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LOS d, (Part 1): Calculate the variance of an equally-weighted portfolio of n stocks. ffice ffice" />
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 = σ2p = (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 = σ2p = (1 / n) σ 21 + [(n - 1) / n]cov
ρ1,2 = (cov1,2) / (σ1 σ2) therefore cov1,2 = (ρ1,2)(σ1 σ2) = (?0.21)(0.57)(0.57) = ?0.068
σ2 = (0.57)2 = 0.32
σ2p = (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 = σ2p = (1 / n) σ 21 + [(n ? 1) / n]cov = [(1 / 17) × 0.48] + [(16 / 17) × 0.36] = 0.028 + 0.339 = 0.367 = 36.7%
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发表于 2009-4-2 11:09
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