I am trying to create a portfolio of only four components using the mean-variance optimization (MVO). I am setting up my problem such that I want to maximize the expected returns with a fixed vol target. I am using a non-linear optimizer to solve this problem.
The problem I am facing is that when I set the non-linear constraint as : variance <= my vol target, the portfolio output seems to be unaffected by this constraint. I do have other constraints (linear and non-linear) that seem to affect the outcome but the fixed vol target constraint is ineffective. By ineffective I mean that if I set a vol target of 5% my portfolio is still generating a vol of 15%.
My questions are : 1) Is maximizing the return implicitly making the portfolio to attain a particular risk irrespective of any risk(vol target) constraints? 2) I am using nlopt C++ library to solve the optimization problem, if their is a possibility that I am not setting up the non-linear constraint correctly how do I debug this? and how do I know if my problem requires some kind of scaling?
Thank you in advance.