Economic Modelling · Rational expectations theory and the efficient markets hypothesis

Testing Market Efficiency and Empirical Evidence

Updated 11 October 2026 · Fact-checked

Testing market efficiency means checking whether prices already reflect a given information set. You do this with event studies (abnormal returns around news), tests of return predictability (autocorrelation, trading rules) and fund performance studies. Every test is a joint test of efficiency and the model of expected returns used.

Understand Testing Market Efficiency and Empirical Evidence

The efficient markets hypothesis (EMH) says prices reflect available information. It comes in three forms. Weak form: prices reflect past price and volume data. Semi-strong form: prices reflect all public information. Strong form: prices reflect all information, including private information. You cannot test the claim directly. You test what it implies.

An event study tests the semi-strong form. You pick an event, such as a results announcement or a dividend change. You compute the abnormal return, which is the actual return minus the return expected from a model such as the market model or CAPM. You add abnormal returns over an event window to get the cumulative abnormal return (CAR). In an efficient market, the price jumps at the announcement and the abnormal return afterwards is about zero. A drift after the announcement suggests a slow reaction. A rise before the announcement suggests leakage or anticipation, which is not a failure if the event was expected.

Tests of return predictability mainly address the weak form. You test whether returns are serially correlated, which a random walk rules out. You also test whether trading rules based on past prices, such as moving averages in technical analysis, beat buy-and-hold after transaction costs. Other tests check whether variables such as dividend yield, size, or value predict returns. Findings of this kind are called anomalies, for example size, value, momentum and January effects.

Fund performance studies test the semi-strong form from another side. If markets are efficient, active managers should not beat a suitable benchmark after fees on a consistent basis. The usual evidence is that, on average, active funds do not beat their benchmarks after costs, and past winners do not reliably repeat. Strong-form tests look at insiders, whose trades often do earn abnormal returns.

The key problem is the joint hypothesis problem. An abnormal return means either the market is inefficient or your expected-return model is wrong. You can never separate the two. Other issues are data mining, transaction costs, thin trading and risk that is not captured by the model. Be balanced in your answer: the evidence broadly supports weak and semi-strong efficiency in major markets, with notable anomalies, and is weakest for strong form.

Key rules to remember

Abnormal return: ARₜ = Rₜ − E(Rₜ); Actual return minus expected return from a model such as the market model or CAPM.
Market model expected return: E(Rₜ) = α + β × R_mₜ; α and β are estimated over a period before the event, called the estimation window.
Cumulative abnormal return: CAR = Σ ARₜ over the event window; Sum of abnormal returns from the start to the end of the window.
Average abnormal return across N firms: AARₜ = (1 ÷ N) × Σ ARᵢₜ; Averaging across firms reduces noise unrelated to the event.
Autocorrelation at lag k: ρₖ = Cov(Rₜ, Rₜ₋ₖ) ÷ Var(Rₜ); Under a random walk with stationary returns, ρₖ = 0 for k ≥ 1. Compare with the approximate 95% band ±1.96 ÷ √n.
Random walk: Pₜ = Pₜ₋₁ + εₜ, with εₜ independent; Price changes are unpredictable from past changes. This is consistent with weak form efficiency but is not identical to it.

How to solve Testing Market Efficiency and Empirical Evidence questions

Use this approach for any question on testing efficiency or interpreting evidence.

1Identify which form of efficiency is being tested: weak, semi-strong or strong.
2State the information set and the test: event study, autocorrelation or trading rule, or fund performance.
3State the expected-return model used (market model, CAPM, benchmark) and the estimation window.
4Compute abnormal returns as actual minus expected, then sum them to a CAR if asked.
5Compare with what efficiency predicts: a jump at the announcement and no drift afterwards, zero autocorrelation, no excess return after costs.
6Conclude, and say whether the result is consistent or inconsistent with that form.
7Add the caveats: joint hypothesis problem, transaction costs, data mining and risk adjustment.

Quickest way: Match test to form, then check the joint hypothesis

When to use it: Use for MCQs and short written parts that ask which form a test addresses or what a result implies.

Past prices or trading rules: weak form.
Public announcements or fund managers using public data: semi-strong form.
Insiders or private information: strong form.
For numbers, compute AR = actual − expected, then add up.
Always finish with one line on the joint hypothesis problem.

Common mistakes in Testing Market Efficiency and Empirical Evidence

Saying an abnormal return proves the market is inefficient.
Students forget that the expected-return model could be wrong.
Fix: State that every test is a joint test of efficiency and the pricing model.
Treating a price rise before an announcement as always showing inefficiency.
Students ignore anticipation and leakage.
Fix: Say the event may have been expected, and judge efficiency by whether drift continues after the news becomes public.
Using the raw return instead of the abnormal return in an event study.
Students skip the step of subtracting the expected return.
Fix: Always compute actual minus model return first, then sum to CAR.
Matching technical analysis to the semi-strong form.
Students mix up past prices with all public information.
Fix: Technical analysis uses past prices only, so it tests the weak form.
Ignoring transaction costs and fees when judging a trading rule or fund.
Gross returns look impressive.
Fix: Compare net returns after costs and risk adjustment with the benchmark.
Stating that zero autocorrelation proves the market is efficient.
Students treat random walk and efficiency as the same.
Fix: Zero autocorrelation is consistent with weak form efficiency but is not proof, since nonlinear patterns or other information could remain.

Worked examples

Example 1

A share has estimated market model α = 0.1% per day and β = 1.2. Over a three-day window around a results announcement, the share returns 2.0%, 1.0% and 0.2%, while the market returns 0.5%, 0.5% and −0.5%. Calculate the CAR and comment.

Show the solution

Expected return day 1 = 0.1 + 1.2 × 0.5 = 0.7%.
Expected return day 2 = 0.1 + 1.2 × 0.5 = 0.7%.
Expected return day 3 = 0.1 + 1.2 × (−0.5) = −0.5%.
AR day 1 = 2.0 − 0.7 = 1.3%.
AR day 2 = 1.0 − 0.7 = 0.3%.
AR day 3 = 0.2 − (−0.5) = 0.7%.
CAR = 1.3 + 0.3 + 0.7 = 2.3%.

Answer: CAR = 2.3%. The positive abnormal returns on days 2 and 3 after the jump on day 1 suggest a slow reaction, which would be inconsistent with semi-strong efficiency. One firm is weak evidence, so average across many firms and remember the joint hypothesis problem.

Example 2

A researcher tests 400 monthly returns on an index and finds the lag-1 autocorrelation is 0.12. Is this significant at about the 5% level, and what does it imply for weak form efficiency?

Show the solution

Under the null of no autocorrelation, the standard error is approximately 1 ÷ √n.
√400 = 20, so the standard error = 1 ÷ 20 = 0.05.
The 95% band is ±1.96 × 0.05 = ±0.098.
The estimate 0.12 is outside ±0.098, so it is significant at about the 5% level.
Interpret: there is evidence of positive serial correlation, which goes against a pure random walk.

Answer: Yes, 0.12 exceeds the band of ±0.098, so it is significant. This is evidence against a pure random walk. But a trading rule must still earn excess return after costs and risk adjustment before you can say weak form efficiency fails in a practical sense.

Exam tips

Always name the form of efficiency being tested before you comment on evidence.
Show the abnormal return formula and the model used, even for short numerical parts.
End every discussion answer with the joint hypothesis problem and one more limitation.
For evidence questions, give both sides: broad support for weak and semi-strong forms, plus named anomalies such as size, value and momentum.
Link fund performance results to implications for passive versus active investing, and keep your claims general rather than quoting figures you cannot verify.

Practice questions from Rational expectations theory and the efficient markets hypothesis

Testing Market Efficiency and Empirical Evidence in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Testing Market Efficiency and Empirical Evidence: frequently asked questions

How do you test the efficient market hypothesis with an event study?

Choose an event and a window. Estimate a model of normal returns, compute abnormal returns as actual minus expected, and sum them to a CAR. If prices adjust fully at the announcement and show no drift afterwards, that supports semi-strong efficiency.

What is the joint hypothesis problem?

Every test of efficiency needs a model of expected returns. If you find abnormal returns, either the market is inefficient or the model is wrong. You cannot tell which from the test alone.

Does the random walk hypothesis mean the market is efficient?

Not exactly. A random walk is consistent with weak form efficiency because past price changes cannot predict future ones. But efficiency is about information being reflected in prices, and it can hold in models that are not strictly random walks.

What evidence is there against efficient markets?

Anomalies such as size, value, momentum and calendar effects are the common examples. Critics say they show inefficiency. Defenders say they may reflect risk, data mining or costs that remove profits after trading.