Strategic Financial Management · Efficient Market Hypothesis

Testing Market Efficiency: Empirical Evidence for the EMH

Updated 11 October 2026 · Fact-checked

Tests of market efficiency check whether prices reflect information. Weak form uses past prices: serial correlation, runs test and filter rules. Semi-strong form uses event studies of abnormal returns around public news. Strong form checks whether insiders or fund managers earn abnormal returns. If abnormal returns are not significantly different from zero, the form holds.

Understand Testing Market Efficiency: Empirical Evidence

The Efficient Market Hypothesis (EMH) says prices fully reflect available information. A claim like this must be tested. Each form of efficiency has its own information set, so each has its own test.

Weak form says prices already reflect all past price and volume data. If true, past prices cannot predict future prices, and price changes look like a random walk. So the tests look for patterns in past price changes: serial correlation, the runs test and filter rules.

Semi-strong form says prices also reflect all public information, such as results, dividends, splits and policy news. The main test is the event study. You pick an event, measure the stock's return around it, subtract the return the stock was expected to earn, and call the difference the abnormal return. If the price adjusts fully on the announcement day and shows no drift afterwards, the market is semi-strong efficient.

Strong form says prices reflect all information, including private information. Tests study the returns of corporate insiders and the performance of professional fund managers. If insiders earn abnormal profits, strong form fails.

The general empirical picture in developed markets: weak form is mostly supported, semi-strong form is largely supported with some exceptions (anomalies), and strong form is generally rejected because insiders can earn abnormal returns. Results differ across markets and periods, so write findings as general evidence, not as certainties.

Key rules to remember

Serial correlation coefficient (lag 1): r = Σ(Rt − R̄)(Rt−1 − R̄) ÷ Σ(Rt − R̄)²; Correlation between today's return and the previous return. A value near 0 supports weak form. A significantly positive or negative value suggests a pattern.
Abnormal return: AR = Actual return − Expected return; Expected return comes from a market model or CAPM: Expected = Rf + β(Rm − Rf), or α + β × Rm.
Cumulative abnormal return: CAR = Σ AR over the event window; A jump on the event day and a flat CAR afterwards supports semi-strong efficiency. A continued drift after the event suggests slow adjustment.
Expected number of runs: E(R) = (2 × n1 × n2 ÷ (n1 + n2)) + 1; n1 = number of positive changes, n2 = number of negative changes. Compare with actual runs. Far fewer runs than expected means momentum; far more means reversal.
Filter rule: Buy when price rises x% above its last low; sell when it falls x% below its last high; Compare net return after transaction costs with buy-and-hold. If the filter does not beat buy-and-hold, weak form is supported.

How to solve Testing Market Efficiency: Empirical Evidence questions

Use this method for any question on tests of efficiency, theory or numerical.

1Identify which form is being tested from the information used: past prices (weak), public news (semi-strong), private information (strong).
2Name the matching test: serial correlation, runs test or filter rule for weak; event study for semi-strong; insider or fund manager returns for strong.
3State what the test measures and what result would mean efficiency (no pattern, zero abnormal return, no excess profit after costs).
4If numbers are given, compute the statistic: correlation, runs count, or abnormal return = actual − expected.
5Compare the result with the benchmark: zero correlation, expected runs, buy-and-hold return, or zero abnormal return.
6Conclude clearly: the form is supported or rejected, and mention transaction costs where a trading rule is involved.
7Add the general empirical finding in one line, noting results vary by market.

Quickest way: Match information set to test

When to use it: For MCQs and short theory questions asking which test fits which form, or what a result implies.

Past prices only: think serial correlation, runs, filter rules, all weak form.
News or announcements: think event study, abnormal return, semi-strong.
Insiders or mutual fund managers: think strong form.
Result near zero or no excess return after costs: efficient. Predictable pattern or consistent excess return: not efficient.
For event studies, remember AR = actual − expected, and check for price movement before and after the event.

Common mistakes in Testing Market Efficiency: Empirical Evidence

Saying a positive serial correlation proves the market is efficient.
Students link correlation tests with a random walk and mix up the direction.
Fix: Efficiency means correlation close to zero. A clearly positive or negative value shows predictability and goes against weak form.
Using raw return instead of abnormal return in an event study.
The stock return jumps on the announcement, so it looks like the answer.
Fix: Always subtract the expected return from the market model or CAPM. Only the abnormal part reflects the news.
Ignoring transaction costs when judging a filter rule.
Gross profit looks attractive.
Fix: Compare the net return after brokerage and other costs with buy-and-hold. Efficiency is rejected only if the rule beats it after costs.
Placing the event study under weak form.
Both use price data.
Fix: Event studies test reaction to public information, so they belong to semi-strong form. Weak form uses only past prices.
Reading a runs test the wrong way round.
Students forget what runs signal.
Fix: Fewer actual runs than expected means trends continue (positive dependence). More runs than expected means reversals. Roughly equal supports randomness.
Stating that evidence rejects EMH everywhere.
Anomalies are remembered more than the main findings.
Fix: State that evidence generally supports weak form, largely supports semi-strong with anomalies, and generally rejects strong form.

Worked examples

Example 1

A stock's price changes over 11 days show 6 rises (+) and 5 falls (−) in this order: + + − − + − + + − + −. Count the runs, compute the expected number of runs and comment on weak form efficiency.

Show the solution

Group the sequence into runs of identical signs: (++) (−−) (+) (−) (++) (−) (+) (−).
That gives 8 actual runs.
n1 = 6 rises, n2 = 5 falls, n = 11.
Expected runs = (2 × 6 × 5 ÷ 11) + 1 = (60 ÷ 11) + 1 = 5.45 + 1 = 6.45.
Actual runs (8) are higher than expected (6.45), which hints at slight reversal, but the gap is small and the sample is tiny.
Without a significance test on a larger sample, you cannot reject randomness.

Answer: Actual runs are 8 against an expected 6.45. The difference is small and the sample is too short to be significant, so the data do not clearly reject weak form efficiency.

Example 2

Company X announced a bonus issue on Day 0. Its beta is 1.2, the risk-free rate is 6% a year and the expected market return is 12% a year. Treat the expected returns as applying to the event period. On Day 0 the stock returned 11% and the market had a 12% return. On Day 1 the stock returned 7% and, in a similar way, the market returned 12%. Compute the abnormal return on each day and the CAR, then comment on semi-strong efficiency.

Show the solution

Expected return = Rf + β(Rm − Rf) = 6 + 1.2 × (12 − 6) = 6 + 7.2 = 13.2%.
Day 0 abnormal return = 11 − 13.2 = −2.2%.
Day 1 abnormal return = 7 − 13.2 = −6.2%.
CAR = −2.2 + (−6.2) = −8.4%.
Both days show negative abnormal returns, so the stock fell short of its expected return after the announcement.
This is a stylised use of annual expected returns for the event days, as the question states.

Answer: AR on Day 0 = −2.2%, on Day 1 = −6.2%, CAR = −8.4%. A negative abnormal return that continues after the announcement day suggests slow adjustment, which would go against semi-strong efficiency. In a real study you would use daily expected returns and test the CAR for significance.

Exam tips

Write the information set first (past prices, public, private). It earns the link marks and sets up the right test.
In numerical questions, show the expected return calculation line before the abnormal return. Marks are given for the method.
Always end with a conclusion sentence: supported or rejected, and why.
For theory answers, give one test and one finding for each form in a short table-like list of bullets.
Do not mix this topic with anomalies. Keep January effect and size effect for the anomalies topic unless the question asks.

Practice questions from Efficient Market Hypothesis

Testing Market Efficiency: 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.

Actuarial Core Principles (IAI)Testing Market Efficiency and Empirical Evidence

Testing Market Efficiency: Empirical Evidence: frequently asked questions

Which tests are used for weak form efficiency?

The common tests are serial correlation, the runs test and filter rules. All use past price changes. If they show no exploitable pattern, weak form is supported.

What is an event study in semi-strong form testing?

An event study measures a stock's abnormal return around a public announcement, such as results or a bonus issue. Abnormal return is actual return minus expected return. If prices adjust fully at the announcement and do not drift afterwards, the market is semi-strong efficient.

How is the filter rule test interpreted?

You follow a rule like buying after a x% rise from a low and selling after a x% fall from a high. If the net return after transaction costs does not beat buy-and-hold, weak form is supported.

How is random walk related to EMH?

A random walk means price changes are unpredictable and independent of past changes. Weak form efficiency implies this, because past prices already carry no usable information. The tests of weak form are essentially tests of random walk.

What does empirical evidence say about the three forms?

Evidence in developed markets generally supports weak form and largely supports semi-strong form, with some anomalies. Strong form is generally rejected, since insiders can earn abnormal returns. Results vary by market and period.