Formula, in Backtesting & Validation
Information Coefficient Formula
The information coefficient (IC) is the correlation between a forecast and the realized outcome it predicts. For a quant signal it is the correlation between predicted and actual returns across the cross-section of assets, or between a ranked signal and forward returns. An IC of 0 is no skill; even a small positive IC, applied across many independent bets, can build a strong information ratio.
4 variables. Published May 26, 2026. By AI Fin Hub Research.
IC = corr(forecast, realized)
Rank IC = corr(rank(forecast), rank(realized)) (Spearman form)
Link to active management: IR = IC x sqrt(breadth) Variables
forecast
Forecast signal
The model's predicted return, score, or rank for each asset at the start of the period.
realized
Realized return
The actual forward return over the holding period. IC measures how well the forecast lined up with what actually happened.
rank(.)
Rank transform
Converting forecasts and outcomes to ranks before correlating gives the rank IC (Spearman), which is robust to outliers and the common choice for equity cross-sectional signals.
breadth
Breadth
The number of independent bets per year. The fundamental law of active management links IC to the information ratio: skill per bet times the square root of the number of independent bets.
Step by step
- 1
Collect paired forecasts and realized outcomes across the cross-section for a period.
Predicted scores and forward returns for 500 stocks this month.
- 2
Compute the correlation between forecasts and realized outcomes (use ranks for rank IC).
The cross-sectional rank correlation is 0.04.
- 3
Average the per-period ICs over the sample and assess their stability.
Mean monthly IC of 0.04 with a positive but noisy time series.
- 4
Translate IC into expected information ratio using breadth via the fundamental law.
With breadth 120 independent bets per year, IR = 0.04 x sqrt(120).
Worked example
Equity cross-sectional signal evaluated for skill
Mean IC per period
0.04
Independent bets per year (breadth)
120
The information ratio implied by the fundamental law is IR = IC x sqrt(breadth) = 0.04 x sqrt(120) = 0.04 x 10.954 = 0.438.
An IC of just 0.04, which sounds negligible, implies an information ratio of about 0.44 when applied across 120 independent bets a year. This is the core insight of the fundamental law: a tiny per-bet edge becomes a respectable risk-adjusted return through breadth. The caveat is that breadth must be genuinely independent, which crowding and shared factor exposure erode in practice.
Common variations
Run the numbers next
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Sources
- Active Portfolio Management , Richard C. Grinold and Ronald N. Kahn, McGraw-Hill (1999)
- The Fundamental Law of Active Management , Richard C. Grinold, Journal of Portfolio Management (1989)
Keep the topic connected
- Formula Fundamental Law of Active Management Formula
The fundamental law of active management: information ratio equals information coefficient times the square root of breadth. With an example.
- Formula Information Ratio Formula
The information ratio formula: active return over a benchmark divided by tracking error. Measures the consistency of excess return, with an example.
- Formula Correlation Formula
The Pearson correlation formula: covariance of two return series over the product of their standard deviations. The key diversification input.
- Learn Alpha
Alpha as risk-adjusted excess return: definition, the beta-adjustment math, and why most claimed alpha disappears once you adjust for the right factors.