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

Q1. 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%.

Q2. 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)   1.82%.

B)   1.00%.

C)   10.00%.

Q3. 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)   36.7%.

B)   32.1%.

C)   37.5%.

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

Q1. 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%.

Correct answer is A)

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%

Q2. 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)   1.82%.

B)   1.00%.

C)   10.00%.

Correct answer is B)

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%

Q3. 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)   36.7%.

B)   32.1%.

C)   37.5%.

Correct answer is A)

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%