Radar Perene / Archive / science

Random walk: yesterday's price does not predict tomorrow's

◦ Index methodology v2.2 (working papers with DOI). See the methodology.

Science

In the book that popularized the subject, the economist Burton Malkiel tells of a classroom experiment: his students built the chart of a fictitious "stock" by tossing a coin — heads, the price rose; tails, it fell. The result had everything a real chart has: trends, corrections, apparent support levels. Shown to a technical analyst, the drawing drew enthusiasm — there was, he said, a clear buy pattern in it. The pattern was a sequence of heads and tails.

A series follows a random walk when each step is independent of the previous ones: the history carries no information about the direction of the next move. Applied to prices, the theory states that the best available description of tomorrow's price is today's price — plus an unpredictable shock.

The English expression dominates the literature; in Portuguese, the concept circulates little and almost always by half. The missing half is precisely the more uncomfortable one: if the theory is even approximately right, most of what gets written every day about "where the market is heading" describes sequences of heads and tails in the vocabulary of intention.

Where the idea comes from

The intuition is older than it looks. In 1900, the French mathematician Louis Bachelier defended a thesis in Paris on price formation at the French exchange — and arrived, decades ahead of modern market statistics, at the conclusion that the movements behaved like pure chance. The thesis slept for half a century before being rediscovered; in the 1960s, Eugene Fama and others tested it with data and computers, and in 1973 Malkiel's book — A Random Walk Down Wall Street — carried the idea to the public.

The underlying argument is not mystical. If some simple rule linked a price's past to its future — "after three drops, it rises" — whoever knew the rule would act on it, and the very act of exploiting it would wear it away. What remains, after that continuous erosion, is a series whose past has already been read by everyone and has therefore stopped containing news. The random walk is less a claim about chaos and more a claim about competition: easy predictions do not survive in a contested arena.

Where the house ran into the theory

It is easy to agree with the random walk in theory and disrespect it in practice — the temptation to see omens in a chart spares no one, including those who do research. This house's antidote is procedural: the hypothesis is written before the test, and the result is published whatever it turns out to be.

One public episode illustrates the cost of that protocol. The third working paper in the house's series, The Tactical Ânima Index, tested whether extreme readings of a proprietary sentiment gauge carried a practical short-term edge — precisely the kind of pattern that, if the random walk is a good description, should not hold up. The published conclusion is negative: the edge under test does not hold. In numbers: the study is on Zenodo, with an active DOI and the adverse finding in the body of the text itself. The price series behaved as the theory dictates — indifferent to what the house's favorite indicator said about it.

Publishing that result cost less than it might seem, because the house's entire archive is built on the same renunciation: the Daily records states and precedents, never forecasts. When the theory and the editorial practice say the same thing, coherence stops being a virtue and becomes routine.

What the random walk does not say

The concept is frequently stretched beyond what it claims, and the stretched versions are easier to attack than the original.

The random walk does not say prices fail to rise over the long run — the formulation used in finance admits a drift, a background wind around which chance does its work. It does not say the market is irrational: the unpredictability of the next step is compatible with prices formed by perfectly attentive people. And it does not say the series has no structure at all — the literature has documented for decades that the agitation of prices has memory: turbulent periods tend to neighbor turbulent periods, even while direction stays unpredictable. What the theory denies is something narrower and harder: that the direction of the past contains the map of the direction of the future.

That is also why the debate stays alive. Researchers have documented departures from the random walk — medium-term regularities, overreactions, seasonal patterns — and the argument over which departures are real and which are mirages of multiple testing is one of the longest-running in the discipline. That argument has a name and an address: the efficient market hypothesis, the next step on this trail.

Frequently asked questions

If prices follow a random walk, is all analysis useless?

No. The theory limits one specific kind of analysis — extracting future direction from past direction. Questions about risk, value, regime and historical precedent remain standing; they do not depend on predicting the next step.

Has the random walk been proven?

No, and it hardly will be — empirical theories are not proven, they are tested. The data support the approximate version (predicting the next step is extraordinarily hard) and record small, unstable departures whose reality the literature still disputes.

Are the random walk and the efficient market the same thing?

Relatives, not twins. The random walk describes the statistical behavior of the series; the efficient market hypothesis proposes the economic explanation — prices incorporate available information. It is possible to construct efficient markets whose prices do not follow a strict random walk.

How does chance produce charts with such convincing "trends"?

Purely random sequences produce long streaks on the same side more often than intuition expects — the same mechanism that lets an honest coin string together six heads. The human eye was trained to find figures; the coin was not trained to hide them.

If the next step will not let itself be predicted, the question of cause remains: why would prices absorb everything that is known so quickly? The classic answer — and the fight around it — is in Efficient market hypothesis: the theory and its critics →

House readings: today's note, in the Daily · the precedents, in the Atlas.

Examining how much random walk lives inside a specific series is workbench material — the kind of exercise the house conducts on request.