Fundemantal law of active management - Investor breadth

IR ≈ IC*(IB)^(1/2), IB = investment breadth, which is defined as the number of independent, active investment decisions made each year.

Question:

scenario 1: Fund manager only invest in one stock for a whole year

scenario 2: Fund manager only invest in one stock for first half of a year and switch to another for the second half of a year (Still one stock)

Will scenario 1 and 2 have the same IB? Thanks!

Good question - In my view, it should be treated as 2 seperate independent active bets. He actively moved his position from 1 stock to another during the year.

We can think of breadth as having two dimensions — one cross-sectional dimension (number of potential assets) and one time series dimension (how many bets per asset per year e.g. 2 in this case).

Thanks, Zuzu. Based on your veiw, the breadth will be as below bold?

scenario 1: Fund manager only invest in one stock for a whole year -> Breadth:1

scenario 2: Fund manager only invest in one stock for first half of a year and switch to another for the second half of a year (Still one stock) -> Breadth:2

How about if Scenario 1 fund manager made the independent decesion not to change the stock after 1H?

Right

" How about if Scenario 1 fund manager made the independent decesion not to change the stock after 1H?"

It will not be **considered “active” (**number of independent, “active” investment decisions made each year).

I think this is the grey area, where this ratio gets critized that it improves as the no. of bets are increased.

Right

" How about if Scenario 1 fund manager made the independent decesion not to change the stock after 1H?"

It will not be **considered “active” (**number of independent, “active” investment decisions made each year).

I think this is the grey area, where this ratio gets critized that it improves as the no. of bets are increased.

Thanks Zuzu! Yes, agree this is gray area…