Question 1

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

Accepted Answer

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

Question 2

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.

Accepted Answer

0.31 + 0.82(0.88) = 1.0316.

Question 3

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

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 4

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

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 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 0.20 and σ_M was 0.16, the β of the portfolio would be approximately

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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.

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 8

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

Accepted Answer

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

Question 9

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.

Accepted Answer

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

Question 10

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.

Accepted Answer

0.25 + 0.75(0.6) = 0.70.

Question 11

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.

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 12

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

Accepted Answer

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

Question 13

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.

Accepted Answer

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

Question 14

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.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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.

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 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.

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 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.

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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.

Accepted Answer

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

Quiz 8: Index Models

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

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.

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

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

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

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

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

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.

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.

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 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

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.

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.

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

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.

Quiz 8: Index Models

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 σM was 0.24, the β of the portfolio would be approximately

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

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

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

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 σM was 0.16, the β of the portfolio would be approximately

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

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 σM was 0.19, the β of the portfolio would be approximately

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.

Suppose the following equation best describes the evolution of β over time: βt = 0.25 + 0.75βt - 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

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 100 stocks in order to construct a mean-variance efficient portfolio constrained by 100 investments. They will need to calculate ____________ covariances.

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

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 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

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 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 0.22 and σ_M was 0.19, the β of the portfolio would be approximately

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.