Set out and explain the fundamental law of active management for portfolios and each of its terms: breadth, the information coefficient, the transfer coefficient, and active risk (aggressiveness)

The fundamental law links expected active return to four inputs. The information coefficient is the correlation between forecast and realised active returns, the measure of skill. Breadth is the number of independent active decisions made per year. The transfer coefficient, between zero and one, measures how far constraints such as long-only rules let forecasts pass into active weights. Active risk is the chosen level of aggressiveness, and the information ratio the strategy can deliver is IR = TC × IC × √BR. Expected active return is that ratio scaled by the risk taken: RA = IR × active risk = TC × IC × √BR × active risk. With constraints, the best achievable Sharpe ratio squared is the benchmark Sharpe squared plus (TC × unconstrained IR) squared. The trap is multiplying by breadth rather than its square root.