Information Coefficient

Every trading signal is a forecast: this stock will beat that one, this factor will pay this month. The information coefficient (IC) measures how good those forecasts are in the simplest possible way — it is the correlation between what you predicted and what actually happened. Line up your forecasts across all the stocks you scored, line up the returns they went on to earn, and take the correlation. That number is the IC.

$$\text{IC} = \operatorname{corr}\!\big(\text{forecast},\ \text{realized return}\big).$$

An IC of 1 would mean perfect foresight; 0 means your signal is noise; negative means it's backwards. The surprise for newcomers is how small a good IC is. Skilled equity signals live around 0.03 to 0.10. That means your forecast and the outcome share only a few percent of their variation — you're right just a hair more often than a coin flip. It looks like almost nothing. The reason it's still worth a fortune is breadth.

The bridge from tiny skill to real money is Grinold's Fundamental Law of Active Management:

$$\text{IR} \approx \text{IC}\times\sqrt{\text{BR}}.$$

The Information Ratio you can actually achieve is your skill per bet (IC) multiplied by the square root of your breadth (BR) — the number of roughly independent bets you make. Skill per bet can be minuscule as long as you get to place the bet thousands of times.

What a real IC looks like

Drag the correlation on the scatter below down toward 0.05. Watch how weak the relationship becomes — the cloud barely tilts, and the $r^2$ collapses to almost nothing. That faint tilt, spread across hundreds of stocks every month, is a professional-grade signal. A signal that produced the tight, obvious cloud of a 0.6 correlation would be too good to be true, and almost certainly a sign of look-ahead error.

Worked example

Suppose your signal ranks stocks with an IC of 0.05, and you rebalance it into roughly 200 independent bets per year. The Fundamental Law gives an information ratio of

$$\text{IR} = 0.05 \times \sqrt{200} = 0.05 \times 14.1 = 0.71 .$$

An IR of 0.71 is a genuinely good active strategy — the kind institutions pay for. It came from a per-bet skill so small you could barely detect it in isolation. Now flip the lesson: if a rival wants the same 0.71 IR but only trades 8 concentrated bets a year, they'd need $\text{IC} = 0.71/\sqrt{8} = 0.25$ — five times the skill. This is the central trade-off of active management: you can win with weak signals if you spread them wide, or you need strong signals if you concentrate. Most systematic desks choose breadth, because a small, reliable edge repeated often beats a big edge you can rarely find.

Where it misleads

• Breadth is easy to overstate. The law assumes independent bets. If your 200 positions are all driven by one macro factor, your true breadth is closer to a handful, and the IR you'll realise is a fraction of the formula's promise.
• IC is noisy. Measured over a short window or a few names, a high IC can be pure luck. Look at the average IC over time and its stability, not a single reading.
• Rank IC is safer. A couple of extreme returns can dominate a raw-correlation IC. Using the correlation of ranks (Spearman) makes it robust to outliers, which is why practitioners usually quote rank IC.
• Look-ahead inflates it. An IC that looks suspiciously high (say 0.3 for a daily equity signal) usually means future information leaked into the forecast. Be more suspicious of a high IC than a low one.