I meant that it's the "weighted" part that can produce negative values (intermediate values, not the final result, but that result will be different if some of the weights changed sign because of the negative price).
So the formula for portfolio variation is this: V(R) = w'Vw where V is a covariance matrix (I'm using correlation matrix instead and multiplying 'w' terms by the corresponding standard deviations, but the end result is the same).
So currently, even before allowing negative prices, 'w' terms can contain negative elements when I'm short. I'm also normalising the current weights such that their ABS values add up to 1. For example I have these positions:
A: pos:1, price:200$
B: pos:-1, price:500$
C: pos:1, price:300$
then my 'w' matrix will be [0.2, -0.5, 0.3].
Let's say I've got this covariance matrix, then my portfolio variance will be this:
View attachment 248437
if however the price of the asset B, which I'm short, is negative, say -500$, it's weight, I guess, should become positive?, which will change the result:
View attachment 248438
I.e. the question is if I'm short something with a negative price, should it's weight be considered positive when calculating portfolio risk?
Or maybe I should just always apply ABS to both positions and prices and be done with it ?