Question

2. If Cov(ex, ey) = 0.01 in the previous question, where op = 0.0156 and xp = (2/3, 1/3)T, what is the residual variance of the portfolio if the single-factor model is not assumed? (a). 0.0112 (b). 0.0156 (c). 0.0200 (d). 0.0333

Answer 1

Due to multiple questions only one question is being answered here.

Question 1.

A single factor model assumes zero correlation between residuals. i.e. Cov ($\varepsilon$_x , $\varepsilon$ _y ) = 0.

Residual variance =
_{Συκαι σ(ε)}

where w_i = weight of  $\varepsilon$_i and $\sigma$ ($\varepsilon$_i) is the variance

Substituting the given values in this formula,

Residual variance = (2/3)² * 0.02 + (1/3)² * 0.06 = 0.0156

Hence the answer is (b)