This paper extends the fundamental law of active investment management by introducing a turnover-adjusted information ratio (IR) that explicitly accounts for both the volatility of the information coefficient (IC) and the costs associated with portfolio turnover. Through mathematical derivations and simulations for mean-variance and quintile portfolios, the authors demonstrate that the turnover-adjusted IR is always lower than the classic IR that ignores turnover costs. More importantly, they find that contrary to the implication of the fundamental law—which suggests that higher breadth (more bets) always improves IR—investment managers can actually improve their performance by limiting or optimizing portfolio turnover. This result aligns with empirical evidence and provides a more realistic framework for evaluating active portfolio strategies.