An abnormal return is the difference between the actual return of an investment and its expected return, indicating unusually large profits or losses over a specified period. We shall look in detail about Abnormal return – its definition, calculation and applications.
Abnormal Return
Definition
An Abnormal Return (AR) is the difference between an asset’s actual return and its expected (or “normal”) return over a given period.
Formally:
AR_i=R_i−E(R_i)
where:
- 𝑅_𝑖 = Actual return of asset i
- E(R_i) = expected or normal return (based on a model or benchmark)
Abnormal return represents how much better or worse an investment performed compared to what we would have expected given its risk profile or market conditions.
- Positive AR: The asset outperformed expectations.
- Negative AR: The asset underperformed expectations.
AR Applications – How It’s Used
- Event Studies (common in finance research): Analysts measure ARs around corporate events such as earnings announcements, mergers, dividend changes, etc., to determine market reaction.
- Example: If a firm announces a merger and its stock jumps 5% more than expected, that’s a +5% abnormal return.
- Portfolio Performance Evaluation: ARs can assess active fund managers — did they beat the benchmark (e.g., S&P 500) after adjusting for risk?
- Market Efficiency Testing: Persistent abnormal returns may indicate market inefficiencies or insider information effects.
Estimating Expected Return E(R_i)
Several models are used to estimate the Expected return, depending on context:
| Model | Formula | Notes |
|---|---|---|
| CAPM | ( E(R_i) = R_f + \beta_i (R_m - R_f) ) | Uses market risk to estimate fair return |
| Fama-French 3-Factor | Adds size & value factors | More refined risk adjustment |
| Benchmark Model | Compare to index (e.g., S&P 500) | Simpler for practical investing |
Cumulative Abnormal Return (CAR)
Cumulative Abnormal Return (CAR) represents the total of all abnormal returns over a specific period. Typically, CAR is calculated over a short time window, often just a few days, because compounding daily abnormal returns over longer periods can introduce bias into the results.
CAR is commonly used to assess the impact of events such as lawsuits, buyouts, or other significant corporate actions on stock prices. Additionally, it serves as a valuable tool for evaluating the accuracy of asset pricing models in predicting expected returns.
In event studies, we often sum ARs over a time window:
CAR = \sum_{t_1}^{t_2} AR_t
This shows the total market impact of an event over multiple days (e.g., [-1, +1] around announcement day).
Example
Suppose:
- Stock return today R_i = 2.5%
- Expected return from CAPM E(R_i) = 1.5%
Then:
ARR = 2.5% – 1.5% = +1%
So the stock earned 1% abnormal return, outperforming expectations.