Deck 8: Index Models

Question 1

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

A) $\beta$ _GM
B) $\beta$ _GE
C) $\sigma$ _M
D)all of the options

Answer 1

all of the options

Question 2

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

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

Answer 2

0.

Question 3

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

Answer 3

D

Question 4

As diversification increases, the unsystematic risk of a portfolio approaches

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

Question 5

As diversification increases, the unique risk of a portfolio approaches

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

Question 6

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

A) $\alpha$ in the CAPM.
B) $\alpha$ + r_f(1 + $\beta$ ).
C) $\alpha$ + r_f(1 - $\beta$ ).
D)1 - $\alpha$ .

Question 7

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.

Question 8

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

A) $\beta$ _k
B) $\beta$ _L
C) $\sigma$ _M
D)all of the options

Question 9

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.

Question 10

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.

Question 11

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.

Question 12

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 $\alpha$ of the asset.
B)the $\beta$ of the asset.
C)the $\sigma$ of the asset.
D)the $\delta$ of the asset.

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

As diversification increases, the total variance of a portfolio approaches

A)0.
B)1.
C)the variance of the market portfolio.
D)infinity.

Question 15

As diversification increases, the standard deviation of a portfolio approaches

A)0.
B)1.
C)infinity.
D)the standard deviation of the market portfolio.

Question 16

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

A) $\beta$ _HPQ
B) $\beta$ _KMP
C) $\sigma$ _M
D)all of the options

Question 17

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

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

Question 18

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 $\alpha$ of the asset.
B)the $\beta$ of the asset.
C)the $\sigma$ of the asset.
D)the $\delta$ of the asset.

Question 19

The index model was first suggested by

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

Question 20

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.
$\sigma$ _M = 0.35; $\sigma$ (e_A) = 0.20; $\sigma$ (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.

Question 21

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 22

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.22 and $\sigma$ _M was 0.19, the $\beta$ of the portfolio would be approximately

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

Question 23

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 24

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

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

Question 25

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 26

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.20 and $\sigma$ _M was 0.16, the $\beta$ of the portfolio would be approximately

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

Question 27

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 28

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 29

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

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

Question 30

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

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

Question 31

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 $\beta$ of the stock is

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

Question 32

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

Question 33

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 34

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 $\beta$ is 0.5.The risk-free rate of return is 12%.The true $\beta$ of the stock is

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

Question 35

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 36

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 37

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 38

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.18 and $\sigma$ _M was 0.24, the $\beta$ of the portfolio would be approximately

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

Question 39

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 40

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 41

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 42

The index model has been estimated for stock A with the following results: R_A = 0.01 + 0.8R_M + e_A.
$\sigma$ _M = 0.20; $\sigma$ (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 43

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

Question 44

Suppose you forecast that the market index will earn a return of 15% in the coming year.Treasury bills are yielding 6%.The unadjusted $\beta$ 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 45

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.

Question 46

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.

Question 47

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.

Question 48

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.

Question 49

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 50

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

Question 51

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.

Question 52

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.

Question 53

In the single-index model represented by the equation r_i= E(r_i) + $\beta$ _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.

Question 54

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.
$\sigma$ _M = 0.25; $\sigma$ (e_A) = 0.20; $\sigma$ (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.

Question 55

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 $\beta$ of the stock is

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

Question 56

The index model for stock A has been estimated with the following result: R_A = 0.01 + 0.9R_M + e_A.
If $\sigma$ _M = 0.25 andR²_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 57

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.

Question 58

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

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

Question 59

The index model for stock B has been estimated with the following result: R_B = 0.01 + 1.1R_M + e_B.
If $\sigma$ _M = 0.20 andR²_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 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.
$\sigma$ _M = 0.20; $\sigma$ (e_A) = 0.20; $\sigma$ (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 you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.18 and $\sigma$ _M was 0.22, the $\beta$ of the portfolio would be approximately

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

Question 62

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 63

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

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

Question 64

The index model for stock A has been estimated with the following result: R_A = 0.01 + 0.94R_M + e_A
If $\sigma$ _M = 0.30 andR²_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 65

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 $\beta$ of the stock is

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

Question 66

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.14 and $\sigma$ _M was 0.19, the $\beta$ of the portfolio would be approximately

A)0.74.
B)0.80.
C)1.25.
D)1.56.

Question 67

Suppose you held a well-diversified portfolio with a very large number of securities, and that the single index model holds.If the $\sigma$ of your portfolio was 0.24 and $\sigma$ _M was 0.18, the $\beta$ of the portfolio would be approximately

A)0.64.
B)1.33.
C)1.25.
D)1.56.

Question 68

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.

Question 69

Suppose the following equation best describes the evolution of $\beta$ over time: $\beta$ _t = 0.30 + 0.70 $\beta$ _t - ₁
If a stock had a $\beta$ of 0.82 last year, you would forecast the $\beta$ to be _______ in the coming year.

A)0.91
B)0.77
C)0.63
D)0.87

Question 70

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 71

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

Question 72

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

Question 73

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

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

Question 74

Suppose you forecast that the market index will earn a return of 12% in the coming year.Treasury bills are yielding 4%.The unadjusted $\beta$ 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 75

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

Question 76

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.