What does the fundamental law of active management formula represent?

The fundamental law of active management explains how active portfolio managers can achieve excess returns over a benchmark. The formula expresses the relationship between the information ratio and two key components: the information coefficient and breadth.

The information ratio measures the expected excess return of the portfolio over the benchmark per unit of risk. The information coefficient represents the skill of the manager in predicting relative returns, while breadth refers to the number of independent investment decisions made over a given period. By multiplying the information coefficient (indicating the manager's ability) with breadth (indicating how many bets or decisions a manager makes), the formula effectively quantifies the potential for generating alpha, or excess return, from active management strategies.

Thus, the formula accurately captures the dynamics of active management, highlighting that both the skill level of the portfolio manager and the quantity of investment opportunities are crucial for performance relative to the benchmark.