I am a MFE student and we have project on the Markowitz portfolio optimization problem.
i am wondering how much impact there will be, if I use a simpler linear optimizater instead of a quadratic one.
Say, i have a target portfolio $x$, my alpha is $a$. I will try to maximize $xa$, and apply a factor exposure limit:
$$l_0 < Ax < l_1$$
while $A$ is my factor exposure
What's the biggest disadvantage of above approach, compared with the classic quadratic approach widely used in Markowitz portfolio optimization.
Can anyone explain to me a bit?