Optimize a portfolio such that the exposure to risk factors is zero and the variance is maximized (instead of traditional minimization problem).
so the optimization problem look like:
With following constraints:
$$\beta_0\,w=0$$ $$\beta_1\,w=0$$ $$\beta_2\,w=0$$ $$\beta_3\,w=0$$
$$\Sigma - covariance\,matrix$$ $$\beta_0..._3 - factor\,exposure$$
I am told that this is a non-convex problem. Can I convert this into an SDP with some relaxations? I could convert the objective function into a quadratic constraint such as below:
$$w^T\,\Sigma\,w > Min$$ Please advise.