Grinold (1989): The Fundamental Law of Active Management

#The Paper at a Glance

Title: The fundamental law of active management

Authors: Richard C. Grinold

Published: Journal of Portfolio Management, 1989

DOI: 10.3905/jpm.1989.409211

Grinold's paper provides the mathematical reason why factor investing works. It's the theoretical backbone of every quantitative investment firm, from AQR to Dimensional to BlackRock.

#The Formula

IR = IC × √N

Where: - IR = Information Ratio (risk-adjusted excess return) - IC = Information Coefficient (correlation between predicted and actual returns) - N = Breadth (number of independent predictions per year)

What Each Component Means

Information Coefficient (IC): How good is each individual prediction? An IC of 0.05 means your predictions are slightly better than a coin flip. An IC of 0.10 is considered excellent.

Breadth (N): How many independent predictions do you make? A stock-picker who analyzes 50 stocks has breadth of 50. A quantitative model ranking 3,000 stocks monthly has breadth of 36,000 (3,000 × 12).

Information Ratio (IR): The ultimate measure of portfolio performance—excess return divided by tracking error.

#Why Multi-Factor Models Win

Single Factor, Single Stock

A single analyst with great skill (IC = 0.10) picking one stock per year: - IR = 0.10 × √1 = 0.10 - Poor risk-adjusted performance

Single Factor, Many Stocks

A quantitative model with modest skill (IC = 0.05) ranking 3,000 stocks: - IR = 0.05 × √3,000 = 2.74 - Excellent risk-adjusted performance

Multiple Factors, Many Stocks

A six-factor model with modest skill per factor (IC = 0.03 each) ranking 3,000 stocks with monthly rebalancing: - Effective breadth: even higher due to independent signals - IR improves further through factor diversification

The multi-factor model wins despite having lower skill per prediction because it makes far more independent predictions.

#The Key Insight: Breadth Matters More Than Skill

The square root of breadth means: - Going from 1 to 100 predictions: 10× improvement - Going from 100 to 10,000 predictions: 10× more improvement - Going from IC = 0.05 to IC = 0.10: only 2× improvement

It's easier to increase breadth than to increase skill. This is why quantitative models that rank thousands of stocks across multiple factors outperform even the most skilled individual stock pickers on a risk-adjusted basis.

#Practical Implications

1. Diversify Across Factors

Using six factors instead of one doesn't just diversify risk—it increases breadth. Each factor provides an independent prediction, multiplying the number of useful signals.

2. Cover Many Stocks

A model that ranks 3,000 stocks has fundamentally more opportunity than one that analyzes 50. Even with lower conviction per stock, the aggregate signal is stronger.

3. Don't Chase High IC

Many investors try to find the "best" single factor or the "perfect" stock pick. The Fundamental Law says this is the wrong approach. Modest skill, broadly applied, beats high skill, narrowly applied.

4. Rebalance Regularly

More frequent (but not too frequent) rebalancing increases breadth. Monthly rebalancing of factor scores provides 12× the breadth of annual rebalancing.

#Limitations

Grinold's framework assumes: - Predictions are truly independent (they often aren't) - Implementation is frictionless (transaction costs reduce net IR) - IC is constant (it varies over time and across stocks)

These limitations mean actual IR will be lower than the formula suggests, but the directional insight remains valid: diversified, systematic approaches have a structural advantage.

#How This Applies to Our Rankings

The Fundamental Law of Active Management is the mathematical justification for our entire approach at Blank Capital Research.

Our model applies six factors to approximately 3,000 stocks, updated regularly. Even if each factor has modest predictive power individually (IC of 0.03-0.05), the combination across thousands of stocks creates a high information ratio.

This is why we use six factors instead of just profitability. This is why we rank 3,000+ stocks instead of just the S&P 500. This is why systematic, multi-factor investing has a structural advantage over stock picking.

See our multi-factor rankings →

#Academic Source

Grinold, R. C. (1989). "The fundamental law of active management." Journal of Portfolio Management, 15(3), 30-37.