The Efficient Markets Hypothesis explained

CM2 · Financial Engineering & Loss Reserving · 12 min read

What the hypothesis claims

A market is efficient with respect to some set of information if prices already reflect it, so that nobody can earn an excess return by trading on it.

Two things in that sentence do the work. "Already reflect" means the price has moved when the information arrived, not gradually afterwards. And "excess return" means return above what the risk taken deserves — so a strategy that earns more by taking more risk is no counter-example at all. A great deal of apparent evidence against efficiency dissolves once the return is adjusted for risk, and spotting that is the examinable skill.

The reason to expect it is competition rather than cleverness. If a piece of information implied a price, and the price were different, somebody would trade until it was not. Efficiency is a statement about how hard it is to find money lying on the floor in a market where many well-resourced people are looking.

The three forms

They are nested: each includes everything in the one before, so if a stronger form holds the weaker ones must too.

Weak form

Prices reflect all information in past prices and trading volumes.

What it rules out: technical analysis. If the whole of the price history is already in today's price, no chart pattern, moving average or momentum rule can produce excess returns. The implication is that price changes are essentially unpredictable from past price changes, which is why the weak form is tested by looking for structure in a return series.

Semi-strong form

Prices reflect all publicly available information: past prices, published accounts, announcements, economic data.

What it rules out: fundamental analysis of public data. Reading an annual report that anyone can read cannot give you an edge, because the price already contains what it says. The implication is that prices adjust to news immediately and fully, which is why the semi-strong form is tested by watching what a price does in the days after an announcement.

Strong form

Prices reflect all information, public and private.

What it rules out: profiting even from inside information. This form is the easiest to doubt, and the usual reasoning is simple: insider dealing is illegal in most markets precisely because it is profitable, and company directors trading their own shares have been found to earn excess returns. Few people defend the strong form, and a question asking you to assess it usually wants that said plainly.

How each form is tested

Weak form: look for predictability in returns. Compute the autocorrelation of a return series, or run a runs test, or backtest a technical rule net of dealing costs. The arithmetic matters less than the standard error, which is the point the worked example below is built around.

Semi-strong form: the event study. Pick an announcement, measure each day's abnormal return — the actual return less what the asset's risk would have predicted — and plot the cumulative abnormal return around the event:

abnormal return = actual return − expected return given the market move

Efficiency predicts a sharp jump on the announcement day and no drift afterwards. A continued climb for weeks after good news is "post-announcement drift", and it is evidence against, because it means the information was available and not yet in the price.

Strong form: look at the people with private information. Study directors' dealings in their own companies, or whether any group of investors persistently earns excess returns.

The anomalies, and what they are worth

A question asking for evidence wants a few of these with a judgement attached, not a list.

Calendar effects. A January effect in small companies, day-of-the-week patterns. Mostly small, mostly in illiquid stocks, and mostly gone once dealing costs are counted — and notably weaker since they were published, which is itself an efficiency argument.
Momentum. Winners over three to twelve months tend to keep winning. This is the most persistent and best documented anomaly, it is awkward for the weak form, and there is a real argument about whether it is a risk premium rather than a free lunch.
Overreaction and long-run reversal. Over three to five years, past losers outperform past winners, the opposite of momentum over short horizons.
Value effects. Shares on low price-to-book or low price-to-earnings ratios have historically outperformed. Whether that is mispricing or compensation for a risk the model does not capture is one of the central unresolved arguments in finance.
Excess volatility. Prices move far more than the eventual dividends justify, which is hard to reconcile with prices being driven by information about those dividends.
Bubbles and crashes. Hard to explain if prices always reflect fundamentals, though it is also hard to prove a bubble while it is happening rather than afterwards.

Two rejoinders cut across all of them, and the second is the one most often left out:

Data mining. Enough researchers testing enough rules on the same data will find patterns that are not there. An anomaly that was found by searching and has not held up out of sample is weak evidence.

The joint hypothesis problem. Measuring an "excess" return needs a model of what the normal return should have been. So every test of market efficiency is simultaneously a test of that model — usually the Capital Asset Pricing Model — and a rejection cannot tell you which of the two failed. This is why the hypothesis is so hard to settle, and saying so is often the most sophisticated thing an answer can contain.

What follows if it is broadly true

The practical consequences are what an actuarial exam is interested in:

Active management does not pay on average, and it cannot, because active managers collectively hold the market and charge fees for it. The argument for indexation is an efficiency argument.
Past performance is weak evidence of skill, because the record needed to distinguish skill from luck is far longer than anyone's career. The worked example puts a number on that and it is startling.
Market prices are the right starting point for a valuation. If a liability can be matched by traded assets, the market's price for them is the best available estimate of its value, which is the assumption behind market-consistent valuation.
The hypothesis is approximate, not absolute. Somebody has to do the analysis that makes prices informative, and they have to be paid for it. A perfectly efficient market would give nobody a reason to gather information, and would therefore not stay efficient.

Where marks are lost

Describing the forms without saying what each rules out. "Weak form means past prices" earns little. "Weak form means technical analysis cannot produce excess returns" is the answer.

Getting the nesting backwards. Strong implies semi-strong implies weak. So evidence against the weak form is evidence against all three, while evidence against the strong form says nothing about the other two.

Treating any outperformance as evidence against efficiency. It has to be excess of the risk taken, and it has to be statistically distinguishable from luck. Most published records fail the second test.

Forgetting dealing costs. A rule that earns 1% a year before costs and turns the portfolio over monthly earns nothing. An anomaly that cannot be traded profitably is not a violation of efficiency in any sense that matters.

Reading an event study as evidence against the semi-strong form because the price jumped. A jump on the day is efficiency working. It is the drift afterwards that would be evidence against.

Questions students ask

If markets are efficient, why does anyone do research?

Because the research is what makes them efficient, and whoever does it first is paid for it. The stable position is a market efficient enough that the marginal analyst earns just enough to cover their costs — so research is worth doing, and buying the output of it second-hand is not. That also explains why efficiency is better in large, heavily covered markets than in small ones.

Does behavioural finance disprove it?

It explains mechanisms by which prices could be wrong — overconfidence, anchoring, herding, loss aversion — and it documents that investors behave in those ways. What it has not established is that those biases are reliably exploitable after costs, which is the claim efficiency actually makes. The two literatures are better read as describing how prices get set and how well the result approximates fair value.

Which form do most people accept?

Broadly: the weak form is widely accepted with momentum as the standing objection; the semi-strong form is accepted as a good approximation in large liquid markets and doubted in small ones; the strong form is rejected by almost everyone. Answering a question with that gradation is better than taking a side.

What does it mean for an actuary rather than a fund manager?

Three things. Use market prices rather than your own view when valuing anything that can be matched by traded assets. Do not build a plan that depends on beating the market. And be sceptical of a track record, because the arithmetic below shows how little most records prove.

A worked example

Three short pieces of arithmetic, one for each form. Every figure is invented for this example — there is no real fund, share or announcement here.

Weak form: is there a pattern in these returns?

Twelve monthly returns, in per cent:

1.2, −0.8, 2.1, 0.4, −1.5, 1.8, 0.2, −0.6, 1.1, 0.9, −0.3, 1.4

They alternate up and down so persistently that the eye sees a rule: a good month is followed by a bad one. Test it with the lag-one autocorrelation.

mean = 5.9 / 12 = 0.4916667
∑(r_t − mean)² = 13.7091667
∑(r_t − mean)(r_t+1 − mean) = −7.0842361
r₁ = −7.0842361 / 13.7091667 = −0.5168

An autocorrelation of −0.52 looks decisive. Now the standard error. If returns were independent, the autocorrelation of a sample of n has a standard error of about 1/√n:

standard error = 1 / √12 = 0.2887
|r₁| / standard error = 0.5168 / 0.2887 = 1.79

Below two. The pattern is not statistically significant. A sample of twelve independent returns would produce an autocorrelation of −0.52 or beyond reasonably often, by chance alone, and twelve observations simply cannot distinguish a real alternation from a run of coincidence.

This is the lesson of the weak-form tests in one calculation, and it is worth more than the arithmetic. For a pattern of 0.10 — a size that would be economically interesting — to clear two standard errors you need (2/0.10)² = 400 observations. Serious weak-form studies use thousands, and that is why: anything less finds patterns in noise. The eye is an unreliable instrument here and the standard error is the corrective.

Semi-strong form: an event study

A company with a beta of 1.2 announces unexpectedly strong results. On the day, the market rose 0.4% and the share rose 6.1%.

expected move = 1.2 × 0.4 = 0.48%
abnormal return = 6.1 − 0.48 = +5.62%

A large, immediate jump. On its own that is consistent with efficiency, not against it: the price moved when the news arrived, which is what the hypothesis predicts. The test is what happens next.

Day	Share	Market	Abnormal return
+1	+0.05%	+0.10%	−0.07%
+2	−0.10%	−0.20%	+0.14%
+3	+0.08%	+0.05%	+0.02%
+4	−0.03%	+0.15%	−0.21%
+5	+0.02%	−0.05%	+0.08%
Cumulative	—	—	−0.04%

Four hundredths of a percentage point over five days, in the opposite direction to the news. No drift. The information was absorbed on the day and there was nothing left to trade on, which supports the semi-strong form.

Contrast what the other answer would look like. Abnormal returns of +0.9%, +0.8%, +0.7% and so on, cumulating to several points over a fortnight, would say the market took weeks to finish reacting to a public announcement — and anyone who bought on the day would have earned an excess return from information everybody had. That is post-announcement drift, and it is the main standing piece of evidence against the semi-strong form.

Strong form, or at least skill: is this manager any good?

A fund has beaten its benchmark by 1.8 percentage points a year over 12 years. The standard deviation of its annual relative return — its tracking error — is 6.0 percentage points.

standard error of the mean = 6.0 / √12 = 1.7321
t = 1.8 / 1.7321 = 1.04

A t statistic of 1.04, with a two-sided p-value of about 0.30. Twelve consecutive years of beating the benchmark by nearly two points a year is not statistically distinguishable from luck.

That result surprises people, so it is worth saying what it does and does not mean. It does not mean the manager is unskilled. It means this record cannot tell you either way, and the reason is that 6% of annual noise swamps 1.8% of annual signal over any length of time a person can be observed for.

How long would it take?

years for t = 2: (2 × 6.0 / 1.8)² = 6.6667² = 44.4 years

Forty-five years at this level of outperformance, and the fund would have to keep the same strategy, the same manager and the same tracking error throughout. If the alpha were 3.0 points a year instead, it would take 16 years — still longer than most managers' tenure.

That arithmetic is the strongest practical argument in the whole topic, and it needs no view on whether markets are efficient. Even if skill exists, track records of normal length cannot identify it, so selecting managers on past returns is selecting mostly on noise. The quickest way to see it is the opposite question: for a 1.8% alpha to be significant over 12 years, the tracking error would have to be below 3.1 points a year, about half what this fund runs. The only records that prove anything are the ones that barely took any risk.

Where this fits in CM2

This page explains one idea from CM2 Financial Engineering & Loss Reserving. The full CM2 syllabus, with what each part is examined on, sits on the course page, and past-paper style mock exams with full solutions are where you find out whether the idea has stuck under time pressure.

The Efficient Markets Hypothesis: the three forms, and how each one is tested