Market Efficiency (The EMH)

The efficient-market hypothesis (EMH) is the intellectual backdrop against which every alpha claim is judged. A strategy that works is, by definition, a claim that the market was not efficient with respect to some information. Understanding the EMH precisely, including the two theorems that make it slippery, is what separates a trader who can defend an edge from one who is fooling themselves.

The three forms

Fama's taxonomy classifies efficiency by the information set $\Omega_t$ that prices already reflect:

• Weak form: prices reflect all past price and volume information. No strategy using only historical returns can earn risk-adjusted profits, technical analysis and pure price-based prediction are worthless.
• Semi-strong form: prices reflect all publicly available information, earnings, filings, news. Prices adjust to public announcements instantly and without bias, so fundamental analysis of public data earns nothing.
• Strong form: prices reflect all information, public and private. Even insiders cannot profit. Almost nobody believes this literally; it is a limiting benchmark.

Each form nests the previous one. The empirical program of the last fifty years has been to test how far up this ladder real markets sit, and the honest answer is "somewhere between weak and semi-strong, with documented exceptions."

The martingale statement

The formal content of weak-form efficiency is that discounted prices follow a martingale with respect to the information set. If $P_t$ is price and $\Omega_t$ the information available at $t$, efficiency (with risk-neutral pricing and no dividends) says

$\mathbb{E}[P_{t+1} \mid \Omega_t] = P_t,$

so expected returns are unforecastable from $\Omega_t$: $\mathbb{E}[r_{t+1} \mid \Omega_t] = 0$ in excess of the required return. Note the martingale property is weaker than the random walk, it permits time-varying volatility and dependence in higher moments (volatility clusters!), it only forbids forecastable drift. A common student error is to equate efficiency with i.i.d. returns; efficiency constrains the conditional mean, not the whole distribution.

The joint-hypothesis problem

Here is the deep issue Fama himself stressed: efficiency is never testable on its own. To ask whether a return is "abnormal" you must first specify what return the asset should earn, a model of equilibrium expected returns (CAPM, The Fama-French Factor Models, a consumption model). So every test of efficiency is a joint test of

$H_0: \text{market is efficient} \quad \textbf{and} \quad \text{the asset-pricing model is correct.}$

When you find a predictable pattern in risk-adjusted returns, you cannot tell whether the market is inefficient or your risk model is wrong. A value premium might be a free lunch (inefficiency) or compensation for a risk the CAPM omits (bad model). This is why the debate between the "risk" camp and the "behavioral" camp over anomalies is, in principle, unresolvable by returns data alone, and why the Factor Investing literature is really a search for the right risk model as much as for alpha.

Grossman-Stiglitz: efficiency cannot be perfect

If prices perfectly reflected all information, then the price itself would reveal everything a costly analyst could learn. But information gathering is costly, so no rational agent would pay to acquire information they could read for free off the price. If no one gathers information, prices cannot reflect it, a contradiction. Grossman and Stiglitz (1980) formalized this: a perfectly informationally efficient market is impossible.

The equilibrium resolution is that markets are nearly efficient with just enough inefficiency to compensate the informed. In their noisy rational-expectations model, prices reveal a signal contaminated by supply noise $z$:

$p = \lambda\big(s - \kappa z\big),$

so the price is informative but not fully revealing. Informed traders earn a return on information that exactly offsets its cost in equilibrium; the fraction of traders who choose to become informed adjusts until net-of-cost profits are equalized. The practical reading for a quant: alpha is the equilibrium wage paid to the people who keep prices efficient. Edges exist, they are bounded by the cost of extracting them, and they decay as more capital learns them (Alpha Decay).

Worked example: an event study

The canonical semi-strong test is an event study. Around an event date $\tau$ (say an earnings surprise), compute abnormal returns $AR_{i,t} = r_{i,t} - \hat{\mathbb{E}}[r_{i,t}]$, where the expectation comes from a market model $r_{i,t} = \hat\alpha_i + \hat\beta_i m_t$ estimated in a pre-event window. Cumulate across the window and average across events:

$CAR(\tau_1, \tau_2) = \frac{1}{N}\sum_{i=1}^N \sum_{t=\tau_1}^{\tau_2} AR_{i,t}.$

Efficiency predicts the CAR jumps at the announcement and is flat afterward, no drift you could trade. The famous violation is post-earnings-announcement drift (PEAD): CARs keep sliding in the direction of the surprise for months, a persistent, tradeable anomaly that has survived decades of scrutiny. PEAD is the cleanest single piece of evidence that the semi-strong form is not literally true.

Failure modes and limits to arbitrage

Documented anomalies, momentum, PEAD, value, the closed-end fund puzzle, index-inclusion pops, show markets are not frictionlessly efficient. But efficiency is defended by limits to arbitrage (Shleifer-Vishny): mispricings persist because correcting them is risky and capital-constrained. Noise-trader risk means a short can move against you before it converges, and if that happens during a drawdown your investors redeem at the worst time. So "the price is wrong" and "you can profitably fix it" are different statements, the gap between them is where real trading lives.

• Anomalies may be data-mined. With thousands of researchers testing signals, some "edges" are pure multiple-testing artifacts (see Factor Investing on the factor zoo).
• Anomalies decay after publication. McLean and Pontiff found average post-publication decay of ~ 30–60%, consistent with arbitrageurs trading them away, efficiency reasserting itself.
• Risk vs. mispricing is genuinely ambiguous. The joint-hypothesis problem means you can rarely prove which one you found.

In interviews

Be able to state the three forms crisply and give a canonical test for each (autocorrelation/variance-ratio for weak, event studies for semi-strong, insider-return studies for strong). The two questions that separate strong candidates: "Why can't you test market efficiency directly?", the joint-hypothesis problem, every test presupposes a model of expected returns, and "If markets were perfectly efficient, would anyone do research?", no, which is Grossman-Stiglitz, and it implies markets sit at an equilibrium level of slight inefficiency that pays for the information gathering. A good closer: efficiency is best treated not as true/false but as a null hypothesis you are constantly, and profitably, trying to reject at the margin. See Statistical Arbitrage for what near-efficiency looks like in practice.