Question 1

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

Accepted Answer

The answer of The index model has been estimated for...

Question 2

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.

Accepted Answer

The answer of Assume that stock market returns do not...

Question 3

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

Accepted Answer

The commonly-used adjustment technique for beta is the Blume's method, which adjusts the beta towards 1 (the market beta) by using the formula: adjusted beta = 1/3 + 2/3 * (estimated beta). Using the given estimated beta of 1.4, the calculation is 1/3 + 2/3 * 1.4 = 1.27.

Question 4

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.

Accepted Answer

The number of unique covariances between n items can be calculated using the formula n(n-1)/2. For 40 stocks, this results in 40(39)/2 = 780 unique covariances.

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 0.24 and σ_M was 0.18, the β of the portfolio would be approximately

Accepted Answer

The beta (β) of the portfolio can be calculated using the formula β = σP / σM, where σP is the standard deviation of the portfolio and σM is the standard deviation of the market. Given σP = 0.24 and σM = 0.18, β = 0.24 / 0.18 = 1.33.

Question 6

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.

Accepted Answer

60; 60In a single-index model, each stock's return is related to the return of a single macroeconomic factor. Therefore, for 60 stocks, the fund needs to calculate 60 estimates of expected returns (one for each stock) and 60 sensitivity coefficients (beta values) to the macroeconomic factor (one beta for each stock).

Question 7

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.

Accepted Answer

The fund needs to calculate 125 expected returns (one for each stock) and 125 variances of returns (one for each stock).

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.

Accepted Answer

In a single-index model, each stock's return is related to a single macroeconomic factor, requiring the calculation of one firm-specific variance per stock (750 in total) and one estimate for the variance of the macroeconomic factor.

Question 9

Suppose the following equation best describes the evolution of β over time:β_t = 0.3 + 0.2β_t ₋₁If a stock had a β of 0.8 last year, you would forecast the β to be _______ in the coming year.

Accepted Answer

The answer of Suppose the following equation best describes the...

Question 10

The index model for stock A has been estimated with the following result:R_A = 0.01 + 0.94R_M + e_AIf σ_M = 0.30 and R²_A = 0.28, the standard deviation of return of stock A is

Accepted Answer

The standard deviation of stock A can be calculated using the formula: σ_A = β_A * σ_M * sqrt(R²_A) + sqrt(1 - R²_A) * σ_eA. Given β_A = 0.94, σ_M = 0.30, and R²_A = 0.28, we find σ_A = 0.5329.

Question 11

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.

Accepted Answer

To calculate the covariances for a portfolio of 132 stocks, you use the formula n(n-1)/2, where n is the number of stocks. For 132 stocks, this is 132(132-1)/2 = 8,646 covariances.

Question 12

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.

Accepted Answer

The forecast for β in the coming year is calculated as β_t = 0.4 + 0.6(0.9) = 0.94.

Question 13

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 ________.

Accepted Answer

The beta (β) of the portfolio can be calculated using the formula: β = σP / σM, where σP is the standard deviation of the portfolio and σM is the standard deviation of the market. Given σP = 0.25 and σM = 0.21, β = 0.25 / 0.21 ≈ 1.19.

Question 14

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

Accepted Answer

The commonly-used adjustment technique for beta, known as the Blume's method, adjusts the beta towards 1 (the market beta), meaning if the original beta is above 1, the adjusted beta will be between 1 and the original beta, hence between 1.0 and 1.35 in this case.

Question 15

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

Accepted Answer

The correct answer is A.The beta of the stock can be calculated using the following formula:β = (Expected return on stock - Risk-free rate) / (Expected return on market - Risk-free rate)Substituting the given values into the formula, we get:β = (0.11 + 0.03) / (0.10 + 0.03) = 1.57

Question 16

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

Accepted Answer

The answer of The beta of a stock has been...

Question 17

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

Accepted Answer

The beta (β) of a portfolio in the single index model is calculated as the ratio of the portfolio's standard deviation (σ) to the market's standard deviation (σ_M), multiplied by the correlation between the portfolio and the market. Assuming a well-diversified portfolio, the correlation is close to 1, so β ≈ σ / σ_M = 0.18 / 0.22 ≈ 0.82.

Question 18

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.

Accepted Answer

The answer of Suppose you forecast that the market index...

Question 19

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.

Accepted Answer

In a single-index model, each stock's return is related to a single macroeconomic factor. Therefore, for 217 stocks, they would need to calculate 217 estimates of expected returns (one for each stock) and 217 estimates of sensitivity coefficients (beta values) to the macroeconomic factor, one for each stock as well.

Question 20

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

Accepted Answer

The single-index model is represented by the equation $R_i = \alpha_i + \beta_i(R_m - R_f) + \epsilon_i$, where $R_i$ is the return on the stock, $\alpha_i$ is the stock's alpha, $\beta_i$ is the stock's beta, $R_m$ is the return on the market index, $R_f$ is the risk-free rate, and $\epsilon_i$ is the error term representing firm-specific events. Given that the alpha ($\alpha_i$) is 0%, the return on the market index ($R_m$) is 10%, the risk-free rate ($R_f$) is 5%, and the stock earns a return that exceeds the risk-free rate by 5% without firm-specific events ($\epsilon_i = 0$), the equation simplifies to $5\% = \beta_i(10\% - 5\%)$. Solving for $\beta_i$ gives $\beta_i = 1.0$, indicating that the stock moves in perfect correlation with the market.

Quiz 8: Index Models

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

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.

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

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.

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 0.24 and σ_M was 0.18, 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 ___ 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 ₋₁If a stock had a β of 0.8 last year, you would forecast the β to be _______ in the coming year.

The index model for stock A has been estimated with the following result:R_A = 0.01 + 0.94R_M + e_AIf σ_M = 0.30 and R²_A = 0.28, the standard deviation of return of stock A is

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.

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.

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 ________.

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

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

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

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

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

Quiz 8: Index Models

The index model has been estimated for stocks A and B with the following results: RA = 0.01 + 0.8RM + eA. RB = 0.02 + 1.1RM + eB. ΣM = 0.30; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is

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.

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

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.

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 0.24 and σM was 0.18, the β of the portfolio would be approximately

Suppose the following equation best describes the evolution of β over time:βt = 0.3 + 0.2βt − 1If a stock had a β of 0.8 last year, you would forecast the β to be _______ in the coming year.

The index model for stock A has been estimated with the following result:RA = 0.01 + 0.94RM + eAIf σM = 0.30 and R2A = 0.28, the standard deviation of return of stock A is

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.

Suppose the following equation best describes the evolution of β over time:βt = 0.4 + 0.6βt − 1.If a stock had a β of 0.9 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 0.25 and σM was 0.21, the β of the portfolio would be approximately ________.

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

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

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

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 0.22, the β of the portfolio would be approximately

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

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

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 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 0.24 and σ_M was 0.18, the β of the portfolio would be approximately

Suppose the following equation best describes the evolution of β over time:β_t = 0.3 + 0.2β_t ₋₁If a stock had a β of 0.8 last year, you would forecast the β to be _______ in the coming year.

The index model for stock A has been estimated with the following result:R_A = 0.01 + 0.94R_M + e_AIf σ_M = 0.30 and R²_A = 0.28, the standard deviation of return of stock A is

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.

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 ________.

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