Mainly wondering how the portfolio optimization model weights two stocks that have negative correlation, versus two stocks that have positive correlation. Does the mean-variance model weight them the same between these two scenarios, meaning it is blind to negative or positive correlation?
If stocks $X$ and $Y$ have a negative correlation of say $\rho = - 0.4$, what can be expected of the weights (their sign, or relative magnitude) the global minimum variance portfolio assigns to each if them in
- a 2-asset portfolio, and
- in a 3-asset portfolio shared with an uncorrelated/correlated asset $C$?
How do these answers change if instead $\rho = +0.4$ is positive?