Can someone explain how the investment manager’s ability is related with TC and IC?
The IC is the investment managers ability, it tells you how many bets out of 100 the manager gets correct, i.e long when the asset outperformed and short when the asset detracted. The TC is scales the investment managers ability, the higher the TC, the less restrictions the manager has, hence the more he can express his investment views.
Since the ex-post information ratio is the product of IC, TC, and Sqrt of BR, an increase in both of the former coefficients will increase the managers information ratio.