IV ExpertWeek 14 • Lesson 43Duration: 50 min

IC Information Coefficient (IC)

The single number that tells you whether your signal actually knows something

Learning Objectives

•Compute and interpret IC for trading signals
•Understand the Fundamental Law of Active Management
•Evaluate IC stability across time and regimes
•Identify common IC pitfalls that inflate apparent skill

Explain Like I'm 5

IC measures how well your predictions line up with what actually happens. A perfect IC of 1.0 means you nailed every rank order. In practice, anything above 0.05 is worth paying attention to.

Think of It This Way

Think of IC like a weather forecaster's track record. They don't need to predict exact temperatures — they just need to consistently get the relative ordering right. "Hotter than yesterday" matters more than "exactly 72 degrees."

1What IC Actually Tells You

The Information Coefficient is the rank correlation between your predicted returns and the realized returns. That's it. No magic, no mystery — just Spearman's rho between what you said would happen and what did happen. Here's the practical cheat sheet: | IC Range | What It Means | Real-World Translation | |----------|---------------|----------------------| | 0.00 | No information | Coin flip with extra steps | | 0.02-0.03 | Weak but usable | Enough for a large, diversified portfolio | | 0.05-0.07 | Solid | Most successful systematic strategies live here | | 0.08-0.10 | Strong | You're doing very well — double-check it's real | | 0.10+ | Suspicious | Either you found gold or you have a data leak | The thing that trips people up: IC doesn't need to be large to be profitable. A 0.05 IC across 500 instruments traded daily is vastly more valuable than a 0.15 IC on a single asset traded monthly. That's where the Fundamental Law comes in.

2Why Spearman, Not Pearson

Pearson correlation measures linear relationships between exact values. Spearman measures rank-order agreement. For trading signals, you almost always want Spearman, and here's why: Your signal doesn't need to predict magnitude. If your model says Asset A will outperform Asset B, and it does, that's useful — regardless of whether you got the exact return right. Pearson is sensitive to outliers in a way that distorts signal quality assessment. One fat-tail return can make a mediocre signal look brilliant, or make a great signal look broken. Spearman, by operating on ranks, is robust to this. The one exception: if your signal output is already a probability or a z-score (bounded, well-behaved), Pearson and Spearman will give nearly identical results. But even then, there's no downside to using Spearman. Grinold & Kahn (2000) formalized this in Active Portfolio Management — IC as rank correlation has become the industry standard for signal evaluation.

3The Fundamental Law of Active Management

Grinold's Fundamental Law is one of the most important relationships in quantitative finance:

IR \approx IC \times \sqrt{BR}

Where: - IR = Information Ratio (risk-adjusted return of active bets) - IC = Information Coefficient (signal quality) - BR = Breadth (number of independent bets per year) This is why large quant funds obsess over breadth. If your IC is 0.05 and you make 1,000 independent bets per year:

IR \approx 0.05 \times \sqrt{1000} \approx 1.58

An IR of 1.58 is exceptional. But the catch is the word independent. If your 1,000 trades are all variations of the same momentum bet, your effective breadth might be 50, not 1,000. The practical implication: you have two levers to improve performance. Finding a better signal (higher IC) is hard and gets harder over time as markets adapt. Increasing breadth — more instruments, more timeframes, more uncorrelated strategies — is often the more tractable path.

4IC Stability and Distribution

A single IC number is almost meaningless without context. What you need is the distribution of IC across time. Rolling IC analysis is the standard approach: compute IC monthly or quarterly, then examine: - Mean: Is it positive and statistically significant? - Std Dev: How volatile is the signal quality? - Hit Rate: What percentage of periods have positive IC? - Drawdowns: Are there extended periods of negative IC? A signal with IC = 0.06 +/- 0.02 (consistently positive) is infinitely more useful than one with IC = 0.10 +/- 0.15 (occasionally brilliant, often useless).

5Common IC Pitfalls

Five traps I've seen destroy IC analyses: 1. Look-ahead bias in signal construction. Your feature uses data that wasn't available at prediction time. This is the most common and most dangerous — IC looks great in backtest, zero in production. 2. Survivorship bias in the cross-section. If you only compute IC across assets that existed throughout the entire sample, you're ignoring all the ones that delisted, defaulted, or were acquired. Survivors tend to look more predictable than the full universe. 3. Ignoring transaction costs. An IC of 0.05 that requires daily rebalancing of illiquid instruments will turn negative after costs. Always compute net-of-cost IC, especially for shorter-horizon signals. 4. Confusing IC with profitability. IC measures rank accuracy, not P&L. A signal can have positive IC but lose money if the spread between winners and losers is too small relative to trading costs. 5. Overfitting via feature selection. If you tested 200 features and picked the one with the highest IC, you haven't found a signal — you've found noise. The multiple testing correction applies here (Bonferroni, FDR, or at minimum a holdout test).

6From IC to Actual Money

The bridge from IC to portfolio returns involves several practical considerations: Alpha transfer coefficient (TC): In practice, you can't perfectly implement your signal rankings. Position limits, liquidity constraints, and existing holdings all reduce how much of your IC translates into actual active bets. The refined Fundamental Law accounts for this:

IR \approx IC \times TC \times \sqrt{BR}

Where TC ranges from 0 to 1 (perfect implementation impossible in practice; 0.5-0.8 is common). Expected alpha from IC:

E[\alpha] = IC \times \sigma \times z

Where

\sigma

is the cross-sectional volatility of returns and

z

is the standardized signal score. This means a signal with IC = 0.05, applied to assets with 20% annualized vol, generates roughly 1% annualized alpha per unit of signal — before costs, before position constraints, before the hundred other things that erode theoretical edge into realized P&L.

Key Formulas

Information Coefficient

Spearman rank correlation between predicted and realized returns

Fundamental Law of Active Management

Information ratio as a function of signal quality and breadth of independent bets

Hands-On Code

Computing IC for Trading Signals

python

import numpy as np
from scipy.stats import spearmanr

def compute_rolling_ic(predictions, realized_returns, window=60):
    """
    Compute rolling IC between signal predictions and realized returns.
    
    Parameters:
        predictions: array of predicted return rankings/scores
        realized_returns: array of actual returns
        window: rolling window size (trading days)
    
    Returns:
        rolling_ic: array of IC values
        ic_stats: dict with mean, std, hit_rate, t_stat
    """
    n = len(predictions)
    rolling_ic = []
    
    for i in range(window, n):
        pred_window = predictions[i-window:i]
        real_window = realized_returns[i-window:i]
        
        # Spearman rank correlation
        ic, p_value = spearmanr(pred_window, real_window)
        rolling_ic.append(ic)
    
    rolling_ic = np.array(rolling_ic)
    
    ic_stats = {
        'mean_ic': np.mean(rolling_ic),
        'std_ic': np.std(rolling_ic),
        'hit_rate': np.mean(rolling_ic > 0),
        't_stat': np.mean(rolling_ic) / (np.std(rolling_ic) / np.sqrt(len(rolling_ic))),
        'ir': np.mean(rolling_ic) / np.std(rolling_ic)
    }
    
    return rolling_ic, ic_stats

Computes rolling Spearman rank correlation between signal predictions and realized returns, returning IC time series and summary statistics including mean, standard deviation, hit rate, and t-statistic.

Knowledge Check

Q1.Why is Spearman rank correlation preferred over Pearson for computing IC?

Q2.According to the Fundamental Law, a signal with IC = 0.05 and 400 independent bets per year has an expected IR of approximately:

Q3.An IC of 0.12 on a single-asset monthly signal should make you:

Assignment

Take a simple momentum signal (e.g., 20-day return) and compute its rolling IC against forward 5-day returns across at least 10 liquid FX pairs. Plot the IC distribution and compute the hit rate, mean IC, and t-statistic. Does the signal quality vary by volatility regime?

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