Information Coefficient

Every active decision is a forecast: this stock will beat the index, that sector will lag, rates will fall. The Information Coefficient measures how good those forecasts turned out to be.

Technically it is the correlation between expected and actual outcomes, so it runs from −1 to +1.

• +1 — the manager predicted every outcome correctly.
• 0 — right half the time, wrong half the time: no better than flipping a coin, and the workbook says no credit should be given.
• −1 — always wrong.

In the Fundamental Law of Active Management, IC is skill — one of the two ingredients, with breadth, that determine a manager's Information Ratio.

The workbook gives a practical shortcut that converts a hit rate into an IC:

IC = 2 × (Right predictions ÷ Total predictions) − 1

A 50% hit rate gives 2 × 0.5 − 1 = 0. A 75% hit rate gives 0.5. A 100% hit rate gives 1.

The forecasts can be about anything the manager acts on — company financials, macroeconomic data, stock price moves, P/E expansion or contraction, business cycles.

Two cautions from the workbook: a large number of observations is needed, because a small sample can produce a high IC by chance rather than skill; and Information Ratio rises linearly with IC, so a higher IC translates directly into a higher IR. The workbook also observes that in India, IC is almost non-existent as a disclosed metric, and data across portfolio managers is not available to compare it.

IC = Correlation(forecast outcomes, actual outcomes)        range −1 to +1

Shortcut:  IC = 2 × (Right ÷ Total) − 1

Fundamental Law:  IR = IC × √Breadth

The workbook's Chapter 18 caselet. A PMS manager forecasts 30 stocks a quarter, each from a different industry. In the four quarters of the past year he got 25, 30, 28 and 20 right.

Right = 25 + 30 + 28 + 20 = 103
Total = 30 × 4 = 120
IC = 2 × (103 ÷ 120) − 1 = 2 × 0.8583 − 1 = 0.72

Illustrative extension — what an IC is worth in rupees. A more realistic manager of a ₹500 crore book makes 160 independent calls a year and gets 84 right:

IC = 2 × (84 ÷ 160) − 1 = 0.05
IR = 0.05 × √160 = 0.05 × 12.65 = 0.63

If the mandate allows 4% active risk, the expected value added is IR × active risk = 0.63 × 4% ≈ 2.5% a year — about ₹12.6 crore on ₹500 crore. A hit rate of just 52.5% is enough, provided the bets are genuinely independent and there are enough of them.

Chapter 18 (Equity Portfolio Management Strategies), sections 18.3 and 18.3.1, defines IC as the skill input to the Fundamental Law of Active Management. Both Chapter 18 caselets compute it from a hit rate — 0.72 and 0.575 — and one asks you to name the metric. Expect the shortcut formula, the meaning of IC = 0, and the link IR = IC × √Breadth.

• IC = 0 means a 50% hit rate, not zero correct forecasts. Zero correct would be IC = −1.
• IC is bounded by −1 and +1. The workbook's own Fundamental Law illustration uses IC = 4 (section 18.3), which the same chapter's definition does not allow. Learn the √2 lesson from that illustration, not the IC value.
• The second caselet's arithmetic contains a slip: it prints "0.72 = 0.575". The correct IC there is 2 × (63 ÷ 80) − 1 = 0.575.
• IC measures skill; breadth measures how often the skill is used. The metric for "how good is the manager at predicting" is IC, not the Information Ratio.
• Small samples mislead. A manager with 8 right out of 10 has IC = 0.6 — and almost no evidence of skill.