Why is lower correlation increases active risk?

Lower correlations with your portfolio and and the benchmark?

Well… think about it. the returns are now FAR MORE LIKELY to be different - even on a daily basis - which means the standard deviation of the active returns will widen.

edit: Here’s another way to think about it, if your portfolio was “perfectly” correlated with the benchmark, active risk would be zero. because there would never be any active return (Rp - Rb) = 0 … and the standard deviation of zero is zero. But, as these correlations break down, and we introduce active return into the portfolio, Rp - Rb will no longer ALWAYS equal zero, which increases active risk (on all time frames where before hand we had a perfectly correlated portfolio).

This is a guess, but you can also think about the actual correlation equation (Cov1,2) / (standard deviation1 x standard deviation2). As the denominator gets bigger, correlation will get smaller…