Reading 66: Portfolio Concepts-LOS d 习题精选 given

土豆妮

Session 18: Portfolio Management: Capital Market Theory and the Portfolio Management Process
Reading 66: Portfolio Concepts

LOS d: Calculate the variance of an equally weighted portfolio of n stocks, explain the capital allocation and the capital market lines (CAL and CML) and the relation between them, and calculate the values of one of the variables given the values of the remaining variables.

 

 

Consider an equally-weighted portfolio comprised of seven assets in which the average asset variance equals 0.31 and the average covariance equals 0.27. What is the variance of the portfolio?

A) 27.5%.

B) 24.16%.

C) 27.00%.

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Portfolio variance = σ²_p = (1 / n) σ ²₁ + [(n ? 1) / n]cov = [(1 / 7) × 0.31] + [(6 / 7) × 0.27] = 0.044 + 0.231 = 0.275 = 27.5%

土豆妮

Consider an equally-weighted portfolio comprised of five assets in which the average asset standard deviation equals 0.57 and the average correlation between all asset pairs is ?0.21. The variance of the portfolio is closest to:

A) 1.00%.

B) 1.82%.

C) 10.00%.

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Portfolio variance = σ²_p = (1 / n) σ ²₁ + [(n - 1) / n]cov

ρ_1,2 = (cov_1,2) / (σ₁ σ₂) therefore cov_1,2 = (ρ_1,2)(σ₁ σ₂) = (?0.21)(0.57)(0.57) = ?0.068 

σ² = (0.57)² = 0.32 

σ²_p = (1 / 5)(0.32) + (4 / 5)(?0.068) = 0.064 + (?0.0544) = 0.0096 or 1.00%

土豆妮

Consider an equally-weighted portfolio comprised of 17 assets in which the average asset standard deviation equals 0.69 and the average covariance equals 0.36. What is the variance of the portfolio?

A) 32.1%.

B) 37.5%.

C) 36.7%.

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Portfolio variance = σ²_p = (1 / n) σ ²₁ + [(n ? 1) / n]cov = [(1 / 17) × 0.48] + [(16 / 17) × 0.36] = 0.028 + 0.339 = 0.367 = 36.7%

土豆妮

Which of the following statements regarding the capital market line (CML) is least accurate? The CML:

A) slope is equal to the expected return of the market portfolio minus the risk-free rate.>

B) implies that all portfolios on the CML are perfectly positively correlated.>

C) dominates everything below the line on the original efficient frontier.>

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The slope of the CML = (the expected return of the market ? the risk-free rate) / (the standard deviation of returns on the market portfolio)

Because the CML is a straight line, it implies that all the portfolios on the CML are perfectly positively correlated.

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土豆妮

Which of the following statements most accurately describes the capital allocation line (CAL) and the capital market line (CML)? The market portfolio:

A) always lies on both the CAL and the CML.

B) may lie on the CAL, but it always lies on the CML.

C) may lie on the CML, but it always lies on the CAL.

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When a minimum variance frontier is constructed in risk return space (i.e., y-axis = expected return, x-axis = standard deviation), the capital allocation line is the line emanating from the riskless return through the highest point of tangency with the minimum variance frontier. When the point of tangency is the market portfolio, the capital allocation line is the capital market line.

土豆妮

The capital market line (CML) is the capital allocation line with the:

A) market portfolio as the tangency portfolio.

B) global minimum-variance portfolio as the tangency portfolio.

C) market portfolio as the global minimum-variance portfolio.

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The CML is the capital allocation line (CAL) with the market portfolio as the tangency portfolio.

土豆妮

The equation of the capital market line (CML) says that the expected return on any portfolio equals the:

A) risk-free rate plus the product of the market risk premium and the market's portfolio standard deviation.

B) risk-free rate plus the product of the market price of risk and the portfolio's standard deviation.

C) risk-free rate plus the product of the market price of risk and the market's portfolio standard deviation.

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The CML is the capital allocation line with the market portfolio as the tangency portfolio. The equation of the CML is:

E(R_P) = R_F + [(E(R_M) – R_F)/s_M] s_p

where:
E(R_M) = the expected return on the market portfolio, M
s_M = the standard deviation of the market portfolio, M
R_F = the risk-free return

The intercept is the risk-free rate, R_F. The slope is equal to [(E(R_T) – R_F) / s_T], where [E(R_T) – R_F] is the expected risk premium on the tangency portfolio.

土豆妮

Which of the following does NOT describe the capital allocation line (CAL)?

A) The CAL is tangent to the minimum-variance frontier.

B) It is the efficient frontier when a risk-free asset is available.

C) It runs through the global minimum-variance portfolio.

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If a risk-free investment is part of the investment opportunity set, then the efficient frontier is a straight line called the capital allocation line (CAL). The CAL is tangent to the minimum-variance frontier of risky assets; therefore, it cannot run through the global minimum-variance portfolio.

土豆妮

If a risk-free asset is part of the investment opportunity set, then the efficient frontier is a:

A) curve called the minimum-variance frontier.

B) straight line called the capital allocation line (CAL).

C) curve called the efficient portfolio set.

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If a risk-free investment is part of the investment opportunity set, then the efficient frontier is a straight line called the capital allocation line (CAL), whether or not risky asset correlations are equal to one. The y-intercept of the CAL is the risk-free rate. The CAL is tangent to the minimum-variance frontier of risky assets.

土豆妮

The capital allocation line (CAL) with the market portfolio as the tangency portfolio is the:

A) minimum variance line.

B) security market line.

C) capital market line.

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The capital market line is the capital allocation line with the market portfolio as the tangency portfolio.