Efficient Market Hypothesis: formula sheet

Key formulas

Core EMH statement

Market price = Intrinsic value, given all available information

Price is an unbiased estimate of value. Errors can occur but are random, not systematic.

Price change under EMH

Price change = Expected return + Unexpected return from new information

Only the unexpected part is driven by news, and news is unpredictable.

Abnormal return

Abnormal return = Actual return − Expected (risk-adjusted) return

Under EMH, abnormal return averages zero over time and cannot be earned consistently.

Conditions for efficiency (checklist)

Free information + Many participants + Low costs + Rational investors

Use this as the standard list of assumptions in written answers.

Weak form

Prices reflect: past prices and volumes

Technical analysis cannot earn consistent abnormal returns. Fundamental analysis and insider information may still work.

Semi-strong form

Prices reflect: past data + all public information

Both technical and fundamental analysis of public data fail. Insider information may still work.

Strong form

Prices reflect: past data + public + private information

Nothing works for abnormal returns, not even insider information.

Nesting of forms

Strong ⊃ Semi-strong ⊃ Weak

Strong form efficiency implies the other two. The reverse does not hold.

Abnormal return

Abnormal return = Actual return − Expected (risk-adjusted) return

Used to test whether information led to returns beyond what risk explains.

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.

Random walk (price change form)

Pₜ = Pₜ₋₁ + expected return + random error (εₜ)

The error term is unpredictable and uncorrelated with past errors. Correlation between successive price changes is close to zero.

Weak form efficiency

Prices reflect all past price and volume data

Technical analysis cannot give excess returns. Fundamental analysis and insider information might.

Semi-strong form efficiency

Prices reflect all publicly available information

Both technical and fundamental analysis of public data fail. Insider information may still help.

Strong form efficiency

Prices reflect all information, public and private

Even insiders cannot earn abnormal returns.

Abnormal return

Abnormal return = Actual return − Expected return (as per risk-return model)

EMH says abnormal returns cannot be earned consistently after adjusting for risk and costs.

Abnormal return

Abnormal return = Actual return − Expected (required) return

Expected return comes from a model such as CAPM. An anomaly means persistent non-zero abnormal returns.

CAPM expected return

E(R) = Rf + β × (Rm − Rf)

Used to test whether a pattern gives returns beyond what risk explains.

Joint hypothesis rule

Test of efficiency = Test of market + Test of pricing model

A rejection may mean the model is wrong rather than the market being inefficient.

Quick revision

• An efficient market is one where prices fully reflect available information.
• In an efficient market, new information is absorbed quickly, so price changes are unpredictable.
• Weak form: prices reflect all past price and volume data; technical analysis cannot earn abnormal returns.
• Semi-strong form: prices reflect all public information; fundamental analysis cannot earn abnormal returns.
• Strong form: prices reflect all information, public and private; even insiders cannot earn abnormal returns.
• Each stronger form includes the information of the weaker form before it.
• Random walk: successive price changes are independent, so past prices do not predict future prices.
• Technical analysis studies past prices; fundamental analysis studies financial and economic data to estimate intrinsic value.
• If the weak form holds, charts are of no use; if the semi-strong form holds, published financial analysis is also of no use.
• Anomalies are patterns that seem to contradict EMH, such as calendar effects and size effects.
• Critics argue that investors are not always rational, which behavioural finance tries to explain.
• Passive investing, such as index funds, is the practical outcome if markets are efficient.

Common mistakes

• Saying an efficient market means prices never change. Fix: Write that prices change whenever new information arrives, and they change quickly.
• Claiming prices are always equal to true value. Fix: Say prices are unbiased estimates. Errors are random, not systematic.
• Saying weak form means prices are weak or inefficient. Fix: Weak refers to the small information set (past prices only). The weak form is the least demanding condition because it covers the smallest information set.
• Treating public announcements as weak-form information. Fix: Weak form covers only past prices and volumes. Results, dividends and mergers are public information and belong to semi-strong.
• Saying a positive serial correlation proves the market is efficient. 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. Fix: Always subtract the expected return from the market model or CAPM. Only the abnormal part reflects the news.
• Saying random walk means prices are random or irrational. Fix: Say that price changes are unpredictable because they respond to new information. Prices themselves reflect available information.
• Saying EMH makes fundamental analysis useless for everyone. Fix: Say that analysts' work is what makes prices efficient. EMH says it cannot earn consistent excess returns after costs once prices adjust.
• Saying an anomaly proves that EMH is false. Fix: Mention the joint hypothesis problem and that many anomalies fade or vanish after costs.
• Linking the January effect to strong-form efficiency. Fix: Link calendar patterns to weak form, since they use past data or timing only.

Exam tips

• Write the definition and the full list of assumptions every time. These are easy marks.
• In case questions, tie each assumption to a fact in the scenario before concluding.
• Avoid absolute words such as 'always' and 'never'. Use 'consistently' and 'on average'.
• For recommendations, link the conclusion to strategy: passive investing if efficient, active analysis if inefficient.
• In MCQs, watch for options that confuse efficiency with constant prices or guaranteed profits.
• Always name the information set first, then the form. Examiners reward this order.
• Link each form to the analysis it challenges: weak to technical, semi-strong to fundamental, strong to insider information.
• For case-based MCQs, underline whether the information is past, public or private before looking at the options.