Deck 6: Efficient Diversification

Question 1

Asset A has an expected return of 15% and a reward-to-variability ratio of .4. Asset B has an expected return of 20% and a reward-to-variability ratio of .3. A risk-averse investor would prefer a portfolio using the risk-free asset and ________.

A) asset A
B) asset B
C) no risky asset
D) The answer cannot be determined from the data given.

Answer 1

A

Question 2

The correlation coefficient between two assets equals ________.

A) their covariance divided by the product of their variances
B) the product of their variances divided by their covariance
C) the sum of their expected returns divided by their covariance
D) their covariance divided by the product of their standard deviations

Answer 2

D

Question 3

The expected rate of return of a portfolio of risky securities is ________.

A) the sum of the securities' covariance
B) the sum of the securities' variance
C) the weighted sum of the securities' expected returns
D) the weighted sum of the securities' variance

Answer 3

C

Question 4

Which one of the following stock return statistics fluctuates the most over time?

A) covariance of returns
B) variance of returns
C) average return
D) correlation coefficient

Question 5

Diversification is most effective when security returns are ________.

A) high
B) negatively correlated
C) positively correlated
D) uncorrelated

Question 6

Many current and retired Enron Corp. employees had their 401k retirement accounts wiped out when Enron collapsed because ________.

A) they had to pay huge fines for obstruction of justice
B) their 401k accounts were held outside the company
C) their 401k accounts were not well diversified
D) none of these options

Question 7

Market risk is also called ________ and ________.

A) systematic risk; diversifiable risk
B) systematic risk; nondiversifiable risk
C) unique risk; nondiversifiable risk
D) unique risk; diversifiable risk

Question 8

Risk that can be eliminated through diversification is called ________ risk.

A) unique
B) firm-specific
C) diversifiable
D) all of these options

Question 9

Which of the following statistics cannot be negative?

A) covariance
B) variance
C) E(r)
D) correlation coefficient

Question 10

The ________ is the covariance divided by the product of the standard deviations of the returns on each fund.

A) covariance
B) correlation coefficient
C) standard deviation
D) reward-to-variability ratio

Question 11

Asset A has an expected return of 20% and a standard deviation of 25%. The risk-free rate is 10%. What is the reward-to-variability ratio?

A) )40
B) )50
C) )75
D) )80

Question 12

The risk that can be diversified away is ________.

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

Question 13

Firm-specific risk is also called ________ and ________.

A) systematic risk; diversifiable risk
B) systematic risk; nondiversifiable risk
C) unique risk; nondiversifiable risk
D) unique risk; diversifiable risk

Question 14

Based on the outcomes in the following table, choose which of the statements below is (are) correct?

I) The covariance of security A and security B is zero.
II) The correlation coefficient between securities A and C is negative.
III) The correlation coefficient between securities B and C is positive.

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

Question 15

Beta is a measure of security responsiveness to ________.

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

Question 16

The ________ decision should take precedence over the ________ decision.

A) asset allocation; stock selection
B) bond selection; mutual fund selection
C) stock selection; asset allocation
D) stock selection; mutual fund selection

Question 17

Approximately how many securities does it take to diversify almost all of the unique risk from a portfolio?

A) 2
B) 6
C) 8
D) 20

Question 18

Adding additional risky assets to the investment opportunity set will generally move the efficient frontier ________ and to the ________.

A) up; right
B) up; left
C) down; right
D) down; left

Question 19

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) equal to the sum of the securities' standard deviations
B) equal to -1
C) equal to 0
D) greater than 0

Question 20

An investor's degree of risk aversion will determine his or her ________.

A) optimal risky portfolio
B) risk-free rate
C) optimal mix of the risk-free asset and risky asset
D) capital allocation line

Question 21

Harry Markowitz is best known for his Nobel Prize-winning work on ________.

A) strategies for active securities trading
B) techniques used to identify efficient portfolios of risky assets
C) techniques used to measure the systematic risk of securities
D) techniques used in valuing securities options

Question 22

The standard deviation of return on investment A is 10%, while the standard deviation of return on investment B is 4%. If the correlation coefficient between the returns on A and B is -.50, the covariance of returns on A and B is ________.

A) -.0447
B) -.0020
C) )0020
D) )0447

Question 23

On a standard expected return versus standard deviation graph, investors will prefer portfolios that lie to the ________ the current investment opportunity set.

A) left and above
B) left and below
C) right and above
D) right and below

Question 24

Rational risk-averse investors will always prefer portfolios ________.

A) located on the efficient frontier to those located on the capital market line
B) located on the capital market line to those located on the efficient frontier
C) at or near the minimum-variance point on the risky asset efficient frontier
D) that are risk-free to all other asset choices

Question 25

Suppose that a stock portfolio and a bond portfolio have a zero correlation. This means that ________.

A) the returns on the stock and bond portfolios tend to move inversely
B) the returns on the stock and bond portfolios tend to vary independently of each other
C) the returns on the stock and bond portfolios tend to move together
D) the covariance of the stock and bond portfolios will be positive

Question 26

Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. The weight of security B in the minimum-variance portfolio is ________.

A) 10%
B) 20%
C) 40%
D) 60%

Question 27

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately ________.

A) 29%
B) 44%
C) 56%
D) 71%

Question 28

A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 35%, while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is .45. Stock A comprises 40% of the portfolio, while stock B comprises 60% of the portfolio. The standard deviation of the return on this portfolio is ________.

A) 23%
B) 19.76%
C) 18.45%
D) 17.67%

Question 29

You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolios have a correlation of .55. The standard deviation of the resulting portfolio will be ________.

A) more than 18% but less than 24%
B) equal to 18%
C) more than 12% but less than 18%
D) equal to 12%

Question 30

The optimal risky portfolio can be identified by finding:
I) The minimum-variance point on the efficient frontier
II) The maximum-return point on the efficient frontier and the minimum-variance point on the efficient frontier
III) The tangency point of the capital market line and the efficient frontier
IV) The line with the steepest slope that connects the risk-free rate to the efficient frontier

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

Question 31

The standard deviation of return on investment A is 10%, while the standard deviation of return on investment B is 5%. If the covariance of returns on A and B is .0030, the correlation coefficient between the returns on A and B is ________.

A) )12
B) )36
C) )60
D) )77

Question 32

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The standard deviation of return on the optimal risky portfolio is ________.

A) 0%
B) 5%
C) 7%
D) 20%

Question 33

An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 24%, while the standard deviation on stock B is 14%. The correlation coefficient between the returns on A and B is .35. The expected return on stock A is 25%, while on stock B it is 11%. The proportion of the minimum-variance portfolio that would be invested in stock B is approximately ________.

A) 45%
B) 67%
C) 85%
D) 92%

Question 34

The term complete portfolio refers to a portfolio consisting of ________.

A) the risk-free asset combined with at least one risky asset
B) the market portfolio combined with the minimum-variance portfolio
C) securities from domestic markets combined with securities from foreign markets
D) common stocks combined with bonds

Question 35

The ________ reward-to-variability ratio is found on the ________ capital market line.

A) lowest; steepest
B) highest; flattest
C) highest; steepest
D) lowest; flattest

Question 36

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The proportion of the optimal risky portfolio that should be invested in stock A is ________.

A) 0%
B) 40%
C) 60%
D) 100%

Question 37

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The expected return on the optimal risky portfolio is approximately ________. (Hint: Find weights first.)

A) 14%
B) 16%
C) 18%
D) 19%

Question 38

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The expected return on the optimal risky portfolio is ________.

A) 14%
B) 15.6%
C) 16.4%
D) 18%

Question 39

A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 24%, while stock B has a standard deviation of return of 18%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is .0380, the correlation coefficient between the returns on A and B is ________.

A) )583
B) )225
C) )327
D) )128

Question 40

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The standard deviation of returns on the optimal risky portfolio is ________.

A) 25.5%
B) 22.3%
C) 21.4%
D) 20.7%

Question 41

Stock A has a beta of 1.2, and stock B has a beta of 1. The returns of stock A are ________ sensitive to changes in the market than are the returns of stock B.

A) 20% more
B) slightly more
C) 20% less
D) slightly less

Question 42

A stock has a correlation with the market of .45. The standard deviation of the market is 21%, and the standard deviation of the stock is 35%. What is the stock's beta?

A) 1
B) )75
C) )60
D) )55

Question 43

According to Tobin's separation property, portfolio choice can be separated into two independent tasks consisting of ________ and ________.

A) identifying all investor imposed constraints; identifying the set of securities that conform to the investor's constraints and offer the best risk-return trade-offs
B) identifying the investor's degree of risk aversion; choosing securities from industry groups that are consistent with the investor's risk profile
C) identifying the optimal risky portfolio; constructing a complete portfolio from T-bills and the optimal risky portfolio based on the investor's degree of risk aversion
D) choosing which risky assets an investor prefers according to the investor's risk-aversion level; minimizing the CAL by lending at the risk-free rate

Question 44

You are recalculating the risk of ACE stock in relation to the market index, and you find that the ratio of the systematic variance to the total variance has risen. You must also find that the ________.

A) covariance between ACE and the market has fallen
B) correlation coefficient between ACE and the market has fallen
C) correlation coefficient between ACE and the market has risen
D) unsystematic risk of ACE has risen

Question 45

Diversification can reduce or eliminate ________ risk.

A) all
B) systematic
C) nonsystematic
D) only an insignificant

Question 46

The part of a stock's return that is systematic is a function of which of the following variables?
I) Volatility in excess returns of the stock market
II) The sensitivity of the stock's returns to changes in the stock market
III) The variance in the stock's returns that is unrelated to the overall stock market

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

Question 47

Which risk can be partially or fully diversified away as additional securities are added to a portfolio?
I) Total risk
II) Systematic risk
III) Firm-specific risk

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

Question 48

A security's beta coefficient will be negative if ________.

A) its returns are negatively correlated with market-index returns
B) its returns are positively correlated with market-index returns
C) its stock price has historically been very stable
D) market demand for the firm's shares is very low

Question 49

Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is ________.

A) 1
B) less than 1
C) between 0 and 1
D) less than or equal to 0

Question 50

An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20%, while the standard deviation on stock B is 15%. The correlation coefficient between the returns on A and B is 0%. The rate of return for stocks A and B is 20% and 10% respectively. The standard deviation of return on the minimum-variance portfolio is ________.

A) 0%
B) 6%
C) 12%
D) 17%

Question 51

A measure of the riskiness of an asset held in isolation is ________.

A) beta
B) standard deviation
C) covariance
D) alpha

Question 52

If an investor does not diversify his portfolio and instead puts all of his money in one stock, the appropriate measure of security risk for that investor is the ________.

A) stock's standard deviation
B) variance of the market
C) stock's beta
D) covariance with the market index

Question 53

The market value weighted-average beta of firms included in the market index will always be ________.

A) 0
B) between 0 and 1
C) 1
D) none of these options (There is no particular rule concerning the average beta of firms included in the market index.)

Question 54

Which of the following provides the best example of a systematic-risk event?

A) A strike by union workers hurts a firm's quarterly earnings.
B) Mad Cow disease in Montana hurts local ranchers and buyers of beef.
C) The Federal Reserve increases interest rates 50 basis points.
D) A senior executive at a firm embezzles $10 million and escapes to South America.

Question 55

Semitool Corp. has an expected excess return of 6% for next year. However, for every unexpected 1% change in the market, Semitool's return responds by a factor of 1.2. Suppose it turns out that the economy and the stock market do better than expected by 1.5% and Semitool's products experience more rapid growth than anticipated, pushing up the stock price by another 1%. Based on this information, what was Semitool's actual excess return?

A) 7%
B) 8.5%
C) 8.8%
D) 9.25%

Question 56

An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20%, while the standard deviation on stock B is 15%. The correlation coefficient between the returns on A and B is 0%. The rate of return for stocks A and B is 20% and 10% respectively. The expected return on the minimum-variance portfolio is approximately ________.

A) 10%
B) 13.6%
C) 15%
D) 19.41%

Question 57

To construct a riskless portfolio using two risky stocks, one would need to find two stocks with a correlation coefficient of ________.

A) -0.5
B) 0.0
C) 0.5
D) -1.0

Question 58

You are constructing a scatter plot of excess returns for stock A versus the market index. If the correlation coefficient between stock A and the index is -1, you will find that the points of the scatter diagram ________ and the line of best fit has a ________.

A) all fall on the line of best fit; positive slope
B) all fall on the line of best fit; negative slope
C) are widely scattered around the line; positive slope
D) are widely scattered around the line; negative slope

Question 59

The term excess return refers to ________.

A) returns earned illegally by means of insider trading
B) the difference between the rate of return earned and the risk-free rate
C) the difference between the rate of return earned on a particular security and the rate of return earned on other securities of equivalent risk
D) the portion of the return on a security that represents tax liability and therefore cannot be reinvested

Question 60

The values of beta coefficients of securities are ________.

A) always positive
B) always negative
C) always between positive 1 and negative 1
D) usually positive but are not restricted in any particular way

Question 61

You run a regression for a stock's return on a market index and find the following Excel output:


The stock is ________ riskier than the typical stock.

A) 32%
B) 15.44%
C) 12%
D) 38%

Question 62

If you want to know the portfolio standard deviation for a three-stock portfolio, you will have to ________.

A) calculate two covariances and one trivariance
B) calculate only two covariances
C) calculate three covariances
D) average the variances of the individual stocks

Question 63

You are considering adding a new security to your portfolio. To decide whether you should add the security, you need to know the security's:
I) Expected return
II) Standard deviation
III) Correlation with your portfolio

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

Question 64

Which of the following statements is (are) true regarding time diversification?
I) The standard deviation of the average annual rate of return over several years will be smaller than the 1-year standard deviation.
II) For a longer time horizon, uncertainty compounds over a greater number of years.
III) Time diversification does not reduce risk.

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

Question 65

Investing in two assets with a correlation coefficient of 1 will reduce which kind of risk?

A) market risk
B) unique risk
C) unsystematic risk
D) none of these options (With a correlation of 1, no risk will be reduced.)

Question 66

As you lengthen the time horizon of your investment period and decide to invest for multiple years, you will find that:
I) The average risk per year may be smaller over longer investment horizons.
II) The overall risk of your investment will compound over time.
III) Your overall risk on the investment will fall.

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

Question 67

Investing in two assets with a correlation coefficient of -.5 will reduce what kind of risk?

A) market risk
B) nondiversifiable risk
C) systematic risk
D) unique risk

Question 68

You run a regression for a stock's return on a market index and find the following Excel output:


________ % of the variance is explained by this regression.

A) 12
B) 35
C) 4.05
D) 80

Question 69

What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 18%. Stock B has a standard deviation of 14%. The portfolio contains 40% of stock A, and the correlation coefficient between the two stocks is -.23.

A) 9.7%
B) 12.2%
C) 14%
D) 15.6%

Question 70

You find that the annual Sharpe ratio for stock A returns is equal to 1.8. For a 3-year holding period, the Sharpe ratio would equal ________.

A) 1.8
B) 2.48
C) 3.12
D) 5.49

Question 71

Which of the following correlation coefficients will produce the most diversification benefits?

A) -.6
B) -.9
C) 0
D) )4

Question 72

You run a regression for a stock's return on a market index and find the following Excel output:


The characteristic line for this stock is Rstock = ________ + ________ Rmarket.

A) )35; .12
B) 4.05; 1.32
C) 15.44; .97
D) )26; 1.36

Question 73

What is the standard deviation of a portfolio of two stocks given the following data: Stock A has a standard deviation of 30%. Stock B has a standard deviation of 18%. The portfolio contains 60% of stock A, and the correlation coefficient between the two stocks is -1.

A) 0%
B) 10.8%
C) 18%
D) 24%

Question 74

What is the most likely correlation coefficient between a stock-index mutual fund and the S&P 500?

A) -1
B) 0
C) 1
D) )5

Question 75

Which of the following correlation coefficients will produce the least diversification benefit?

A) -.6
B) -.3
C) 0
D) )8

Question 76

You run a regression for a stock's return on a market index and find the following Excel output:


This stock has greater systematic risk than a stock with a beta of ________.

A) )50
B) 1.5
C) 2
D) 3

Question 77

Decreasing the number of stocks in a portfolio from 50 to 10 would likely ________.

A) increase the systematic risk of the portfolio
B) increase the unsystematic risk of the portfolio
C) increase the return of the portfolio
D) decrease the variation in returns the investor faces in any one year

Question 78

You run a regression for a stock's return on a market index and find the following Excel output:


The beta of this stock is ________.

A) )12
B) )35
C) 1.32
D) 4.05

Question 79

Which of the following is a correct expression concerning the formula for the standard deviation of returns of a two-asset portfolio where the correlation coefficient is positive?

A) σ2rp < (W12σ12 + W22σ22)
B) σ2rp = (W12σ12 + W22σ22)
C) σ2rp = (W12σ12 - W22σ22)
D) σ2rp > (W12σ12 + W22σ22)

Question 80

A portfolio of stocks fluctuates when the Treasury yields change. Since this risk cannot be eliminated through diversification, it is called ________.

A) firm-specific risk
B) systematic risk
C) unique risk
D) none of the options