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

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?

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?
• so it's pointless to aim for portfolios with negative correlation, making those with zero correlation better? i should add that I wasn't implying all assets in the portfolio have to be negative, nor was I implying (-1) perfectly negative. i just mean mildly negative $\rho$s. see edits – develarist Sep 28 at 16:42