page 101 of schweser volume 3 it says "MVO and the EF can be constructed on either a constrained or unconstrained basis. Unconstrained allows short selling of asset classes …
For the unconstrained version Black (1972) proposed a 2-fund theorem that the asset class weights of any minimum variance portfolio can be found as a weighted average of the asset class weights of a pair of minimum variance portfolios"
I don’t understand the part in bold… the MV Portfolio is one with defined weight per asset is it not? so it’s one portfolio? if by some chance there were two different portfolios with the same risk/return but different assets they would be interchangeable… is this what they are referring to ?
it’s just saying that Black created this 2 fund theorem when he was creating his unconstrained formula. but basically i believe it’s just saying if you take 2 portfolios on the Eff Front, you’ll still get a portfolio on the Eff Front.
The theorem will be tested in section about corner portfolios, asking you to calculate the avg weight of asset classes based on 2 corner portfolios in order to create an optimized portfolio to meet some required return for xyz.
I’m pretty sure corner portfolios are just created as reference points so we can actually do the calculation. But also so we don’t have to put all your eggs in one basket. It allows us to hirer multiple fund managers and still be on the EF. So in a way yes you are looking for a midpoint portfolio because in reality you aren’t going to find that 1 manager who can deliver your required return / risk objectives.