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

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.

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

Accepted Answer

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

Question 4

The single-index model

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

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

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

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

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

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

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

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.

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

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

Accepted Answer

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

Question 15

The security characteristic line (SCL)

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

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

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

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

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

Accepted Answer

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

Quiz 8: Index Models