The 17x Value Puzzle: Investors Pay Far More for Information Than It's Worth

Forum topic · 二一 · 2026-05-13

Summary

A finance paper by Ohad Kadan and Asaf Manela (arXiv:2605.11180) derives an elegant formula for the value of private information in financial markets: the covariance between price changes and order flow. Applying this to US stock market high-frequency data, the authors estimate the total value of information at roughly $3.5 million per stock per year — only about 0.04% of market capitalization. Yet investors spend approximately 0.67% of market value annually searching for excess returns (based on French's 2008 estimates), a gap of about 17 times. The paper frames this as a puzzle and explores possible explanations: an arms-race dynamic in zero-sum information acquisition, systematic overestimation of informational advantage (an information illusion rooted in behavioral economics), or statistical methods missing slower-moving information. The authors conclude that the information market may be among the least efficient markets, leaving the puzzle open for future research.

This post discusses a finance paper that asks a deceptively simple question: how much are traders' expensive private information actually worth?

The Formula

Two finance professors derived a concise measure of the value of information:

\text{Value of Information} = \text{Cov}( \Delta P, Q )

That is, the covariance between price changes (ΔP) and order flow (Q). The intuition: in a competitive market with market makers, an informed trader's profit exactly equals noise traders' losses — and those losses can be estimated from the correlation between price moves and order flow. Every profitable informed trade leaves a micro "footprint" in the price-order flow relationship.

The Numbers

Using US stock market high-frequency data:

Average value of information per stock per year: about $3.5 million
As a share of market capitalization: roughly 0.04%

Compare this to what investors actually spend:

Annual fees paid in the pursuit of excess returns: roughly 0.67% of market value (based on French 2008)

0.67% vs 0.04% — a gap of about 17 times.

The Puzzle

If the total value of all information is only 0.04% of market cap, why do investors willingly pay 0.67% per year to "acquire information"? Possible explanations:

1. Arms race: Massive spending on information acquisition forms a zero-sum arms race — you spend $10 million on information not because it pays back, but to avoid being eaten by competitors. Like two neighboring countries each spending 10% of GDP on the military: wasteful in aggregate, yet each feels it "must."

2. Overestimation of information value: Investors systematically overestimate the value of insider information. Behavioral economics has demonstrated this "information illusion" — people believe knowing a bit more means big profits, but markets absorb information astonishingly fast.

3. The covariance method may underestimate true value: The approach might miss "slow" information that isn't reflected in second-level high-frequency trading.

The paper leaves the puzzle to future researchers: the total value of information is far below what people spend searching for it. The "market for information" may be the least efficient market in the world.

The post opens with a Feynman anecdote: when pulled to Los Alamos during WWII to do atomic bomb calculations, his first question was "Are you sure this is worth doing?" — compute the cost-benefit ratio first, then decide. The paper asks the same of information spending.

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*Paper info*

Title: The Value of Information: A Puzzle
Authors: Ohad Kadan, Asaf Manela
arXiv: 2605.11180
Categories: q-fin.GN, econ.GN, q-fin.TR
Key finding: True value of information ≈ 0.04% of market cap; spending on searching for information ≈ 0.67% — a ~17x gap.