Question 1

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

Accepted Answer

0.4 + 0.6(0.9) = 0.94.

Question 2

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.

Accepted Answer

Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(0.85) + 1/3 = 0.90.

Question 3

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.

Accepted Answer

The expected returns of each of the 40 securities must be calculated. In addition, the 40 variances around these returns must be calculated.

Question 4

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

Accepted Answer

0.3 + 0.2(0.8) = 0.46.

Question 5

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%

Accepted Answer

Adjusted beta = 2/3(1.5) + 1/3 = 1.33; E(r_M) = 4% + 1.33(8%) = 14.66%.

Question 6

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.

Accepted Answer

5% = 0% + b(5%); b = 1.0.

Question 7

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.

Accepted Answer

11% = 0% + b(7%); b = 1.571.

Question 8

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

Accepted Answer

For the single-index model, n(750) estimates of firm-specific variances must be calculated and 1 estimate for the variance of the common macroeconomic factor.

Question 9

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.

Accepted Answer

For a single-index model, n(217), expected returns and n(217) sensitivity coefficients to the macroeconomic factor must be estimated.

Question 10

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

Accepted Answer

s²p/s²m = b²; (0.25)²/(0.21)² = 1.417; b = 1.19.

Question 11

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

Accepted Answer

(n² - n)/2 = (1,600 - 40)/2 = 780 covariances must be calculated.

Question 12

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.

Accepted Answer

Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.8) + 1/3 = 1.53.

Question 13

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

Accepted Answer

(n² - n)/2 = (17,424 - 132)/2 = 8,646 covariances must be calculated.

Question 14

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.

Accepted Answer

The expected returns of each of the 125 securities must be calculated. In addition, the 125 variances around these returns must be calculated.

Question 15

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.

Accepted Answer

Adjusted beta = 2/3 sample beta + 1/3(1); = 2/3(1.4) + 1/3 = 1.27.

Question 16

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.

Accepted Answer

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

Question 17

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.

Accepted Answer

R² = b²s²M/s²; s² = [(0.94) ²(0.30) ²]/0.28; s² = 0.284; s = 0.5329.

Question 18

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.

Accepted Answer

For a single-index model, n(60), expected returns and n(60) sensitivity coefficients to the macroeconomic factor must be estimated.

Question 19

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.

Accepted Answer

Cov(R_A, R_B) = b_Ab_Bs²M = 0.8(1.1)(0.30)² = 0.0792.

Question 20

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.

Accepted Answer

s²p/s²m = b²; (0.18)²/(0.22)² = 0.669; b = 0.82.

Quiz 8: Index Models

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.

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

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.

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.

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.

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

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

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 ________.

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.

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

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.

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.

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

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

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

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

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