[1980phipsi]

It’s much clearer when you write these problems in terms of matrix math. The minimum variance portfolio is very important in finance.

[thomasahle]

How would you write this with matrices? It seems like there are many ways you could generalize.

[1980phipsi]

Let w be the vector of weights and S be the comformable matrix of covariances. The portfolio variance is given by w’Sw. So just minimize that with whatever constraints you want. If you just asssume weights sum to one, it is a classic quadratic optimization with linear equality constraints. Well known solutions.