Equity - EOC Question 9 it says: If you double the tracking risk the breadth is constant but the IC falls because a smaller portion of the managers insight is translated into the portfolio.
Can someone explain what effect doubeling the tracking risk has?
I understand it from the true information ratio perspectiv = (Active Return/Active Risk) as active risk gets larger if i increase tracking risk, but how does is affect the IC in the formular IR = IC*Breadth?
Breadth and IC tend to be inversely related. As you increase your coverage, the information you have as a ratio of the portfolio goes down.
Looking at it from another way, if you cover 99% of the stock market, then you have massive breadth, but your active return and risk are close to zero, giving you a 0 zero IR, hence the IC has to go down to reflect the poorer inforrmation advantage, and equalize the formula.
Active risk does not change IC. IC is reduced in this problem due to restriction on shorting. If manager cannot short then only part of his knowledge can be used. Doubling risk does not translates into double alpha since you are missing short alpha.