Active Share & Active Risk

Good morning everyone,

Yes, I know there are a lot of posts on this thread already, still find it unclear…

Active risk: volatility of the portfolio´s returns, in relation to benchmark (standard deviation of active return)

Active share: difference in weights relative to benchmark

So:

  1. Diversification means: low idiosyncratic risk -> l ow active ris k, low active share?

  2. Sector rotator : large deviations permitted, so it has a high active risk

Diversified sector rotator: high active risk , low active share

Concentrated sector rotator: high active risk , high active share

  1. stock picker: also high active risk

However when diversified: low active risk(??? isn´t it supposed to have high active risk), and high active share?

Concentrated stock picker: high active risk, high active share

  1. diversified multi-factor investor: high active share, low active risk?

How to remember all this? To me, diversification would always mean low active risk, low active share…

Thank you!

C.

Also, why does a diversified sector rotator exhibit high active risk, low active share

but a diversified stock picker: low active risk, high active share?

Could someone please help with this? Many thanks!