Deck 6: Efficient Diversification

Question 1

Your client,Bo Regard,holds a complete portfolio that consists of a portfolio of risky assets (P)and T-Bills.The information below refers to these assets. $$\begin{array} { l c } \text { E( } \left. \mathrm { R } _ { \mathrm { p } } \right) & 12.00 \% \\\text { Standard Deviation of P } & 7.20 \% \\\text { T-Bill rate } & 3.60 \% \\& \\\text { Proportion of Complete Portfolio in P } & 80 \% \\\text { Proportion of Complete Portfolio in T-Bills } & 20 \% \\& \\\text { Composition of P: } \\\text { Stock A } & 40.00 \% \\\text { Stock B } &25.00 \% \\\text { Stock C } & 35.00 \% \\\text { Total } & 100.00 \% \\\hline \hline\end{array}$$
What is the standard deviation of Bo's complete portfolio?

A) 7.20%
B) 5.40%
C) 6.92%
D) 4.98%
E) 5.76%

Answer 1

5.76%

Question 2

Beta is the measure of

A) firm specific risk.
B) diversifiable risk.
C) market risk.
D) unique risk.
E) none of these.

Answer 2

C

Question 3

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio,P,constructed with 2 risky securities,X and Y.The weights of X and Y in P are 0.60 and 0.40,respectively.X has an expected rate of return of 0.14 and variance of 0.01,and Y has an expected rate of return of 0.10 and a variance of 0.0081.What would be the dollar value of your positions in X,Y,and the T-bills,respectively,if you decide to hold a portfolio that has an expected outcome of $1,200?

A) Cannot be determined
B) $54;$568;$378
C) $568;$54;$378
D) $378;$54;$568
E) $108;$514;$378

Answer 3

B

Question 4

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio,P,constructed with 2 risky securities,X and Y.The weights of X and Y in P are 0.60 and 0.40,respectively.X has an expected rate of return of 0.14 and variance of 0.01,and Y has an expected rate of return of 0.10 and a variance of 0.0081.What would be the dollar values of your positions in X and Y,respectively,if you decide to hold 40% percent of your money in the risky portfolio and 60% in T-bills?

A) $240;$360
B) $360;$240
C) $100;$240
D) $240;$160
E) cannot be determined

Question 5

Given an optimal risky portfolio with expected return of 12% 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) 0.35
E) 0.36

Question 6

The risk that can be diversified away is

A) firm specific risk.
B) beta.
C) systematic risk.
D) market risk.
E) none of these.

Question 7

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 these.

Question 8

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio,P,constructed with 2 risky securities,X and Y.The weights of X and Y in P are 0.60 and 0.40,respectively.X has an expected rate of return of 0.14 and variance of 0.01,and Y has an expected rate of return of 0.10 and a variance of 0.0081.If you want to form a portfolio with an expected rate of return of 0.11,what percentages of your money must you invest in the T-bill and P,respectively?

A) 0.25;0.75
B) 0.19;0.81
C) 0.65;0.35
D) 0.50;0.50
E) cannot be determined

Question 9

Your client,Bo Regard,holds a complete portfolio that consists of a portfolio of risky assets (P)and T-Bills.The information below refers to these assets. $$\begin{array} { l c } \text { E( } \left. \mathrm { R } _ { \mathrm { p } } \right) & 12.00 \% \\\text { Standard Deviation of P } & 7.20 \% \\\text { T-Bill rate } & 3.60 \% \\& \\\text { Proportion of Complete Portfolio in P } & 80 \% \\\text { Proportion of Complete Portfolio in T-Bills } & 20 \% \\& \\\text { Composition of P: } \\\text { Stock A } & 40.00 \% \\\text { Stock B } &25.00 \% \\\text { Stock C } & 35.00 \% \\\text { Total } & 100.00 \% \\\hline \hline\end{array}$$
What are the proportions of Stocks A,B,and C,respectively in Bo's complete portfolio?

A) 40%,25%,35%
B) 8%,5%,7%
C) 32%,20%,28%
D) 16%,10%,14%
E) 20%,12.5%,17.5%

Question 10

When wealth is shifted from the risky portfolio to the risk-free asset,what happens to the relative proportions of the various risky assets within the risky portfolio?

A) They all decrease.
B) Some increase and some decrease.
C) They all increase.
D) They are not changed.
E) The answer depends on the specific circumstances.

Question 11

Your client,Bo Regard,holds a complete portfolio that consists of a portfolio of risky assets (P)and T-Bills.The information below refers to these assets. $$\begin{array} { l c } \text { E( } \left. \mathrm { R } _ { \mathrm { p } } \right) & 12.00 \% \\\text { Standard Deviation of P } & 7.20 \% \\\text { T-Bill rate } & 3.60 \% \\& \\\text { Proportion of Complete Portfolio in P } & 80 \% \\\text { Proportion of Complete Portfolio in T-Bills } & 20 \% \\& \\\text { Composition of P: } \\\text { Stock A } & 40.00 \% \\\text { Stock B } &25.00 \% \\\text { Stock C } & 35.00 \% \\\text { Total } & 100.00 \% \\\hline \hline\end{array}$$
What is the equation of Bo's Capital Allocation Line?

A) E(r_C)= 7.2 + 3.6 * Standard Deviation of C
B) E(r_C)= 3.6 + 1.167 * Standard Deviation of C
C) E(r_C)= 3.6 + 12.0 * Standard Deviation of C
D) E(r_C)= 0.2 + 1.167 * Standard Deviation of C
E) E(r_C)= 3.6 + 0.857 * Standard Deviation of C

Question 12

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 which includes the portfolios with the lowest standard deviation.
D) the set of portfolios that have zero standard deviation.
E) both a and b are true.

Question 13

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) b and c.

Question 14

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio,P,constructed with 2 risky securities,X and Y.The weights of X and Y in P are 0.60 and 0.40,respectively.X has an expected rate of return of 0.14 and variance of 0.01,and Y has an expected rate of return of 0.10 and a variance of 0.0081.If you want to form a portfolio with an expected rate of return of 0.10,what percentages of your money must you invest in the T-bill,X,and Y,respectively if you keep X and Y in the same proportions to each other as in portfolio P?

A) 0.25;0.45;0.30
B) 0.19;0.49;0.32
C) 0.32;0.41;0.27
D) 0.50;0.30;0.20
E) cannot be determined

Question 15

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.
E) none of these.

Question 16

In a top-down analysis of portfolio construction

A) decisions about which executives will manage the portfolio are made first,then capital allocation decisions are made.
B) decisions about asset allocation are made first,then specific securities are chosen.
C) decisions about specific securities are made first,then asset allocation decisions are made.
D) all securities transactions must be approved by upper-level management.
E) an investor's first decision would be about how much to hold in her favorite stock.

Question 17

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.
E) firm-specific risk.

Question 18

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) both securities' returns are positively correlated and securities' returns are high.

Question 19

Your client,Bo Regard,holds a complete portfolio that consists of a portfolio of risky assets (P)and T-Bills.The information below refers to these assets. $$\begin{array} { l c } \text { E( } \left. \mathrm { R } _ { \mathrm { p } } \right) & 12.00 \% \\\text { Standard Deviation of P } & 7.20 \% \\\text { T-Bill rate } & 3.60 \% \\& \\\text { Proportion of Complete Portfolio in P } & 80 \% \\\text { Proportion of Complete Portfolio in T-Bills } & 20 \% \\& \\\text { Composition of P: } \\\text { Stock A } & 40.00 \% \\\text { Stock B } &25.00 \% \\\text { Stock C } & 35.00 \% \\\text { Total } & 100.00 \% \\\hline \hline\end{array}$$
What is the expected return on Bo's complete portfolio?

A) 10.32%
B) 5.28%
C) 9.62%
D) 8.44%
E) 7.58%

Question 20

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) market risk.

Question 21

Which of the following statements is(are)true regarding the variance of a portfolio of two risky securities?

A) The higher the coefficient of correlation between securities,the greater the reduction in the portfolio variance.
B) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
C) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.
D) a and b.
E) a and c.

Question 22

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } \text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \\1 & 0.10 & 10 \% & 8 \% \\2 & 0.20 & 13 \% & 7 \% \\3 & 0.20 & 12 \% & 6 \% \\4 & 0.30 & 14 \% & 9 \% \\5&0.20 & 15 \% & 8 \%\end{array}$$
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) 0.76;0.24
E) 0.23;0.77

Question 23

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.
E) none of these.

Question 24

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 these.

Question 25

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.
E) none of these.

Question 26

Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz? $$\begin{array}{l}\begin{array} { r r r } \text { Portfolio }&\text{Expected Return }& \text { Standard Deviation } \\\hline\mathrm { W } & 9 \% & 21 \% \\\mathrm { X } & 5 \% & 7 \% \\\mathrm { Y } & 15 \% & 36 \% \\\mathrm { Z } & 12 \% & 15 \%\end{array}\end{array}$$

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 27

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } \text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \\1 & 0.10 & 10 \% & 8 \% \\2 & 0.20 & 13 \% & 7 \% \\3 & 0.20 & 12 \% & 6 \% \\4 & 0.30 & 14 \% & 9 \% \\5&0.20 & 15 \% & 8 \%\end{array}$$
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%
E) none of these

Question 28

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 and invest the remainder in the optimal risky portfolio.
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) b and c

Question 29

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } \text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \\1 & 0.10 & 10 \% & 8 \% \\2 & 0.20 & 13 \% & 7 \% \\3 & 0.20 & 12 \% & 6 \% \\4 & 0.30 & 14 \% & 9 \% \\5&0.20 & 15 \% & 8 \%\end{array}$$
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 these

Question 30

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } \text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \\1 & 0.10 & 10 \% & 8 \% \\2 & 0.20 & 13 \% & 7 \% \\3 & 0.20 & 12 \% & 6 \% \\4 & 0.30 & 14 \% & 9 \% \\5&0.20 & 15 \% & 8 \%\end{array}$$
The coefficient of correlation between A and B is

A) 0.47.
B) 0.60.
C) 0.58
D) 1.20.
E) none of these.

Question 31

Which of the following statement(s)is(are)true regarding the selection of a portfolio from those that lie on the Capital Allocation Line?

A) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors.
B) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors.
C) Investors choose the portfolio that maximizes their expected utility.
D) a and c.
E) b and c.

Question 32

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } \text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \\1 & 0.10 & 10 \% & 8 \% \\2 & 0.20 & 13 \% & 7 \% \\3 & 0.20 & 12 \% & 6 \% \\4 & 0.30 & 14 \% & 9 \% \\5&0.20 & 15 \% & 8 \%\end{array}$$
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%
E) none of these

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) c and d.

Question 34

Consider the following probability distribution for stocks A and B: $$\begin{array} { c c c c } \text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \\1 & 0.10 & 10 \% & 8 \% \\2 & 0.20 & 13 \% & 7 \% \\3 & 0.20 & 12 \% & 6 \% \\4 & 0.30 & 14 \% & 9 \% \\5&0.20 & 15 \% & 8 \%\end{array}$$
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%
E) none of these

Question 35

Which statement about portfolio diversification is correct?

A) Proper diversification can reduce or 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 these statements are correct.

Question 36

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 these.

Question 37

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.
E) none of these.

Question 38

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 39

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.
E) none of these.

Question 40

The measure of risk in a Markowitz efficient frontier is:

A) specific risk.
B) standard deviation of returns.
C) reinvestment risk.
D) beta.
E) none of these.

Question 41

Discuss the characteristics of indifference curves,and the theoretical value of these curves in the portfolio building process

Question 42

You are evaluating two investment alternatives.One is a passive market portfolio with an expected return of 10% and a standard deviation of 16%.The other is a fund that is actively managed by your broker.This fund has an expected return of 15% and a standard deviation of 20%.The risk-free rate is currently 7%.Answer the questions below based on this information.
a.What is the slope of the Capital Market Line?
b.What is the slope of the Capital Allocation Line offered by your broker's fund?
c.Draw the CML and the CAL on one graph.
d.What is the maximum fee you broker could charge and still leave you as well off as if you had invested in the passive market fund? (Assume that the fee would be a percentage of the investment in the broker's fund,and would be deducted at the end of the year. )
e.How would it affect the graph if the broker were to charge the full amount of the fee?

Question 43

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)with the highest reward-to-variability ratio.
II)that will maximize his utility.
III)with the steepest slope.
IV)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 44

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 45

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 46

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 47

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 48

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 49

The optimal proportion of the risky asset in the complete portfolio is given by the equation y* = [E(r_P)- r_f]/(.01A*Variance of P).For each of the variables on the right side of the equation,discuss the impact the variable's effect on y* and why the nature of the relationship makes sense intuitively.Assume the investor is risk averse.

Question 50

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 51

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 52

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 53

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 54

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.
E) None of these are true.

Question 55

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 56

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) negative

Question 57

Security X has expected return of 12% and standard deviation of 20%.Security Y has expected return of 15% and standard deviation of 27%.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) 0.013
E) 0.054

Question 58

Given an optimal risky portfolio with expected return of 14% and standard deviation of 22% and a risk free rate of 6%,what is the slope of the best feasible CAL?

A) 0.64
B) 0.14
C) 0.08
D) 0.33
E) 0.36

Question 59

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 60

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 61

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

Question 62

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