I have three securities whose variance covariance matrix looks like this:
DE5 FR10 IT15 DE5 0.0376 0.0350 0.0243 FR10 0.0350 0.0658 0.0658 IT15 0.0243 0.0658 0.1335
How do I weight each of the three to minimize variance of the package, excluding the (0, 0, 0) solution. I don't mind "going short" IE, a mixture of positive and negative coefficients.
Can this be done with regression? I suspect not as weights will depend on which variable is chosen as dependent.
Is there a straightforward linear-algebra way of doing this without bringing in heavyweight quadratic programming package? I have many of these to do.
Ideally I'd like some code in R.