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 = B1r1 + B2r2 + re
Equation 2: r2 = B12 .r12 + B22 .r22 + 2.B1.B2.r1r2 + 2.B1.r1re + 2.B2.r2.re + r2e
Steps: Apply expectations on both sides. Use formulae for variance to get:
Equation 3: var(r) = B12.var(r1) + B22.var(r2) + 2.B1B2.cov(r1,r2) + var(re)
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.