Information and the Efficiency of the Capital Markets

I. Arbitrage and the Price of Risk

Chapters IV and V develop the concept of the Security Market Line: in a market at equilibrium, every security lies on that line, its expected return determined by its beta — the price of risk. But markets are seldom at equilibrium. News arrives and expectations diverge, and a security’s price departs from the line: for a time it is mispriced. The mechanism that restores it is arbitrage. When a stock trades below the line (its price too high for its risk) or above it (too low), investors who identify the discrepancy sell the overpriced security and buy the underpriced one, and their trading returns the price to the line. This chapter examines that mechanism more closely — how mispricings arise as information arrives, and how quickly and completely arbitrage removes them.

This search is the mechanism at work. Arbitrageurs study cash flows, discount rates, and the firm-specific factors that move a single stock — the health of a chief executive, the reception of a product, a pending lawsuit. Opportunities for this “arbitrage in expectations” are uncommon, and briefer still once found, because speed matters: once the buying begins, the price adjusts and the opportunity closes. The chapter’s central question is simply how good this mechanism is — how rapidly, and how thoroughly, do mispricings vanish?

The Invisible Hand of the Arbitrageur

Market efficiency is a statement about speed: how quickly relevant information becomes embedded in prices. The mechanism is a kind of invisible hand — an overpriced asset attracts short-sellers who push it down, an underpriced one attracts buyers who push it up. This is informational efficiency, about how fast news enters prices, not the Pareto efficiency of how resources are allocated. Two forces govern it: liquidity, since an illiquid market cannot react quickly, and psychology, since a crowd can over- or under-react when the meaning of the news is hard to judge.

Information once travelled only as fast as people did. In the eighteenth century a price change in Amsterdam reached London on the Thursday after the Monday it occurred — the time a fast messenger needed to cross the Channel. Today the same information reaches every market within seconds.

II. Regnault and the Value of a Secret

The idea that prices already reflect what is knowable is usually dated to the 1950s and 1960s. In fact it was stated and tested nearly a century earlier — and by someone who actually worked the market. Jules Regnault (1834–1894), a broker’s assistant in Second-Empire Paris, taught himself mathematics in a garret near the Bourse and in 1863 published Calcul des chances et philosophie de la bourse, arguably the first statistical theory of the stock market. He built the theory, tested it against data, and then used it to grow rich, retiring as a rentier with a fortune held, tellingly, mostly in bonds.

Regnault began with a direct question: who actually makes money in the market? For the ordinary investor, he argued, trading is a fair game at best; the only reliable profit belongs to those who know something the public does not.

“There is only one certain way of making a sure profit at the Stock Market, which is to only trade in guaranteed information unknown to the public … accessible only to a happy few, who is admitted to … those private meetings where the great political and financial decisions are plotted. This is the primary cause of the detrimental inequality which it is impossible to escape.”
— Jules Regnault, Calcul des chances (1863), §15

His example was close at hand: the French rente, the government bond whose price swung on decisions taken in ministries, where a civil servant “who takes advantage of his position and State secrets” held every advantage. Nathan Rothschild is the legend of the type — his courier network is said to have brought him word of Waterloo before London had it, letting him trade ahead of the news. Regnault’s insight, in modern terms, is that markets are efficient with respect to public information but not necessarily private: the advantage lies in what is not yet known. This reframes the question. If only private information pays, then what matters is how quickly private information ceases to be private and is reflected in the price.

Consider what happens when private information becomes public. A major corporate event — a merger, a disaster, a rate decision — instantly rewrites expected cash flows, and the price moves. The Bhopal chemical disaster collapsed Union Carbide’s stock within minutes; a Federal Reserve rate decision moves stocks the same day, not the day after. The tool for seeing this is the event study, which lines up many such events at day zero and averages the cumulative abnormal return around them.

The pattern is characteristic of an efficient market, with a revealing wrinkle. Part of the adjustment happens on the announcement day, and none afterward — no drift, because no public news remains to trade on. But much of the run-up comes before the announcement: private information entering the price ahead of the news, as Regnault described, until the announcement makes it public and the remaining gap closes at once. Efficiency also constrains managers: genuine news moves prices, but cosmetic accounting does not, and a figure buried in a footnote will not fool the market.

Three Degrees of Efficiency

How much information is already in the price? The answer is not all-or-nothing, and the standard taxonomy names three nested degrees.

Strong-form efficiency holds that all information, even private, is already in the price — a demanding benchmark few accept. Semi-strong-form holds that all public information is reflected: annual reports, news, analyst opinion. Most believe the U.S. equity market is close to this, though the definition frays at the edges — is a document public the instant it is posted online? Weak-form efficiency, the mildest claim, holds only that past prices cannot be used to earn excess profits. Each form contains the ones below it: past prices are themselves public, so strong implies semi-strong implies weak.

III. The Random Walk

Regnault’s second great idea followed from his first. If the crowd’s trading has already incorporated all public information into the price, then only new information can move it — and new information, by definition, is unpredictable. At any instant, he reasoned, a price is as likely to rise as to fall, a coin toss, because if the odds tilted, arbitrage (his word) would level them. Successive changes are therefore independent: the past holds no usable signal about the future. The shape this implies for prices over time is a random walk. He illustrated it with a simple analogy for the wisdom of the crowd.

From independence Regnault drew a sharp, testable prediction. If each interval adds its own independent jostle to the price, the spread of prices around their starting point must widen — not in proportion to time, but to its square root, because it is variances, not deviations, that add up. In his own capitals: the deviation of prices is in direct relation to the square root of time. It is the signature of the random walk — the same √time law Louis Bachelier would rediscover in 1900 and physicists would attach to Brownian motion.

Then Regnault did what almost no one in his century thought to do with a market: he checked the prediction against data. Using monthly prices of the French 3% rente from 1825 to 1862, he measured the typical price deviation over a month and over a year — and found them in almost exactly the √time ratio the theory demanded.

“Is there,” Regnault asked, “a better example of the harmony of theory and experience?” The fit is the first empirical confirmation of the random walk — the founding test of the efficient-market hypothesis, run ninety years before the phrase existed.

Regnault also drew a sobering corollary. The fair game is fair only before costs. Each trade pays a brokerage fee, so the expected profit of a round trip, zero before costs, is negative after them. Because the speculator’s edge grows only as √time while the fees accumulate trade by trade, frequent short-term trading tends steadily toward loss — Regnault estimated that a heavy speculator would be wiped out, on average, within about forty trades. Patient long-term investment, he concluded, is a fundamentally different activity from short-term speculation — a distinction the fund scorecard at the end of this chapter will confirm.

Like Bachelier after him, Regnault was forgotten for the better part of a century. He deserves to be remembered as the first to state the efficient-market idea clearly, test it against data, and follow it to its unsettling conclusions.

Fama’s Regressions and the Modern Case

Regnault’s √time law was the first confirmation; the modern case for efficiency was built on regressions. In the 1960s Eugene Fama and others ran the test Regnault could not, correlating each day’s return with the returns before it across thousands of stocks. The serial correlation came back indistinguishable from zero: the past, statistically, said nothing about the future. It was weak-form efficiency again — now with a mountain of data behind it.

Fama’s other landmark went beyond correlations. With Lawrence Fisher, Michael Jensen, and Richard Roll (1969), he ran the first true event study — the same tool we met with mergers, now turned on the 940 stock splits in the record from 1926 to 1960. Aligning every split on its own month 0 and averaging the abnormal returns around it produced the picture that became the emblem of market efficiency.

The most telling evidence comes from the events that appear to refute efficiency: bubbles. If any pattern should be exploitable, it is the industry that has just doubled or just halved. Robin Greenwood, Andrei Shleifer, and Yang You examined exactly this in modern U.S. data, tracking what becomes of an industry after a sharp run-up or run-down. In later work, using a database of industry returns reaching back to the nineteenth century, we tested their finding out of sample — on a century of earlier history the original data could not reach.

The result is the same in both panels. Measured net of the market, industries that had just soared and industries that had just crashed — opposite recent histories — went on to earn essentially the market’s return, along nearly the same path. The divergence is all in the past; there is no excess return to come, either way. This is the fourth of our six master pictures: two paths far apart before the event, together after it. The market had already priced whatever the boom or crash would mean, leaving nothing on the table for the investor who arrived late. That the modern result (right panel) reappears in the earlier data (left) makes the case stronger — it is not an artifact of a single period.

Testing the Three Forms

Merger announcements are a natural experiment on strong-form efficiency. Insiders — lawyers, bankers, managers — often know before the public, and prices frequently drift up before an official announcement, a sign that private information does leak into the price (and that some of the trading behind it is illegal). But the large jump on the announcement day shows the leakage is incomplete: the market is not fully strong-form efficient, exactly Regnault’s point about the value of a secret.

For semi-strong efficiency, the record is a good first approximation with nagging exceptions. Money managers pore over public information yet, as a group, show no consistent risk-adjusted edge. Backtests do turn up apparent anomalies — the “Dogs of the Dow,” post-earnings-announcement drift — but trading costs and thin liquidity tend to eat the paper profits, and few investors sustain them.

For weak-form efficiency, the news is subtler than the early researchers hoped. There is faint short-run momentum (days), reversals at a few weeks, and slow mean-reversion over years — Fama and French found four-year returns drifting back toward their long-run means. But the cycles are so long, and the statistics so noisy, that trading them profitably is another matter. Charles Henry Dow was chasing the same long swings a century ago; today’s hedge funds chase them with neural networks. If it truly worked, one wonders, why would they sell you the software?

The verdict on patterns is the one Regnault would have predicted: for widely traded securities, prices are close to a random walk, and if they were not, arbitrageurs would quickly make them so — buying the underpriced, shorting the overpriced, until the pattern is gone.

The Scorecard: Active versus Passive

There is a blunter test of efficiency than any regression: the track record of the professionals paid to beat the market. If prices were riddled with exploitable patterns, skilled managers would harvest them, and active funds would routinely outrun a simple index. They do not. The standard scorecard — S&P’s SPIVA study, which measures active funds against their benchmarks — is stark and stubborn.

Over a single year, roughly six in ten active large-cap funds trail the S&P 500; stretch the horizon to twenty years and the figure climbs above ninety percent. This is Regnault’s corollary at industrial scale, and it has a name — William Sharpe’s “arithmetic of active management.” Since all investors together are the market, the average actively managed dollar must earn the market return before costs, and therefore must fall short of it after fees. Beating the index is not merely hard; on average, and net of costs, it is arithmetically impossible. For most investors the rational move is to stop trying and simply buy the market.

And the competition is only intensifying. The collective wisdom a price aggregates once came from human analysts alone; today it includes algorithms and machine-learning models trading in microseconds — artificial intelligence as well as human. To beat the market now is to out-think not just the crowd on the steps of the Bourse but the machines behind them. The efficient-market hypothesis is, in the end, a statement of humility: the price already knows more than you do.

IV. A Hidden Ancestor: Regnault and the Arbitrage Pricing Theory

There is a final irony worth pausing on. The Arbitrage Pricing Theory of Chapter VI — Stephen Ross’s elegant alternative to the CAPM — rests on nothing more than the refusal to leave a free lunch on the table: if two portfolios carried the same risk but sold at different prices, arbitrageurs would trade the gap away, so in equilibrium the gap cannot exist. From that single, simple motive Ross built a pricing theory flexible enough to admit many sources of systematic risk, and free of the CAPM’s heavy machinery — the utility curves, the assumptions about aggregate holdings and identical beliefs. At its core it is Regnault’s idea: speculators seek out information and act on it quickly, and prices adjust to reflect it.

Ross, of course, had never heard of Regnault, who by 1976 had been forgotten for a century. The insight that so naturally underpins the modern theory of arbitrage was not, in fact, its foundation. It is the same irony as Bachelier and Black–Scholes: a nineteenth-century figure reaching a result that the twentieth century would rediscover independently, and build upon, without ever knowing he had come first.

V. Conclusion

Efficient-market theory is a strong approximation for liquid, well-regulated markets. How quickly does information get incorporated into prices? In a word, quickly — because arbitrageurs are ceaselessly collecting, processing, and trading on it. And efficiency is a public good: it keeps prices anchored to economic value, lowers the cost of judging what a security is worth, and lets ordinary investors trade with confidence. The speculator hunting a profit is, without meaning to be, a servant of that efficiency.