Abnormal Return

An abnormal return is the difference between the return an investment actually earned over a period and the return it was expected to earn, given its risk and what the wider market did. A positive abnormal return means the asset beat expectations; a negative one means it fell short. Researchers, fund analysts, regulators and courts use the measure to isolate the effect of a specific event, such as an earnings surprise or a takeover bid, from ordinary market movement.

The concept depends on a model of "normal" performance, most often the capital asset pricing model or a simple market model. It is closely related to alpha, which describes a manager's average abnormal return over time, and to the efficient market hypothesis, which predicts that abnormal returns should be short-lived and unpredictable.

Suppose the whole class does better in an exam because the paper was easy. A student whose mark rose by the same amount as everyone else did nothing special. A student whose mark rose much more than the class did something unusual. Abnormal return asks the same question about investments: how much of a gain or loss was simply the tide lifting all boats, and how much belonged to this particular asset?

To answer it, analysts first estimate what the asset "should" have done on a normal day given how the market moved, then compare that with what really happened. The gap is the abnormal part, and it is often where the news is.

The basic calculation is:

Under the CAPM the expected return is:

• $R_{\text{actual}}$ is the asset's realised return over the period.
• $E(R)$ is the expected return from the chosen model.
• $R_f$ is the risk-free rate.
• $\beta$ is the asset's beta, its sensitivity to market moves.
• $R_m$ is the return on a market benchmark.

Take a share with a beta of 1.2 that returned 8% in a month when the market returned 5% and the risk-free rate was 2%. Expected return is 2% + 1.2 × (5% − 2%) = 2% + 3.6% = 5.6%. The abnormal return is 8% − 5.6% = 2.4%. Summing daily abnormal returns over several days gives the cumulative abnormal return (CAR), a standard figure in event studies.

The event study method, set out in a 1969 paper by Eugene Fama, Lawrence Fisher, Michael Jensen and Richard Roll on stock splits, measures abnormal returns in a short window around an announcement. It has many applications:

• Corporate events. Researchers measure how shares react to earnings releases, dividend changes and mergers and acquisitions.
• Securities litigation. Experts in US fraud cases use abnormal returns after a corrective disclosure to estimate investor losses.
• Market surveillance. Unusual abnormal returns before public news can point regulators towards possible insider trading.
• Fund evaluation. Persistent positive abnormal returns, adjusted for risk, suggest skill rather than luck.
• Crypto research. Studies apply the same method to token listings, exchange hacks and regulatory news, usually using a broad crypto index as the market return.

Abnormal returns arise when new information changes investors' view of an asset's future cash flows or risk. Reported earnings per share that beat forecasts, a surprise bid, a lawsuit or a product failure can all move a share beyond what the market alone explains. Less liquid assets can also show abnormal returns from order flow rather than news, as a large buyer or seller pushes the price. In efficient markets the reaction should happen quickly; slow drifts after news, such as the well-documented tendency for prices to keep moving after earnings surprises, are treated as anomalies that challenge pure efficiency.

An abnormal return is only as good as the model behind the expected return. If the model leaves out a relevant risk factor, apparent outperformance may simply be compensation for that risk, a problem known as the joint hypothesis problem. Results also depend on the choice of benchmark, the estimation window used to calculate beta and the length of the event window. Overlapping events, thin trading and extreme volatility can blur the signal, which is especially common in small-cap stocks and crypto assets. For these reasons analysts usually test significance statistically rather than reading a single figure, and they compare results across several models to see whether the finding holds.