expected return of 10%, a standard deviation of 15%, and a Beta of 0.6 while Stock N has an expected return of 20%, a standard deviation of 25% and a beta of 1.04, and the correlation between the two stocks is 0.50. What is the beta for a portfolio with 80% invested in Stock M and 20% invested in Stock N?

A) 0.688
B) 0.738
C) 0.878
D) 0.968

Question 43

The questions relate to the following table of information:


-What is the expected return for a portfolio with 60% invested in X and 40% invested in Y?

A) 14.4%
B) 14.9%
C) 15.6%
D) 16.1%

Question 44

The questions relate to the following table of information:


-What is the standard deviation for a portfolio with 60% invested in X and 40% invested in Y?

A) 32.4%
B) 36.1%
C) 41.2%
D) 45.6%

Question 45

The questions relate to the following table of information:


-What is the beta for a portfolio with 60% invested in X and 40% invested in Y?

A) 1.12
B) 1.22
C) 1.32
D) 1.42

Question 46

The questions relate to the following table of information:


-What is the covariance between Stock X and Stock Y?

A) 0.025
B) 0.033
C) 0.047
D) 0.054

Question 47

The questions relate to the following table of information:


-What is the percent invested in Stock X to yield the minimum variance portfolio with Stock X and Stock Y?

A) 0.21
B) 0.38
C) 0.51
D) 0.69

Question 48

The questions relate to the following table of information:


-What is the expected return for a portfolio with 20% invested in X and 80% invested in Y?

A) 14.9%
B) 15.6%
C) 16.5%
D) 17.2%

Question 49

The questions relate to the following table of information:


-What is the standard deviation for a portfolio with 20% invested in X and 80% invested in Y?

A) 41.2%
B) 45.8%
C) 47.1%
D) 49.6%

Question 50

The questions relate to the following table of information:


-What is the beta for a portfolio with 20% invested in X and 80% invested in Y?

A) 1.14
B) 1.24
C) 1.34
D) 1.44