Question 1

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

Accepted Answer

(n² - n)/2 = (15,625 - 125)/2 = 7,750 covariances must be calculated.

Question 2

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

Accepted Answer

For the single-index model, n(500) estimates of firm-specific variances must be calculated and 1 estimate for the variance of the common macroeconomic factor.

Question 3

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.

Accepted Answer

11% = 0% + b(11%); b = 1.0.

Question 4

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

Accepted Answer

The expected returns of each of the 150 securities must be calculated.In addition, the 150 variances around these returns must be calculated.

Question 5

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.

Accepted Answer

s²p/s²m = b²; (0.22)²/(0.19)² = 1.34; b = 1.16.

Question 6

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

Accepted Answer

For a single-index model, n(125), expected returns and n(125) sensitivity coefficients to the macroeconomic factor must be estimated.

Question 7

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.

Accepted Answer

Betas, on average, equal one; thus, betas over time regress toward the mean, or 1.Therefore, if historic betas are less than 1, adjusted betas are between 1 and the calculated beta.

Question 8

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

Accepted Answer

The expected returns of each of the 100 securities must be calculated.In addition, the 100 variances around these returns must be calculated.

Question 9

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.

Accepted Answer

Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(2.3) + 1/3 = 1.867.

Question 10

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

Accepted Answer

(n² - n)/2 = (22,500 - 150)/2 = 11,175 covariances must be calculated.

Question 11

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

Accepted Answer

0.31 + 0.82(0.88) = 1.0316.

Question 12

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

Accepted Answer

For a single-index model, n(175), expected returns and n(175) sensitivity coefficients to the macroeconomic factor must be estimated.

Question 13

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

Accepted Answer

0.25 + 0.75(0.6) = 0.70.

Question 14

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.

Accepted Answer

Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.2) + 1/3 = 1.13.

Question 15

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.

Accepted Answer

s²p/s²m = b²; (0.2)^2/(0.16)² = 1.56; b = 1.25.

Question 16

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.

Accepted Answer

s²p/s²m = b²; (0.18)²/(0.24)² = 0.5625; b = 0.75.

Question 17

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

Accepted Answer

(n² - n)/2 = (10,000 - 100)/2 = 4,950 covariances must be calculated.

Question 18

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

Accepted Answer

For a single-index model, n(200), expected returns and n(200) sensitivity coefficients to the macroeconomic factor must be estimated.

Question 19

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.

Accepted Answer

Betas, on average, equal one; thus, betas over time regress toward the mean, or 1.Therefore, if historic betas are greater than 1, adjusted betas are between 1 and the calculated beta.

Question 20

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.

Accepted Answer

Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.6) + 1/3 = 1.40.

Quiz 8: Index Models

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.

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

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.

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

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

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.

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

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.

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.

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.

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

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

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

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.

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

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