The Fundamental Law of Active Management
Source: Grinold, R. C. (1989). Journal of Portfolio Management 15(3), 30–37.
TL;DR
States the fundamental law of active management: a manager's information ratio (risk-adjusted active
return) is approximately the skill per bet (information coefficient, IC) times the **square root of
the number of independent bets (breadth, N)**: IR ≈ IC · √N. Small edges, applied widely and
independently, beat large edges applied narrowly.
What it documents (models)
A decomposition of investment value-add into skill and breadth, formalizing why diversification
across many independent forecasts is as important as forecast quality.
The law
IC: the cross-sectional correlation between forecasts and realized returns — how good the signal is.
Breadth (N): the number of independent bets per period.
IR ≈ IC · √N, with a transfer-coefficient adjustment for real-world constraints (Clarke, de Silva
& Thorley) that captures how much of the theoretical IR survives long-only/turnover limits.
Why it matters
The intellectual basis for systematic, breadth-driven quantitative investing: a tiny IC (e.g.,
0.05) becomes a respectable IR when applied across thousands of stocks and rebalances.
Explains why broad cross-sectional strategies (momentum, value across the universe) can work despite
weak per-name predictability — directly relevant to the low signal-to-noise of return forecasting.
Limitations and risks
Assumes bets are independent; correlated signals shrink effective breadth dramatically.
Real constraints (long-only, costs, capacity) reduce the realized IR via the transfer coefficient;
the law is an idealized upper bound.
Key references
Grinold, R. (1989) — The Fundamental Law of Active Management — Journal of Portfolio Management
Grinold, R. & Kahn, R. (2000) — Active Portfolio Management — McGraw-Hill
Clarke, R., de Silva, H. & Thorley, S. (2002) — Portfolio Constraints and the Fundamental Law of Active Management — Financial Analysts Journal
