The information ratio is a measure of a manager’s opportunities. If we assume that the manager exploits those opportunities in a way that is mean/variance-efficient, then the value added by the manager will be proportional to the information ratio squared.

IR = IC⋅√BR⋅TC

Four elements comprise the fundamental law of active management:

• IR is information ratio, which is active return of a strategy compared to a benchmark index relative to the volatility of the active return.
• IC is information coefficient. This measure of skill is the correlation of each forecast with the actual outcomes.
• BR is breadth. It is defined as the number of independent forecasts of exceptional return we make per year.
• TC is transfer coefficient. It is the correlation between actual portfolio P and ideal portfolio Q, which measures the quality of implementation.

The fundamental law of active management has several implications. First, successful strategies require some winning combination of skill, breadth, and efficiency. Skill is the hardest to obtain. Breadth, i.e., diversification, can be the easiest to obtain—for example, by following more stocks—but it works only in combination with skill. We can increase efficiency by eliminating constraints.

Every active manager, no matter their investment style, must articulate some winning combination of skill, breadth, and efficiency.