Reading 68: LOS a (Part 1) ～ Q1- 3

1．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)   27.5%.

D)   26.71%.

The correct answer was B)

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

2．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%.

D)   36.77%.

The correct answer was C)

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

3．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)   10.00%.

B)   1.82%.

C)   1.00%.

D)   18.24%.

The correct answer was C)

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%