What is the Fundamental Law of Active Management and what does it tell us?

The Fundamental Law of Active Management is an elegant decomposition of active portfolio performance into two components: skill and breadth.

The formula:

IR ≈ IC × √BR

Where:

• IR (Information Ratio): Active return / Active risk (tracking error). Measures risk-adjusted active performance.
• IC (Information Coefficient): Correlation between the manager's forecasts and actual outcomes. Measures skill per decision.
• BR (Breadth): Number of independent investment decisions per year. Measures opportunity set.

Intuition:

A manager's value-added (IR) depends on:

1. How good each forecast is (IC) — even small skill matters
2. How many independent bets they can make (BR) — more opportunities compound skill

Why √BR matters:

The square root reflects diversification. Making 100 independent bets is not 100× better than making 1 — it's 10× better. This is the same principle as portfolio diversification reducing risk.

Practical implications:

Strategy	IC	BR	IR
Concentrated stock picker (20 stocks)	0.10	20	0.10 × √20 = 0.45
Quantitative strategy (500 stocks)	0.03	500	0.03 × √500 = 0.67
Macro trader (10 bets/year)	0.15	10	0.15 × √10 = 0.47
High-frequency (1000 trades/day)	0.005	250,000	0.005 × √250K = 2.50

Key insight: A quant strategy with very low skill per trade (IC = 0.03) can still outperform a concentrated manager with much higher skill per pick (IC = 0.10) — simply by making many more independent bets.

Caveats and the transfer coefficient (TC):

The full version of the law includes a transfer coefficient:

IR ≈ TC × IC × √BR

TC (range 0 to 1) measures how effectively the manager translates insights into portfolio positions. Constraints like:

• Long-only mandates (can't short overvalued stocks)
• Sector limits
• Tracking error limits
• Position size limits

...all reduce TC below 1, meaning some of the manager's skill is wasted due to implementation constraints.

Example: Pinnacle Quantitative Fund has IC = 0.04 across 400 independent stock bets, but long-only constraints give TC = 0.60.

• IR = 0.60 × 0.04 × √400 = 0.60 × 0.04 × 20 = 0.48
• Without constraints (TC = 1): IR = 0.04 × 20 = 0.80
• Constraints cost 40% of potential alpha!

Exam tip: CFA Level II tests the formula, interpretation of each component, and especially the role of the transfer coefficient. Know that IC is typically very small (0.02-0.10) and that breadth compensates for low skill.

Practice the Fundamental Law in our CFA Level II question bank.