Reading 64: Portfolio Concepts-LOS D习题精选 assets, stocks, average, 2010

honeycfa

LOS d, (Part 1): Calculate the variance of an equally-weighted portfolio of n stocks.

 

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) 24.16%.

B) 27.5%.

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%

honeycfa

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%

honeycfa

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) 36.7%.

C) 37.5%.

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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%

honeycfa

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

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

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

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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honeycfa

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

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

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

C) market portfolio as the tangency portfolio.

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

honeycfa

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 CML, but it always lies on the CAL.

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

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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.

honeycfa

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

A) capital market line.

B) minimum variance line.

C) security market line.

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

honeycfa

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

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

B) curve called the minimum-variance frontier.

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.

honeycfa

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

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

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

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

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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.

honeycfa

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 price of risk and the portfolio's standard deviation.

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