Should portfolios have zero or negative correlation between assets? [closed]

Question

1. Is it more optimal to have a portfolio whose assets are negatively correlated? (I am not requiring all assets to be negatively correlated in this case, nor (-1) perfectly negative correlation either. I just mean moderately negative $\rho$ values, with little to no zero or positive correlations)
2. and is it more realistic, or smarter than the previous, to construct a portfolio whose majority of assets have a correlation of 0?

Why, and how to reconcile the answers to the above two?

Answer 1

While the close vote might be reasonable, there is mathematical arguments that show there is a limit to how negatively correlated a set of assets can be. It is even a classic quant interview question: Let the correlation matrix be $$\Omega = \rho \mathbf{1} + (1-\rho)I_d,$$

where $\mathbf 1$ is the $d \times d$ matrix with 1's everywhere. What is the range of $\rho \in (-1,1)$ that are valid?

Essentially, you can have only a few number of truly negatively correlated assets, but infinitely many with zero correlation.