# What's the disadvantage of using linear programming for portfolio optimization?

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?

• Please write explicitly what you are trying to maximise and the constraints – Kian Aug 9 '15 at 12:09