Deck 7: Optimal Risky Portfolios

Question 1

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.

Answer 1

B
Explanation: 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.

Question 2

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)is a weighted average of the securities' returns and the weighted sum of the securities' variances and covariances.
E)None of the options

Answer 2

A
Explanation: The expected return of a portfolio of risky securities is a weighted average of the securities' returns.

Question 3

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.

Answer 3

D
Explanation: 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.

Question 4

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 options

Question 5

Unique risk is also referred to as

A)systematic risk, diversifiable risk.
B)systematic risk, market risk.
C)diversifiable risk, market risk.
D)diversifiable risk, firm-specific risk.
E)None of the options

Question 6

Which of the following statement(s) is(are) false regarding the variance of a portfolio of two risky securities
I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.

A)I only
B)II only
C)III only
D)I and II
E)I and III

Question 7

Nonsystematic risk is also referred to as

A)market risk, diversifiable risk.
B)firm-specific risk, market risk.
C)diversifiable risk, market risk.
D)diversifiable risk, unique risk.

Question 8

Systematic risk is also referred to as

A)market risk, nondiversifiable risk.
B)market risk, diversifiable risk.
C)unique risk, nondiversifiable risk.
D)unique risk, diversifiable risk.
E)None of the options

Question 9

Nondiversifiable 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.

Question 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.

Question 11

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)securities' returns are positively correlated and high.

Question 12

Which of the following statement(s) is(are) true regarding the selection of a portfolio from those that lie on the capital allocation line
I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors.
II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors.
III) Investors choose the portfolio that maximizes their expected utility.

A)I only
B)II only
C)III only
D)I and III
E)II and III

Question 13

The risk that can be diversified away is

A)firm specific risk.
B)beta.
C)systematic risk.
D)market risk.

Question 14

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.

Question 15

Which of the following statement(s) is(are) true regarding the variance of a portfolio of two risky securities
I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.

A)I only
B)II only
C)III only
D)I and II
E)I and III

Question 16

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.

Question 17

The risk that cannot be diversified away is

A)firm-specific risk.
B)unique.
C)nonsystematic risk.
D)market risk.

Question 18

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.

Question 19

The standard deviation of a portfolio of risky securities is

A)the square root of the weighted sum of the securities' variances.
B)the square root of the sum of the securities' variances.
C)the square root of the weighted sum of the securities' variances and covariances.
D)the square root of the sum of the securities' covariances.

Question 20

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 that includes the portfolios with the lowest standard deviation.
D)the set of portfolios that have zero standard deviation.

Question 21

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.

Question 22

Consider the following probability distribution for stocks A and B: 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%

Question 23

Which of the following statement(s) is(are) false regarding the selection of a portfolio from those that lie on the capital allocation line
I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors.
II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors.
III) Investors choose the portfolio that maximizes their expected utility.

A)I only
B)II only
C)III only
D)I and II
E)I and III

Question 24

Which statement about portfolio diversification is correct

A)Proper diversification can 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 statements is correct.

Question 25

Consider the following probability distribution for stocks A and B: The coefficient of correlation between A and B is

A)0.46.
B)0.60.
C)0.58.
D)1.20.

Question 26

Consider the following probability distribution for stocks A and B: 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%

Question 27

Consider the following probability distribution for stocks A and B: 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)0.77; 0.23
E)0.23; 0.77

Question 28

Given an optimal risky portfolio with expected return of 6% 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)0.13
E)0.36

Question 29

Consider the following probability distribution for stocks A and B: 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.

Question 30

The measure of risk in a Markowitz efficient frontier is:

A)specific risk.
B)standard deviation of returns.
C)reinvestment risk.
D)beta.

Question 31

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%. 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

Question 32

Consider the following probability distribution for stocks A and B: 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 options

Question 33

A statistic that measures how the returns of two risky assets move together is:

A)variance.
B)standard deviation.
C)covariance.
D)correlation.
E)covariance and correlation.

Question 34

Consider two perfectly negatively correlated risky securities A and

A)8.5%
B)9.0%
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%.The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
C)8.9%
D)9.9%

Question 35

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.

Question 36

Consider the following probability distribution for stocks A and B: The expected rate of return and standard deviation of the global minimum variance portfolio, G, are __________ and __________, respectively.

A)10.07%; 1.05%
B)8.97%; 2.03%
C)10.07%; 3.01%
D)8.97%; 1.05%

Question 37

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.
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)borrow some money at the risk-free rate and invest in the optimal risky portfolio and invest only in risky securities

Question 38

Consider the following probability distribution for stocks A and B: The variances of stocks A and B are _____ and _____, respectively.

A)1.5%; 1.9%
B)2.2%; 1.2%
C)3.2%; 2.0%
D)1.5%; 1.1%

Question 39

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.

Question 40

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.

Question 41

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.

Question 42

Consider the following probability distribution for stocks A and B: The standard deviations of stocks A and B are _____ and _____, respectively.

A)1.56%; 1.99%
B)2.45%; 1.66%
C)3.22%; 2.01%
D)1.54%; 1.11%

Question 43

Consider the following probability distribution for stocks A and B: 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%

Question 44

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)any negative number.

Question 45

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 options.

Question 46

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

Question 47

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.

Question 48

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 options

Question 49

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.

Question 50

Security X has expected return of 12% and standard deviation of 18%.Security Y has expected return of 15% and standard deviation of 26%.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)0.033
E)0.054

Question 51

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.

Question 52

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.

Question 53

Given an optimal risky portfolio with expected return of 20% and standard deviation of 24% and a risk free rate of 7%, what is the slope of the best feasible CAL

A)0.64
B)0.14
C)0.62
D)0.33
E)0.54

Question 54

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.

Question 55

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.

Question 56

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.

Question 57

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.

Question 58

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

Question 59

Given an optimal risky portfolio with expected return of 12% and standard deviation of 26% and a risk free rate of 5%, what is the slope of the best feasible CAL

A)0.64
B)0.27
C)0.08
D)0.33
E)0.36

Question 60

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) The one with the highest reward-to-variability ratio.
II) The one that will maximize his utility.
III) The one with the steepest slope.
IV) The one with the lowest slope.

A)I and III
B)I and IV
C)II and IV
D)I only
E)I, II, and III

Question 61

Consider the following probability distribution for stocks A and B: 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%

Question 62

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.

Question 63

Consider the following probability distribution for stocks C and D: 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%; 8.70%
B)9.945%; 11.12%
C)8.225%; 8.70%
D)10.275%; 11.12%

Question 64

Security X has expected return of 7% and standard deviation of 14%.Security Y has expected return of 11% and standard deviation of 22%.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)-0.0139
E)-0.1512

Question 65

Consider two perfectly negatively correlated risky securities A and

A)9.5%
B)10.4%
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%.The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
C)10.9%
D)9.9%

Question 66

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

Question 67

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%. 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

Question 68

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%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

A)9.5%
B)11.4%
C)10.9%
D)9.9%
E)None of the options

Question 69

State Markowitz's mean-variance criterion.Give some numerical examples of how the criterion would be applied.

Question 70

Draw a graph of a typical efficient frontier.Explain why the efficient frontier is shaped the way it is.

Question 71

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.

Question 72

Consider the following probability distribution for stocks C and D: The coefficient of correlation between C and D is

A)0.67.
B)0.50.
C)-0.50.
D)-0.67.
E)None of the options

Question 73

Consider the following probability distribution for stocks C and D: The standard deviations of stocks C and D are _____ and _____, respectively.

A)7.62%; 11.24%
B)11.24%; 7.62%
C)10.35%; 12.93%
D)12.93%; 10.35%

Question 74

Consider the following probability distribution for stocks C and D: The expected rates of return of stocks C and D are _____ and _____, respectively.

A)4.4%; 9.5%
B)9.5%; 4.4%
C)6.3%; 8.7%
D)8.7%; 6.2%
E)None of the options

Question 75

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

Question 76

Consider the following probability distribution for stocks A and B: The coefficient of correlation between A and B is

A)0.474.
B)0.612.
C)0.590.
D)1.206.

Question 77

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

Question 78

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%. 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)0.46; 0.54
D)0.45; 0.55
E)0.76; 0.24

Question 79

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)-0.0151

Question 80

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