PE, correlation w/public equities public, returns, benefit, because, positive

Muddahudda

(1) Private equity returns vs. (2) public equity returns... my notes are contradictory:

- (1) has a low correlation with (2), when measured with short-term returns
- (1) has strong positive correlation with (2), when measured with less-frequently-measured returns

So, I would conclude that PE doesn't have much diversification benefit? because high positive correlation with public equities

Thoughts?