Originally Posted by

**nuadre** Hi all,

Just wondering if anyone can help me with a proof/solution on how to get from equation 2 to equation 3. It is for deriving the variance of portfolio return using a multifactor model.

Equation 1: r = B_{1}r_{1 + }B_{2}r_{2 }+ r_{e}

Equation 2: r^{2} = B_{12 }.r_{12} + B_{22 }.r_{22} + 2.B_{1}.B_{2.}r_{1}r_{2} + 2.B_{1}_{.}r_{1}r_{e} + 2.B_{2.}r_{2.}re + r_{2e}

Steps: Apply expectations on both sides. Use formulae for variance to get:

Equation 3: var(r) = B_{12}.var(r_{1}) + B_{22}.var(r_{2}) + 2.B_{1}B_{2}.cov(r_{1},r_{2}) + var(r_{e})

I am having trouble with "apply expectations on both sides". Can someone please show me how to do this/what you end up with. I can then work from there to get eq 3.

Thank you in advance.