Who pays for the information in market prices?

If a market price already reflects the information I could buy, paying for the same information seems wasteful. Yet someone must have done the work that made the price informative.

That is the tension I want to understand. Maxwell’s demon offers an appealing image: an observer sees distinctions hidden by a broader description, then acts on them. But a trader’s profit cannot establish that this is what happened. Risk, a service provided to someone else, and luck can also produce a positive result. I need an economic account before the physical analogy can do useful work.

The price depends on people who pay to learn

Grossman and Stiglitz formalize this tension. In their model, informed traders pay to observe a signal; others observe the price. Prices transmit information imperfectly, with noise preventing outsiders from extracting the signal exactly. The incentive to acquire information and the informativeness of prices are determined together. Perfect information revelation is incompatible with sustaining costly information acquisition under the model’s assumptions. On the Impossibility of Informationally Efficient Markets, 1980

Informed trading can help make prices informative. The people doing it are part of the adjustment process. Their potential compensation and the information already embedded in prices cannot always be treated as independent facts.

This explains why costly information and incomplete revelation can coexist. It does not show that a particular signal works, or that an information advantage can support a firm. Whether a specific activity is viable remains an empirical question.

Paying for research does not explain the return

Imagine two accounts that both finish the year up. One held broad market exposure; the other repeatedly supplied liquidity. Those descriptions already suggest different explanations for their returns. The first may have been compensated for bearing market risk. The second earned spreads while taking inventory and adverse-selection risk: the possibility of trading with someone whose information makes the quoted price unattractive.

Neither account’s positive balance is, by itself, evidence of an informational advantage. Nor does naming a risk prove that it explains the entire return. That requires a model, data and a comparison.

Alpha is a more specific claim than profit. It describes a return unexplained by a chosen model of normal returns. The choice matters: an apparent excess under one model can become compensation for an omitted exposure under another. Information and trading costs matter too, and a performance claim should state which costs its returns include. Fama calls this the joint-hypothesis problem: a test of market efficiency also tests the pricing model used to judge it. An anomaly does not identify which one failed. Efficient Capital Markets: II, 1991

This is why I would not define alpha with a single line subtracting fees, risk, maintenance and decay from a signal. Fees are cash charges. Risk adjustment requires a benchmark or model. Maintenance can be an operating expense shared across strategies. Decay changes the expected opportunity over time. They all matter, but adding their names to one equation does not make them commensurable or prevent double counting.

For a particular strategy, an accounting calculation can be much simpler: gross trading profit less the specified execution, financing and operating expenses. That tells us whether the activity paid its stated bills. Whether the remaining return is unusual given its risks is a further question.

What I keep from Maxwell’s demon

Maxwell imagined a being that could watch individual molecules and selectively open a small door between two parts of a gas. By sorting faster and slower molecules, it appeared able to create a temperature difference without the usual expenditure of work. Its observations and selective actions seemed to evade a constraint expressed at the level of the whole system.

The resolution requires including the demon’s physical operation in that system. In the Landauer–Bennett account, measurement need not itself impose an unavoidable entropy cost: it can, in principle, be reversible. Erasing an unknown memory record, or otherwise merging distinct logical states, is different. For a cyclic device, restoring the information-processing apparatus cannot simply be left outside the accounting. Bennett explains both reversible measurement and the role of logically irreversible operations in Notes on Landauer’s Principle, Reversible Computation, and Maxwell’s Demon.

That distinction limits the trading analogy. A market-data subscription is not a thermodynamic erasure cost. A price is not a temperature, and there is no second law that sets a trader’s transaction bill or guarantees competition will eliminate a particular return.

What I keep is the question about the observer’s work. A trader acts on a particular information set, at a particular time, through a limited set of orders. Acquiring the information and implementing the decision belong in the account. The analogy directs my attention there; the market model must still supply the incentives, costs and feasible actions.

Follow one decision through its costs

Consider a deliberately constructed example. Eight candidates arrive. Each has a signal giving its expected gross payoff, before costs. To isolate the accounting, assume those expectations are correct. Each candidate has two equally likely potential payoffs, eight units above or below its expectation. The signal therefore does not reveal the eventual outcome.

A fixed rule trades candidates whose expected gross payoff is positive. It selects four, with expectations of 6, 4, 3 and 2 units: 15 in total. Observing the batch costs 2 units. Execution costs either 1 or 4 units for each selected trade. All amounts use the same arbitrary monetary unit and horizon; there is no annualization or market calibration.

I kept the selection rule unchanged in the higher-cost case so that only the bill changes. Allowing the rule to adapt would answer another question: which trades to choose at each cost. This example instead asks whether the same decisions remain worthwhile. It is not an optimized strategy comparison.

Each envelope below is a candidate trade. Its signal is visible before you open it; the result inside is not. Open one, then continue or play the sequence. Changing the cost reprices the same candidates and decisions; it does not draw another sample.

The displayed realization gives the four selected trades a gross total of −1. Net of costs, this run loses 7 units in the lower-cost case and 19 in the higher-cost case. Both can occur even though the assumed expected net payoff differs in sign. These outcomes were chosen to make the distinction visible; they are not sampled trading results or an estimate of how often losses occur.

Skipping a candidate contributes zero trading payoff. The model can reveal its potential outcome because the example defines it. In real trading, an unsubmitted order’s fill and execution price are counterfactuals; a later price alone does not tell us what that order would have earned.

This example grants accurate expectations and full execution at a fixed charge. Actual research has to establish the signal’s calibration, feasible fills, dependence between outcomes, and the costs at the intended size. Even the positive expected net figure here is not alpha: the model supplies no risk benchmark, capital requirement or alternative investment against which to measure abnormal performance.

The market changes when the trade is attempted

An execution bill is useful bookkeeping, but a fixed subtraction has limits. A quote can disappear before an order reaches it. A limit order may fill precisely when its price has become unattractive. Increasing size can change the price paid and the inventory that must subsequently be carried. Those effects can change the distribution of gross payoffs, not merely add a constant charge after the fact.

For that reason, a backtest that selects the right timestamps can still represent the wrong activity. If it assumes a fill at a price that was unavailable, its gross result already needs revision. Calling the entire discrepancy “slippage” and subtracting a second, overlapping impact estimate would not repair the model.

The same care applies to market-making explanations. A spread received on a fill is one component of the result. Subsequent price movement, inventory management, hedging and execution expenses affect whether providing that liquidity was worthwhile. Better observation can help distinguish conditions, but the ability to describe a detailed order book is not evidence that the distinction was profitable to act on.

Competition adds another dependency. Other participants can act on similar information, changing prices and the conditions under which a signal was estimated. A signal’s historical expected payoff is therefore something to re-estimate under current conditions, not a fixed resource with a separate universal “decay charge.”

What would convince me?

I would want a claim made at the level where it can fail. Which information was available at the decision time? Which orders could actually have filled? Which expenses are already included? Against what risks and benchmark is the result being judged? How much of the apparent advantage survives data and periods that were not used to choose it?

Those questions demand different evidence. A clean event history can establish what a system knew. Execution records can constrain a fill model. Out-of-sample observations can challenge a forecast. A risk model can test an explanation for returns, while remaining open to misspecification. None substitutes for all the others.

For a particular trading claim, I would start by naming the proposed advantage and the observation that would make me abandon that explanation. If worse fills erase the result, the execution assumptions need work. If another risk model explains it, the claim about abnormal returns changes. Paying for information gives the activity a cost; evidence must establish what it bought.