Question 1

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.

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 2

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

Accepted Answer

0.18 + 0.63(1.09) = 0.8667.

Question 3

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.

Accepted Answer

The benefits of diversification are limited to the level of systematic risk.

Question 4

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

Accepted Answer

The single index model both greatly reduces the number of calculations and enhances the understanding of the relationship between systematic and unsystematic risk on security returns.

Question 5

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.

Accepted Answer

R² = b²s²M/s²; 0.5 = [(1.1)²(0.2)²]/s²; s = 0.3111.

Question 6

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

Accepted Answer

All of the factors mentioned, as well as variance of earnings, firm size, and debt-to-asset ratio, were found to help predict betas.

Question 7

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.

Accepted Answer

This example is discussed in the textbook. The main point for the students to remember is that the single-index model drastically reduces the number of inputs required.

Question 8

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.

Accepted Answer

The expected value of unanticipated macroeconomic events is zero, because by definition it must average to zero or it would be incorporated into the expected return.

Question 9

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.

Accepted Answer

Economic forces, such as business cycles, interest rates, and technological changes, tend to have similar impacts on many firms.

Question 10

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.

Accepted Answer

Cov(R_A, R_B) = b_Ab_Bs²_M = 0.5(1.3)(0.25)² = 0.0406.

Question 11

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.

Accepted Answer

R² = b²s²M/s²; 0.25 = [(0.81)(0.25)²]/s²; s = 0.4500.

Question 12

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%

Accepted Answer

Adjusted beta = 2/3(1.3) + 1/3 = 1.20; E(r_M) = 6% + 1.20(9%) = 16.8%.

Question 13

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.

Accepted Answer

One "cost" of the single-index model is that it allows for only two kinds of risk-macro risk and micro risk.

Question 14

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.

Accepted Answer

σ_B = [(0.8)²(0.2)² + (0.1)²]^1/2 = 0.1887.

Question 15

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.

Accepted Answer

The security characteristic line, which plots the excess return of the security as a function of the excess return of the market, allows one to estimate both the alpha and the beta of the security.

Question 16

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.

Accepted Answer

The textbook discusses a model in which macroeconomic events are used as a single index for security returns. The e_i term represents the impact of unanticipated firm-specific events. The e_i term has an expected value of zero. Only unanticipated events would affect the return.

Question 17

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%.

Accepted Answer

6% = a + 12% (1 - 0.5); a = 0%.

Question 18

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.

Accepted Answer

The student needs to remember that it is the excess returns that are plotted and that the security's returns are plotted as a dependent variable.

Question 19

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.

Accepted Answer

Stock returns are usually highly positively correlated with each other. Stock returns are affected by both macroeconomic events and firm-specific events.

Question 20

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.

Accepted Answer

σ_A = [(0.8)²(0.2)² + (0.2)²]^1/2 = 0.2561.

Quiz 8: Index Models

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

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

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

The single-index model

The index model for stock B has been estimated with the following result: RB = 0.01 + 1.1RM + eB. If σM = 0.20 and R2B = 0.50, the standard deviation of the return on stock B is

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

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

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

Covariances between security returns tend to be

The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.5RM + eA. RB = 0.02 + 1.3RM + eB. ΣM = 0.25; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is

The index model for stock A has been estimated with the following result: RA = 0.01 + 0.9RM + eA. If σM = 0.25 and R2A = 0.25, the standard deviation of return of stock A is

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.

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

The index model has been estimated for stock A with the following results: RA = 0.01 + 0.8RM + eA. ΣM = 0.20; σ(eA) = 0.10. The standard deviation of the return for stock A is

The security characteristic line (SCL)

In the single-index model represented by the equation ri = E(ri) + βiF + ei, the term ei represents

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

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

Security returns

The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.8RM + eA. RB = 0.02 + 1.2RM + eB. ΣM = 0.20; σ(eA) = 0.20; σ(eB) = 0.10. The standard deviation for stock A is

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.

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

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

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

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

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

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