Deck 8: Index Models

Question 1

If the index model is valid, _________ would be helpful in determining the covariance between assets HPQ and KMP.

A) β_HPQ
B) β_KMP
C) σ_M
D) all of the options
E) None of the options are correct.

Answer 1

D
Explanation: If the index model is valid β_HPQ, β_KMP, and σ_M are determinants of the covariance between HPQ and KMP.

Question 2

The index model has been estimated for stocks A and B with the following results: R_A = 0.03 + 0.7R_M + e_A.
R_B = 0.01 + 0.9R_M + e_B.
Σ_M = 0.35; σ(e_A) = 0.20; σ(e_B) = 0.10.
The covariance between the returns on stocks A and B is

A) 0.0384.
B) 0.0406.
C) 0.1920.
D) 0.0772.
E) 0.4000.

Answer 2

D
Explanation: Cov(R_A, R_B) = b_Ab_Bs²_M = 0.7(0.9)(0.35)² = 0.0772.

Question 3

As diversification increases, the total variance of a portfolio approaches

A) 0.
B) 1.
C) the variance of the market portfolio.
D) infinity.
E) None of the options are correct.

Answer 3

C
Explanation: As more and more securities are added to the portfolio, unsystematic risk decreases and most of the remaining risk is systematic, as measured by the variance of the market portfolio.

Question 4

Rosenberg and Guy found that __________ helped to predict a firm's beta.

A) the firm's financial characteristics
B) the firm's industry group
C) firm size
D) the firm's financial characteristics and the firm's industry group
E) All of the options are correct.

Question 5

Rosenberg and Guy found that ___________ helped to predict firms' betas.

A) debt/asset ratios
B) market capitalization
C) variance of earnings
D) all of the options
E) None of the options are correct.

Question 6

The index model was first suggested by

A) Graham.
B) Markowitz.
C) Miller.
D) Sharpe.

Question 7

As diversification increases, the standard deviation of a portfolio approaches

A) 0.
B) 1.
C) infinity.
D) the standard deviation of the market portfolio.
E) None of the options are correct.

Question 8

As diversification increases, the unique risk of a portfolio approaches

A) 1.
B) 0.
C) infinity.
D) (n - 1) × n.

Question 9

As diversification increases, the firm-specific risk of a portfolio approaches

A) 0.
B) 1.
C) infinity.
D) (n - 1) × n.

Question 10

If a firm's beta was calculated as 0.6 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of

A) less than 0.6 but greater than zero.
B) between 0.6 and 1.0.
C) between 1.0 and 1.6.
D) greater than 1.6.
E) zero or less.

Question 11

In a factor model, the return on a stock in a particular period will be related to

A) firm-specific events.
B) macroeconomic events.
C) the error term.
D) both firm-specific events and macroeconomic events.
E) neither firm-specific events nor macroeconomic events.

Question 12

According to the index model, covariances among security pairs are

A) due to the influence of a single common factor represented by the market index return.
B) extremely difficult to calculate.
C) related to industry-specific events.
D) usually positive.
E) due to the influence of a single common factor represented by the market index return and usually positive.

Question 13

A single-index model uses __________ as a proxy for the systematic risk factor.

A) a market index, such as the S&P 500
B) the current account deficit
C) the growth rate in GNP
D) the unemployment rate.

Question 14

The intercept in the regression equations calculated by beta books is equal to

A) α in the CAPM.
B) α + r_f(1 + β).
C) α + r_f(1 - β).
D) 1 - α.

Question 15

If the index model is valid, _________ would be helpful in determining the covariance between assets GM and GE.

A) β_GM
B) β_GE
C) σ_M
D) all of the options
E) None of the options are correct.

Question 16

Beta books typically rely on the __________ most recent monthly observations to calculate regression parameters.

A) 12
B) 36
C) 60
D) 120

Question 17

If the index model is valid, _________ would be helpful in determining the covariance between assets K and L.

A) β_k
B) β_L
C) σ_M
D) all of the options
E) None of the options are correct.

Question 18

Analysts may use regression analysis to estimate the index model for a stock. When doing so, the intercept of the regression line is an estimate of

A) the α of the asset.
B) the β of the asset.
C) the σ of the asset.
D) the δ of the asset.

Question 19

As diversification increases, the unsystematic risk of a portfolio approaches

A) 1.
B) 0.
C) infinity.
D) (n - 1) × n.

Question 20

Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of

A) the α of the asset.
B) the β of the asset.
C) the σ of the asset.
D) the δ of the asset.

Question 21

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.18 and σ_M was 0.24, the β of the portfolio would be approximately

A) 0.75.
B) 0.56.
C) 0.07.
D) 1.03.

Question 22

Suppose the following equation best describes the evolution of β over time: β_t = 0.31 + 0.82β_{t - 1}.
If a stock had a β of 0.88 last year, you would forecast the β to be _______ in the coming year.

A) 0.88
B) 0.82
C) 0.31
D) 1.03

Question 23

If a firm's beta was calculated as 1.3 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of

A) less than 1.0 but greater than zero.
B) between 0.3 and 0.9.
C) between 1.0 and 1.3.
D) greater than 1.3.
E) zero or less.

Question 24

If a firm's beta was calculated as 0.8 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of

A) less than 0.8 but greater than zero.
B) between 1.0 and 1.8.
C) between 0.8 and 1.0.
D) greater than 1.8.
E) zero or less.

Question 25

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.20 and σ_M was 0.16, the β of the portfolio would be approximately

A) 0.64.
B) 0.80.
C) 1.25.
D) 1.56.

Question 26

The beta of Apple stock has been estimated as 2.3 using regression analysis on a sample of historical returns. A commonly-used adjustment technique would provide an adjusted beta of

A) 2.20.
B) 1.87.
C) 2.13.
D) 1.66.

Question 27

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 500 stocks in order to construct a mean-variance efficient portfolio constrained by 500 investments. They will need to calculate ________ estimates of firm-specific variances and ________ estimate/estimates for the variance of the macroeconomic factor.

A) 500; 1
B) 500; 500
C) 124,750; 1
D) 124,750; 500
E) 250,000; 500

Question 28

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.22 and σ_M was 0.19, the β of the portfolio would be approximately

A) 1.34.
B) 1.16.
C) 1.25.
D) 1.56.

Question 29

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 125 stocks in order to construct a mean-variance efficient portfolio constrained by 125 investments. They will need to calculate ____________ covariances.

A) 125
B) 7,750
C) 15,625
D) 11,750

Question 30

Suppose the following equation best describes the evolution of β over time: β_t = 0.25 + 0.75β_{t - 1}.
If a stock had a β of 0.6 last year, you would forecast the β to be _______ in the coming year.

A) 0.45
B) 0.60
C) 0.70
D) 0.75

Question 31

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 100 stocks in order to construct a mean-variance efficient portfolio constrained by 100 investments. They will need to calculate _____________ expected returns and ___________ variances of returns.

A) 100; 100
B) 100; 4950
C) 4950; 100
D) 4950; 4950

Question 32

The beta of JCP stock has been estimated as 1.2 using regression analysis on a sample of historical returns. A commonly-used adjustment technique would provide an adjusted beta of

A) 1.20.
B) 1.32.
C) 1.13.
D) 1.0.

Question 33

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 175 stocks in order to construct a mean-variance efficient portfolio constrained by 175 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor.

A) 175; 15,225
B) 175; 175
C) 15,225; 175
D) 15,225; 15,225

Question 34

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 200 stocks in order to construct a mean-variance efficient portfolio constrained by 200 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor.

A) 200; 19,900
B) 200; 200
C) 19,900; 200
D) 19,900; 19.900

Question 35

Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 16%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 11%, and there are no firm-specific events affecting the stock performance. The β of the stock is

A) 0.67.
B) 0.75.
C) 1.0.
D) 1.33.
E) 1.50.

Question 36

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate _____________ expected returns and ___________ variances of returns.

A) 150; 150
B) 150; 22500
C) 22500; 150
D) 22500; 22500

Question 37

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 100 stocks in order to construct a mean-variance efficient portfolio constrained by 100 investments. They will need to calculate ____________ covariances.

A) 45
B) 100
C) 4,950
D) 10,000

Question 38

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 125 stocks in order to construct a mean-variance efficient portfolio constrained by 125 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor.

A) 125; 15,225
B) 15,625; 125
C) 7,750; 125
D) 125; 125

Question 39

The beta of Exxon stock has been estimated as 1.6 using regression analysis on a sample of historical returns. A commonly-used adjustment technique would provide an adjusted beta of

A) 1.20.
B) 1.32.
C) 1.13.
D) 1.40.

Question 40

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 150 stocks in order to construct a mean-variance efficient portfolio constrained by 150 investments. They will need to calculate ____________ covariances.

A) 12
B) 150
C) 22,500
D) 11,175

Question 41

If a firm's beta was calculated as 1.6 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of

A) less than 0.6 but greater than zero.
B) between 0.6 and 1.0.
C) between 1.0 and 1.6.
D) greater than 1.6.
E) zero or less.

Question 42

Suppose the following equation best describes the evolution of β over time: _t = 0.18 + 0.63β_{t - 1}.
If a stock had a β of 1.09 last year, you would forecast the β to be _______ in the coming year.

A) 0.87
B) 0.18
C) 0.63
D) 0.81

Question 43

The idea that there is a limit to the reduction of portfolio risk due to diversification is

A) contradicted by both the CAPM and the single-index model.
B) contradicted by the CAPM.
C) contradicted by the single-index model.
D) supported in theory, but not supported empirically.
E) supported both in theory and by empirical evidence.

Question 44

The single-index model

A) greatly reduces the number of required calculations relative to those required by the Markowitz model.
B) enhances the understanding of systematic versus nonsystematic risk.
C) greatly increases the number of required calculations relative to those required by the Markowitz model.
D) greatly reduces the number of required calculations relative to those required by the Markowitz model and enhances the understanding of systematic versus nonsystematic risk.
E) enhances the understanding of systematic versus nonsystematic risk and greatly increases the number of required calculations

Question 45

The index model for stock B has been estimated with the following result: R_B = 0.01 + 1.1R_M + e_B.
If σ_M = 0.20 and R²_B = 0.50, the standard deviation of the return on stock B is

A) 0.1111.
B) 0.2111.
C) 0.3111.
D) 0.4111.

Question 46

In their study about predicting beta coefficients, which of the following did Rosenberg and Guy find to be factors that influence beta? I) Industry group
II) Variance of cash flow
III) Dividend yield
IV) Growth in earnings per share

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

Question 47

Suppose you are doing a portfolio analysis that includes all of the stocks on the NYSE. Using a single-index model rather than the Markowitz model

A) increases the number of inputs needed from about 1,400 to more than 1.4 million.
B) increases the number of inputs needed from about 10,000 to more than 125,000.
C) reduces the number of inputs needed from more than 125,000 to about 10,000.
D) reduces the number of inputs needed from more than 5 million to about 10,000.
E) increases the number of inputs needed from about 150 to more than 1,500.

Question 48

The expected impact of unanticipated macroeconomic events on a security's return during the period is

A) included in the security's expected return.
B) zero.
C) equal to the risk-free rate.
D) proportional to the firm's beta.
E) infinite.

Question 49

Covariances between security returns tend to be

A) positive because of SEC regulations.
B) positive because of Exchange regulations.
C) positive because of economic forces that affect many firms.
D) negative because of SEC regulations.
E) negative because of economic forces that affect many firms.

Question 50

The index model has been estimated for stocks A and B with the following results: R_A = 0.01 + 0.5R_M + e_A.
R_B = 0.02 + 1.3R_M + e_B.
Σ_M = 0.25; σ(e_A) = 0.20; σ(e_B) = 0.10.
The covariance between the returns on stocks A and B is

A) 0.0384.
B) 0.0406.
C) 0.1920.
D) 0.0050.
E) 0.4000.

Question 51

The index model for stock A has been estimated with the following result: R_A = 0.01 + 0.9R_M + e_A.
If σ_M = 0.25 and R²_A = 0.25, the standard deviation of return of stock A is

A) 0.2025.
B) 0.2500.
C) 0.4500.
D) 0.8100.

Question 52

Suppose you forecast that the market index will earn a return of 15% in the coming year. Treasury bills are yielding 6%. The unadjusted β of Mobil stock is 1.30. A reasonable forecast of the return on Mobil stock for the coming year is _________ if you use a common method to derive adjusted betas.

A) 15.0%
B) 15.5%
C) 16.0%
D) 16.8%

Question 53

One "cost" of the single-index model is that it

A) is virtually impossible to apply.
B) prohibits specialization of efforts within the security analysis industry.
C) requires forecasts of the money supply.
D) is legally prohibited by the SEC.
E) allows for only two kinds of risk-macro risk and micro risk.

Question 54

The index model has been estimated for stock A with the following results: R_A = 0.01 + 0.8R_M + e_A.
Σ_M = 0.20; σ(e_A) = 0.10.
The standard deviation of the return for stock A is

A) 0.0356.
B) 0.1887.
C) 0.1600.
D) 0.6400.

Question 55

The security characteristic line (SCL)

A) plots the excess return on a security as a function of the excess return on the market.
B) allows one to estimate the beta of the security.
C) allows one to estimate the alpha of the security.
D) All of the options.
E) None of the options are correct.

Question 56

In the single-index model represented by the equation r_i = E(r_i) + β_iF + e_i, the term e_i represents

A) the impact of unanticipated macroeconomic events on security i's return.
B) the impact of unanticipated firm-specific events on security i's return.
C) the impact of anticipated macroeconomic events on security i's return.
D) the impact of anticipated firm-specific events on security i's return.
E) the impact of changes in the market on security i's return.

Question 57

An analyst estimates the index model for a stock using regression analysis involving total returns. The estimated intercept in the regression equation is 6% and the β is 0.5. The risk-free rate of return is 12%. The true β of the stock is

A) 0%.
B) 3%.
C) 6%.
D) 9%.

Question 58

The security characteristic line (SCL) associated with the single-index model is a plot of

A) the security's returns on the vertical axis and the market index's returns on the horizontal axis.
B) the market index's returns on the vertical axis and the security's returns on the horizontal axis.
C) the security's excess returns on the vertical axis and the market index's excess returns on the horizontal axis.
D) the market index's excess returns on the vertical axis and the security's excess returns on the horizontal axis.
E) the security's returns on the vertical axis and Beta on the horizontal axis.

Question 59

Security returns

A) are based on both macro events and firm-specific events.
B) are based on firm-specific events only.
C) are usually positively correlated with each other.
D) are based on firm-specific events only and are usually positively correlated with each other.
E) are based on both macro events and firm-specific events and are usually positively correlated with each other.

Question 60

The index model has been estimated for stocks A and B with the following results: R_A = 0.01 + 0.8R_M + e_A.
R_B = 0.02 + 1.2R_M + e_B.
Σ_M = 0.20; σ(e_A) = 0.20; σ(e_B) = 0.10.
The standard deviation for stock A is

A) 0.0656.
B) 0.0676.
C) 0.2561.
D) 0.2600.

Question 61

Suppose the following equation best describes the evolution of β over time: β_t = 0.4 + 0.6β_{t - 1}.
If a stock had a β of 0.9 last year, you would forecast the β to be _______ in the coming year.

A) 0.45
B) 0.60
C) 0.70
D) 0.94

Question 62

The beta of a stock has been estimated as 0.85 using regression analysis on a sample of historical returns. A commonly-used adjustment technique would provide an adjusted beta of

A) 1.01.
B) 0.95.
C) 1.13.
D) 0.90.

Question 63

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 40 stocks in order to construct a mean-variance efficient portfolio constrained by 40 investments. They will need to calculate _____________ expected returns and ___________ variances of returns.

A) 100; 100
B) 40; 40
C) 4950; 100
D) 4950; 4950
E) None of the options are correct.

Question 64

Suppose the following equation best describes the evolution of β over time: β_t = 0.3 + 0.2β_{t - 1}
If a stock had a β of 0.8 last year, you would forecast the β to be _______ in the coming year.

A) 0.46
B) 0.60
C) 0.70
D) 0.94

Question 65

Suppose you forecast that the market index will earn a return of 12% in the coming year. Treasury bills are yielding 4%. The unadjusted β of Mobil stock is 1.50. A reasonable forecast of the return on Mobil stock for the coming year is _________ if you use a common method to derive adjusted betas.

A) 15.0%
B) 15.5%
C) 16.0%
D) 14.7%

Question 66

Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 10%. The risk-free rate of return is 5%. The stock earns a return that exceeds the risk-free rate by 5%, and there are no firm-specific events affecting the stock performance. The β of the stock is

A) 0.67.
B) 0.75.
C) 1.0.
D) 1.33.
E) 1.50.

Question 67

Consider the single-index model. The alpha of a stock is 0%. The return on the market index is 10%. The risk-free rate of return is 3%. The stock earns a return that exceeds the risk-free rate by 11%, and there are no firm-specific events affecting the stock performance. The β of the stock is

A) 1.57.
B) 0.75.
C) 1.17.
D) 1.33.
E) 1.50.

Question 68

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 750 stocks in order to construct a mean-variance efficient portfolio constrained by 750 investments. They will need to calculate ________ estimates of firm-specific variances and ________ estimate/estimate(s) for the variance of the macroeconomic factor.

A) 750; 1
B) 750; 750
C) 124,750; 1
D) 124,750; 750
E) 562,500; 750

Question 69

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 217 stocks in order to construct a mean-variance efficient portfolio constrained by 217 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor.

A) 217; 47,089
B) 217; 217
C) 47,089; 217
D) 47,089; 47,089
E) None of the options are correct.

Question 70

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.25 and σ_M was 0.21, the β of the portfolio would be approximately ________.

A) 0.64
B) 1.19
C) 1.25
D) 1.56

Question 71

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 40 stocks in order to construct a mean-variance efficient portfolio constrained by 40 investments. They will need to calculate ____________ covariances.

A) 45
B) 780
C) 4,950
D) 10,000

Question 72

The beta of a stock has been estimated as 1.8 using regression analysis on a sample of historical returns. A commonly-used adjustment technique would provide an adjusted beta of

A) 1.20.
B) 1.53.
C) 1.13.
D) 1.0.

Question 73

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 132 stocks in order to construct a mean-variance efficient portfolio constrained by 132 investments. They will need to calculate ____________ covariances.

A) 100
B) 132
C) 4,950
D) 8,646

Question 74

Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 125 stocks in order to construct a mean-variance efficient portfolio constrained by 125 investments. They will need to calculate _____________ expected returns and ___________ variances of returns.

A) 125; 125
B) 125; 15,625
C) 15,625; 125
D) 15,625; 15,625
E) None of the options are correct.

Question 75

The beta of a stock has been estimated as 1.4 using regression analysis on a sample of historical returns. A commonly-used adjustment technique would provide an adjusted beta of

A) 1.27.
B) 1.32.
C) 1.13.
D) 1.0.

Question 76

If a firm's beta was calculated as 1.35 in a regression equation, a commonly-used adjustment technique would provide an adjusted beta of

A) equal to 1.35.
B) between 0.0 and 1.0.
C) between 1.0 and 1.35.
D) greater than 1.35.
E) zero or less.

Question 77

The index model for stock A has been estimated with the following result: R_A = 0.01 + 0.94R_M + e_A
If σ_M = 0.30 and R²_A = 0.28, the standard deviation of return of stock A is

A) 0.2025.
B) 0.2500.
C) 0.4500.
D) 0.5329.

Question 78

Assume that stock market returns do follow a single-index structure. An investment fund analyzes 60 stocks in order to construct a mean-variance efficient portfolio constrained by 60 investments. They will need to calculate ________ estimates of expected returns and ________ estimates of sensitivity coefficients to the macroeconomic factor.

A) 200; 19,900
B) 200; 200
C) 60; 60
D) 19,900; 19.900
E) None of the options are correct.

Question 79

The index model has been estimated for stocks A and B with the following results: R_A = 0.01 + 0.8R_M + e_A.
R_B = 0.02 + 1.1R_M + e_B.
Σ_M = 0.30 σ(e_A) = 0.20 σ(e_B) = 0.10.
The covariance between the returns on stocks A and B is

A) 0.0384.
B) 0.0406.
C) 0.1920.
D) 0.0050.
E) 0.0792.

Question 80

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds. If the σ of your portfolio was 0.18 and σ_M was 0.22, the β of the portfolio would be approximately

A) 0.64.
B) 1.19.
C) 0.82.
D) 1.56.