Do we need this for the exam ?
why not? its another way of stating the IR…and its one formula so…
and its easy
IR = IC*Breadth^.5 can’t do the squareroot sign 
The reading also states that " The number of independent decisions available per period does not necessarily increase with the size of the universe " But if the universe is larger aren’t there more decision to be made ? Anyone explain.
The other thing with this law . Can’t we improve the overall IR if we just increase the number of decisions irrespective of IC ?
you cant increase the number of independend decision and not decrease IC. IC is your investment insight, as you increase decisions it will decrease. Question is, will it decrease by more then the square root increase of breadth or not
maybe a good concept in theory but practically speaking how the heck do you quantify these things? Does is say anywhere in the curriculum for example how the IC is determined?
I don’t know if it’s in the CFA curriculum, but IC is often taken as the correlation coefficient between your prediction of returns and actual returns. If the universe increases in size, you may or may not get independent decisions. For example, your decision about what’s happening with the DAX (Germany) may not be independent of what’s happening with the CAC (France), since the markets may covary a lot. Still, it is possible to improve your decision making somewhat, as long as they are not 100% correlated.