Deck 11: Optimal Portfolio Choice and the Capital Asset Pricing Model

Question 1

Suppose over the next year Ball has a return of 12.5%,Lowes has a return of 20%,and Abbott Labs has a return of -10%.The value of your portfolio over the year is:

A) $21,000
B) $20,000
C) $20,700
D) $21,500

Answer 1

$20,700

Question 2

Suppose over the next year Ball has a return of 12.5%,Lowes has a return of 20%,and Abbott Labs has a return of -10%.The weight of Ball Corporation in your portfolio after one year is closest to:

A) 20.0%
B) 12.5%
C) 20.7%
D) 21.7%

Answer 2

21.7%

Question 3

Which of the following statements is false?

A) Stock returns will tend to move together if they are affected similarly by economic events.
B) Stocks in the same industry tend to have more highly correlated returns than stocks in different industries.
C) Almost all of the correlations between stocks are negative, illustrating the general tendency of stocks to move together.
D) With a positive amount invested in each stock, the more the stocks move together and the higher their covariance or correlation, the more variable the portfolio will be.

Answer 3

Almost all of the correlations between stocks are negative, illustrating the general tendency of stocks to move together.

Question 4

Which of the following statements is false?

A) Without trading, the portfolio weights will decrease for the stocks in the portfolio whose returns are above the overall portfolio return.
B) The expected return of a portfolio is simply the weighted average of the expected returns of the investments within the portfolio.
C) Portfolio weights add up to 1 so that they represent the way we have divided our money between the different individual investments in the portfolio.
D) A portfolio weight is the fraction of the total investment in the portfolio held in an individual investment in the portfolio.

Question 5

Which of the following statements is false?

A) The covariance and correlation allow us to measure the co-movement of returns.
B) Correlation is the expected product of the deviations of two returns from their means.
C) Because the prices of the stocks do not move identically, some of the risk is averaged out in a portfolio.
D) The amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face common risks and their prices move together.

Question 6

Which of the following equations is incorrect?

A) x_i =
B) R_p = Σ_i x_iR_i
C) R_p = x₁R₁ + x₂R₂ + ... + x_nR_n
D) E[R_p] = E[Σ_i x_iR_i]

Question 7

Which of the following statements is false?

A) While the sign of the correlation is easy to interpret, its magnitude is not.
B) Independent risks are uncorrelated.
C) When the covariance equals 0, the returns are uncorrelated.
D) To find the risk of a portfolio, we need to know more than the risk and return of the component stocks; we need to know the degree to which the stocks' returns move together.

Question 8

A portfolio weight is ________ of individual investment in the total investment portfolio.

A) a percentage
B) a weighted average
C) a simple average
D) a geometric average

Question 9

By combining stocks into a portfolio,we reduce risk through

A) higher expected return.
B) higher rate of return.
C) higher average return.
D) diversification.

Question 10

Suppose over the next year Ball has a return of 12.5%,Lowes has a return of 20%,and Abbott Labs has a return of -10%.The weight of Abbott Labs in your portfolio after one year is closest to:

A) -10.0%
B) 43.5%
C) 45.0%
D) 50.0%

Question 11

Suppose over the next year Ball has a return of 12.5%,Lowes has a return of 20%,and Abbott Labs has a return of -10%.The weight of Lowes in your portfolio after one year is closest to:

A) 20.0%
B) 34.8%
C) 30.0%
D) 36.0%

Question 12

Use the information for the question(s) below.
Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at $30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share.
The weight on Abbott Labs in your portfolio is:

A) 50%
B) 40%
C) 30%
D) 20%

Question 13

Suppose you invest $15,000 in Merck stock and $25,000 in Home Depot stock.You expect a return of 16% for Merck and 12% for Home Depot.What is the expected return on your portfolio?

A) 13.50%
B) 14.00%
C) 13.75%
D) 14.50%

Question 14

Suppose you invest $15,000 in Merck stock and $25,000 in Home Depot stock.You receive an actual return of -8% for Merck and 12% for Home Depot.What is the actual return on your portfolio?

A) 4.50%
B) 4.00%
C) 10.00%
D) 2.00%

Question 15

Suppose over the next year Ball has a return of 12.5%,Lowes has a return of 20%,and Abbott Labs has a return of -10%.The return on your portfolio over the year is:

A) 0%
B) 7.5%
C) 3.5%
D) 5.0%

Question 16

The amount of risk that will remain in a portfolio depends on the degree to which the stocks are exposed to

A) independent risks.
B) diversifiable risks.
C) common risks.
D) idiosyncratic risks.

Question 17

Use the information for the question(s) below.
Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at $30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share.
The weight on Ball Corporation in your portfolio is:

A) 50%
B) 40%
C) 20%
D) 30%

Question 18

Which of the following statements is false?

A) Dividing the covariance by the volatilities ensures that correlation is always between -1 and +1.
B) Volatility is the square root of variance.
C) The closer the correlation is to 0, the more the returns tend to move together as a result of common risk.
D) If two stocks move together, their returns will tend to be above or below average at the same time, and the covariance will be positive.

Question 19

Use the information for the question(s) below.
Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $50 per share, 200 shares of Lowes (LOW) at $30 per share, and 100 shares of Ball Corporation (BLL) at $40 per share.
The weight on Lowes in your portfolio is:

A) 40%
B) 20%
C) 50%
D) 30%

Question 20

The amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face ________ risks and their prices move together.

A) common
B) independent
C) firm-specific
D) unique

Question 21

Use the table for the question(s) below.
Consider the following returns:

Calculate the correlation between Home Depot's and IBM's returns.

Question 22

Use the table for the question(s) below.
Consider the following returns:

The variance on a portfolio that is made up of equal investments in Lowes and IBM stock is closest to:

A) 0.62
B) 0.05
C) 0.12
D) 0.06

Question 23

Use the table for the question(s) below.
Consider the following covariances between securities:

The variance on a portfolio that is made up of a $6,000 investment in Microsoft stock and a $4,000 investment in Wal-Mart stock is closest to:

Question 24

Which of the following equations is incorrect?

A) Cov(R_i,R_j) = Σ(R_i - R_i)(R_j - R_j)
B) Var(R_p) = x₁^2Var(R₁) + x₂^2Var(R₂) + 2X₁X₂Cov(R₁,R₂)
C) Corr(R_i,R_j) =
D) Cov(R_i,R_j) = E[(R_i - E[R_i])(R_j - E[R_j])]

Question 25

The risk of a portfolio depends on how each stock's ________ moves in relation to it.

A) dividend
B) risk
C) price
D) return

Question 26

Which of the following statements is false?

A) A stock's return is perfectly positively correlated with itself.
B) When the covariance equals 0, the stocks have no tendency to move either together or in opposition to one another.
C) The closer the correlation is to -1, the more the returns tend to move in opposite directions.
D) The variance of a portfolio depends only on the variance of the individual stocks.

Question 27

Use the table for the question(s) below.
Consider the following returns:

Calculate the variance on a portfolio that is made up of equal investments in Home Depot and IBM stock.

Question 28

Use the table for the question(s) below.
Consider the following returns:

The volatility on Lowes' returns is closest to:

A) 35%
B) 10%
C) 13%
D) 42%

Question 29

Use the table for the question(s) below.
Consider the following covariances between securities:

The variance on a portfolio that is made up of a $6,000 investment in Duke Energy stock and a $4,000 investment in Wal-Mart stock is closest to:

A) 0.050
B) 0.045
C) 0.051
D) -0.020

Question 30

Use the table for the question(s) below.
Consider the following returns:

The volatility on Home Depot's returns is closest to:

A) 35%
B) 31%
C) 42%
D) 18%

Question 31

Use the table for the question(s) below.
Consider the following returns:

Calculate the covariance between Home Depot's and IBM's returns.

Question 32

Use the table for the question(s) below.
Consider the following returns:

The correlation between Lowes' and IBM's returns is closest to:

A) 0.71
B) 0.60
C) 0.62
D) 0.05

Question 33

Use the table for the question(s) below.
Consider the following returns:

The covariance between Lowes' and IBM's returns is closest to:

A) 0.05
B) 0.06
C) 0.10
D) 0.71

Question 34

Which of the following statements is false?

A) The variance of a portfolio is equal to the weighted average correlation of each stock within the portfolio.
B) The variance of a portfolio is equal to the sum of the covariances of the returns of all pairs of stocks in the portfolio multiplied by each of their portfolio weights.
C) The variance of a portfolio is equal to the weighted average covariances of each stock within the portfolio.
D) The volatility declines as the number of stocks in a portfolio grows.

Question 35

Use the table for the question(s) below.
Consider the following covariances between securities:

The variance on a portfolio that is made up of equal investments in Duke Energy and Microsoft stock is closest to:

A) 0.065
B) 0.090
C) 0.149
D) -0.020

Question 36

Use the table for the question(s) below.
Consider the following returns:

The covariance between Lowes' and Home Depot's returns is closest to:

A) 0.10
B) 0.29
C) 0.12
D) 0.69

Question 37

Use the table for the question(s) below.
Consider the following returns:

The variance on a portfolio that is made up of equal investments in Lowes and Home Depot stock is closest to:

A) 0.12
B) 0.10
C) 0.69
D) 0.29

Question 38

Use the table for the question(s) below.
Consider the following returns:

The volatility on IBM's returns is closest to:

A) 3%
B) 13%
C) 16%
D) 18%

Question 39

Which of the following statements is false?

A) If two stocks move in opposite directions, one will tend to be above average when the other is below average, and the covariance will be negative.
B) The correlation between two stocks has the same sign as their covariance, so it has a similar interpretation.
C) The covariance of a stock with itself is simply its variance.
D) The covariance allows us to gauge the strength of the relationship between stocks.

Question 40

Use the table for the question(s) below.
Consider the following returns:

The correlation between Lowes' and Home Depot's returns is closest to:

A) 0.58
B) 0.29
C) 0.69
D) 0.10

Question 41

Consider an equally weighted portfolio that contains 20 stocks.If the average volatility of these stocks is 35% and the average correlation between the stocks is .4,then the volatility of this equally weighted portfolio is closest to:

A) 0.17
B) 0.41
C) 0.14
D) 0.37

Question 42

Use the table for the question(s) below.
Consider the following covariances between securities:

What is the variance on a portfolio that has $3,000 invested in Duke Energy,$4,000 invested in Microsoft,and $3,000 invested in Wal-Mart stock?

Question 43

Use the table for the question(s) below.
Consider the following covariances between securities:

What is the variance on a portfolio that has $2,000 invested in Duke Energy,$3,000 invested in Microsoft,and $5,000 invested in Wal-Mart stock?

Question 44

Use the table for the question(s) below.
Consider the following expected returns, volatilities, and correlations:

The expected return of a portfolio that is equally invested in Duke Energy and Microsoft is closest to:

A) 28%
B) 29%
C) 24%
D) 23%

Question 45

Suppose you have $10,000 in cash to invest.You decide to sell short $5,000 worth of Kinston stock and invest the proceeds from your short sale,plus your $10,000 into one-year Canadian Treasury Bills earning 5%.At the end of the year,you decide to liquidate your portfolio.Kinston Industries has the following realized returns: The return on your portfolio is closest to:

A) -0.5%
B) 13.5%
C) -2.5%
D) 14.5%

Question 46

Consider an equally weighted portfolio that contains 100 stocks.If the average volatility of these stocks is 50% and the average correlation between the stocks is .7,then the volatility of this equally weighted portfolio is closest to:

A) 0.72
B) 0.59
C) 0.40
D) 0.50

Question 47

Which of the following statements is false?

A) A short sale is a transaction in which you buy a stock that you do not own and then agree to sell that stock back in the future.
B) The efficient portfolios are those portfolios offering the lowest possible level of volatility for a given level of expected return.
C) A positive investment in a security can be referred to as a long position in the security.
D) It is possible to invest a negative amount in a stock or security which is called a short position.

Question 48

Use the table for the question(s) below.
Consider the following expected returns, volatilities, and correlations:

The expected return of a portfolio that consists of a long position of $10,000 in Wal-Mart and a short position of $2,000 in Microsoft is closest to:

A) 21%
B) 12%
C) 27%
D) 18%

Question 49

Which of the following statements is false?

A) When stocks are perfectly positively correlated, the set of portfolios is identified graphically by a straight line between them.
B) An investor seeking high returns and low volatility should only invest in an efficient portfolio.
C) When the correlation between securities is less than 1, the volatility of the portfolio is reduced due to diversification.
D) Efficient portfolios can be easily ranked, because investors will choose from among them those with the highest expected returns.

Question 50

Which of the following statements is false?

A) The volatility declines as the number of stocks in a portfolio grows.
B) An equally weighted portfolio is a portfolio in which the same amount is invested in each stock.
C) As the number of stocks in a portfolio grows large, the variance of the portfolio is determined primarily by the average covariance among the stocks.
D) When combining stocks into a portfolio that puts positive weight on each stock, unless all of the stocks are uncorrelated with the portfolio, the risk of the portfolio will be lower than the weighted average volatility of the individual stocks.

Question 51

Which of the following statements is false?

A) We say a portfolio is long for those stocks that have negative portfolio weights.
B) The efficient portfolios are those portfolios offering the highest possible expected return for a given level of volatility.
C) When two stocks are perfectly negatively correlated, it becomes possible to hold a portfolio that bears absolutely no risk.
D) The lower the correlation of the securities in a portfolio, the lower the volatility we can obtain.

Question 52

Consider an equally weighted portfolio that contains five stocks.If the average volatility of these stocks is 40% and the average correlation between the stocks is .5,then the volatility of this equally weighted portfolio is closest to:

A) 0.17
B) 0.44
C) 0.41
D) 0.19

Question 53

Which of the following formulas is incorrect?

A) Variance of an equally Weighted Portfolio = (1 - )(Average Variance of Individual Stocks) +
(Average covariance between the stocks)
B) Variance of a portfolio =
C) Variance of a portfolio =
D) Variance of a portfolio =

Question 54

Which of the following statements is false?

A) We say a portfolio is an efficient portfolio whenever it is possible to find another portfolio that is better in terms of both expected return and volatility.
B) We can rule out inefficient portfolios because they represent inferior investment choices.
C) The volatility of the portfolio will differ, depending on the correlation between the securities in the portfolio.
D) Correlation has no effect on the expected return on a portfolio.

Question 55

A hyperbola curve represents the set of portfolios that we can create using ________ weights.

A) risk
B) return
C) arbitrary
D) cost

Question 56

Which of the following statements is false?

A) The expected return of a portfolio is equal to the weighted average expected return, but the volatility of a portfolio is less than the weighted average volatility.
B) Each security contributes to the volatility of the portfolio according to its volatility, scaled by its covariance with the portfolio, which adjusts for the fraction of the total risk that is common to the portfolio.
C) Nearly half of the volatility of individual stocks can be eliminated in a large portfolio as a result of diversification.
D) The overall variability of the portfolio depends on the total co-movement of the stocks within it.

Question 57

Correlation has ________ effect on the expected return of a portfolio.

A) a positive
B) zero
C) a negative
D) none of the above

Question 58

Use the table for the question(s) below.
Consider the following expected returns, volatilities, and correlations:

Consider a portfolio consisting of only Duke Energy and Microsoft. The percentage of your investment (portfolio weight)that you would place in Duke Energy stock to achieve a risk-free investment would be closest to:

A) 15%
B) 80%
C) 23%
D) 10%

Question 59

Which of the following statements is false?

A) Graphically, the efficient portfolios are those on the northeast edge of the set of possible portfolios, an area which we call the efficient frontier.
B) To arrive at the best possible set of risk and return opportunities, we should keep adding stocks until all investment opportunities are represented.
C) We say a portfolio is short for those stocks that have negative portfolio weights.
D) Adding new investment opportunities allows for greater diversification and improves the efficient frontier.

Question 60

Use the table for the question(s) below.
Consider the following expected returns, volatilities, and correlations:

The volatility of a portfolio that is equally invested in Duke Energy and Microsoft is closest to:

A) 8%
B) 9%
C) 11%
D) 6%

Question 61

Which of the following statements is false?

A) Margin investing is a risky investment strategy.
B) Because our return on the risk-free investments is fixed and does not move with (or against) our portfolio, the correlation between the risk-free investment and the portfolio is always equal to one.
C) Short selling the risk-free investment is equivalent to borrowing money at the risk-free interest rate through a standard loan.
D) Margin investing can provide higher expected returns than investing in the efficient portfolio using only the funds we have available.

Question 62

Use the information for the question(s) below.
Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 6% interest rate to invest in the stock market. You invest the entire $20,000 in an exchange traded fund (ETF) with a 12% expected return and a 20% volatility.
Assuming that the EFT you invested in returns -10%,then the realized return on your investment is closest to:

A) -20%
B) -10%
C) -24%
D) -26%

Question 63

Which of the following statements is false?

A) A portfolio that consists of a long position in the risk-free investment is known as a levered portfolio.
B) The optimal portfolio will not depend on the investor's personal tradeoff between risk and return.
C) The volatility of the risk-free investment is zero.
D) Our total volatility is only a fraction of the volatility of the efficient portfolio, based on the amount we invest in the risk free asset.

Question 64

Which of the following statements is false?

A) The Sharpe ratio measures the ratio of volatility-to-reward provided by a portfolio.
B) Borrowing money to invest in stocks is referred to as buying stocks on margin.
C) The Sharpe ratio is the number of standard deviations the portfolio's return would have to fall to under-perform the risk-free investment.
D) The slope of the line through a given portfolio is often referred to as the Sharpe ratio of the portfolio.

Question 65

Aggressive investors will invest more,choosing a portfolio that is near ________ or even beyond it by buying stocks on margin.

A) the risk-free investment
B) the efficient frontier
C) the efficient frontier of risky investment
D) the tangent portfolio

Question 66

Use the information for the question(s) below.
Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk-free rate of interest is 5%.
The Sharpe ratio for your portfolio is closest to:

A) 1.2
B) 0.6
C) 1.0
D) 0.7

Question 67

Use the information for the question(s) below.
Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk-free rate of interest is 5%.
You want to maximize your expected return without increasing your risk.Without increasing your volatility beyond its current 10%,the maximum expected return you could earn is closest to:

A) 12.0%
B) 12.5%
C) 13.4%
D) 15.0%

Question 68

Which of the following statements is false?

A) An investor's preferences will determine only how much to invest in the tangent or efficient portfolio versus the risk-free investment.
B) Conservative investors will invest a small amount in the tangent or efficient portfolio, choosing a portfolio on the line near the risk-free investment.
C) Only aggressive investors will choose to hold the portfolio of risky assets, the tangent or efficient portfolio.
D) Aggressive investors will invest more in the tangent portfolio, choosing a portfolio that is near the tangent portfolio or even beyond it by buying stocks on margin.

Question 69

Consider a portfolio consisting of only Microsoft and Wal-Mart stock.Calculate the expected return on such a portfolio when the weight on Microsoft stock is 0%,25%,50%,75%,and 100%.

Question 70

Conservative investors will invest ________ amount,choosing a portfolio on the line near the risk-free investment.

A) a large
B) a zero
C) a small
D) an indifferent

Question 71

Use the information for the question(s) below.
Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 6% interest rate to invest in the stock market. You invest the entire $20,000 in an exchange traded fund (ETF) with a 12% expected return and a 20% volatility.
The expected return on your investment is closest to:

A) 18%
B) 20%
C) 12%
D) 24%

Question 72

Use the table for the question(s) below.
Consider the following expected returns, volatilities, and correlations:

The volatility of a portfolio that consists of a long position of $10,000 in Wal-Mart and a short position of $2,000 in Microsoft is closest to:

A) 9%
B) 14%
C) 11%
D) 12%

Question 73

Both conservative and aggressive investors will choose to hold the same portfolio of risky assets,

A) the risk-free investment.
B) the tangent portfolio.
C) the inefficient portfolio.
D) the risk-equal portfolio.

Question 74

What is the efficient frontier and how does it change when more stocks are used to construct portfolios?

Question 75

Which of the following equations is incorrect?

A) E[R_xp] = r_f + x(E[R_p] - r_f)
B) E[R_xp] = (1 - x)r_f + xE[R_p]
C) Sharpe ratio =
D) SD( R_xp) = xSD(R_p)

Question 76

Which of the following statements is false?

A) The tangent portfolio is efficient and, once we include the risk-free investment, all efficient portfolios are combinations of the risk-free investment and the tangent portfolio.
B) The optimal portfolio of risky investments depends on how conservative or aggressive the investor is.
C) By combining the efficient portfolio with the risk-free investment, an investor will earn the highest possible expected return for any level of volatility her or she is willing to bear.
D) The efficient portfolio is the tangent portfolio, the portfolio with the highest Sharpe ratio in the economy.

Question 77

Which of the following statements is false?

A) If we increase the fraction invested in the efficient portfolio beyond 100% we are short selling the risk-free investment.
B) As we increase the fraction invested in the efficient portfolio, we increase our risk premium, but not our risk, proportionately.
C) To earn the highest possible expected return for any level of volatility we must find the portfolio that generates the steepest possible line when combined with the risk-free investment.
D) Every investor should invest in the tangent portfolio independent of his or her taste for risk.

Question 78

Use the information for the question(s) below.
Suppose you have $10,000 in cash and you decide to borrow another $10,000 at a 6% interest rate to invest in the stock market. You invest the entire $20,000 in an exchange traded fund (ETF) with a 12% expected return and a 20% volatility.
The volatility of your investment is closest to:

A) 40%
B) 20%
C) 30%
D) 24%

Question 79

Consider a portfolio consisting of only Microsoft and Wal-Mart stock.Calculate the volatility of such a portfolio when the weight on Microsoft stock is 0%,25%,50%,75%,and 100%.

Question 80

Use the information for the question(s) below.
Suppose that you currently have $250,000 invested in a portfolio with an expected return of 12% and a volatility of 10%. The efficient (tangent) portfolio has an expected return of 17% and a volatility of 12%. The risk-free rate of interest is 5%.
The Sharpe ratio for the efficient portfolio is closest to:

A) 0.7
B) 1.0
C) 1.4
D) 1.2