A question about active share and active risk

Hello all, A manager can pursue a higher active share without necessarily increasing active risk, vice versa. Who knows what vice versa means here? A manager can pursue a higher active risk (return), without necessarily increasing active weight? If so, is this possible? Thank you.

vice versa: The manager can pursue a low active share but the replacement positions he can select can be way different than the benchmark, thereby causing high active risk.

To 125mph,

In your opinion, one can take more risk when the weight and sizing positions are closer to the benchmark. How can this be done? Increasing the positions of derivatives?

By betting on securities and sectors ( as a stock picker)

Exactly.

To shrubaks123 and 125mph,

Right. Thank you.

The active share formula is always positive for the difference between weights, right?

Manager A

Security 1: 90 %

Security 2: 10 %

Benchmark

Security 1: 50 %

Security 2: 50 %

Active share:

(40 % + 40 %) / 2 = 40 %

Anyone?

Yup.

The formula for active share is:

active share = ½Σ|weight_portfolio,i − weightbenchmark_,i|

Note the absolute value.