What is an abnormal return?
An abnormal return measures how much an investment’s actual return differs from what was expected for that investment over a given period. It is simply the realized return minus the expected (or predicted) return. Abnormal returns can be positive (outperformance) or negative (underperformance). They are used to assess whether returns are unusually large or small after accounting for the level of risk and the market environment.
Key definitions
– Realized return: the actual percentage gain or loss an investor experienced over a period.
– Expected return: the return predicted for the asset based on a pricing model, a benchmark, or long-run historical averages.
– Abnormal return (AR): AR = Realized return − Expected return.
– Cumulative abnormal return (CAR): the sum of abnormal returns over a sequence of time periods (e.g., days around a corporate event).
Why abnormal returns matter
– Performance assessment: They reveal whether a portfolio or security beat or lagged what was fair given its risk exposure.
– Manager evaluation: Positive abnormal returns, if persistent and statistically significant, can indicate manager skill.
– Event studies: CARs are commonly used to measure the stock-price impact of news (earnings, lawsuits, mergers).
– Red flags: Very large abnormal returns can also indicate data issues, market manipulation, or fraud; they merit further investigation.
How to estimate the expected return
A common method is the capital asset pricing model (CAPM), which states:
Expected return = Risk-free rate + Beta × (Market expected return − Risk-free rate).
Beta is a measure of the asset’s sensitivity to market movements. Other methods include multi-factor models, historical averages, or using an index benchmark.
Cumulative abnormal return (CAR) — a caution
CAR = sum of ARs across the chosen time window. Analysts often use short windows (days) because compounding many small abnormal returns over long spans can introduce bias and make interpretation harder.
Step-by-step checklist for measuring abnormal returns
1. Define the period (single period vs. multi-day event window).
2. Choose an expected-return model (e.g., CAPM, multifactor, or benchmark index). Write down your inputs: risk-free rate, expected market return, beta, etc.
3. Calculate the expected return for the asset for each period.
4. Measure the realized return for each period.
5. Compute AR = Realized − Expected for each period.
6. If needed, compute CAR by summing ARs across the window.
7. Check robustness: try alternate benchmarks, adjust for dividends/fees, and test statistical significance if you are making claims about abnormal performance.
8. Document assumptions and data sources.
Worked numeric examples
Example 1 — Portfolio using CAPM (step-by-step)
Assumptions:
– Risk-free rate = 2.0%
– Expected market return = 15.0%
– Portfolio beta = 1.25
– Portfolio realized return = 25.0%
1. Expected portfolio return (CAPM) = 2.0% + 1.25 × (15.0% − 2.0%)
= 2.0% + 1.25 × 13.0%
= 2.0% + 16.25% = 18.25%
2. Abnormal return = Realized − Expected = 25.0% − 18.25% = 6.75%
Interpretation: The portfolio outperformed its CAPM-predicted return by 6.75 percentage points for the period.
Example 2 — Single stock
Assumptions:
– Risk-free rate = 5.0%
– Expected market return = 12.0%
– Stock beta = 2.0
– Stock realized return = 9.0%
1. Expected stock return (CAPM) = 5.0% + 2.0 × (12.0% − 5.0%)
= 5.0% + 2.0 × 7.0%
= 5.0% + 14.0% = 19.0%
2. Abnormal return = 9.0% − 19.0% = −10.0%
Interpretation: The stock underperformed its CAPM benchmark by ten percentage points over the period.
Practical notes and caveats
– Model sensitivity: Abnormal returns depend entirely on how you compute expected returns. Different models or input assumptions (e.g., a different market return or beta) will change AR.
– Significance: A single-period abnormal return may be driven by noise; use statistical tests or repeated observations to judge whether outperformance is meaningful.
– Adjust for corporate actions: Include dividends, splits, and fees so returns are comparable.
– Time horizon: CARs over long horizons can be influenced by compounding and nonstationary risk parameters; short event windows are standard in event studies.
Further reading (reputable sources)
– Investopedia — Abnormal Return: https://www.investopedia.com/terms/a/abnormalreturn.asp
– Investopedia — Capital Asset Pricing Model (CAPM): https://www.investopedia.com/terms/c/capm.asp
– U.S. Securities and Exchange Commission (SEC) — Investor publications on mutual fund and performance: https://www.sec.gov/oiea/investor-alerts-and-bulletins/ib_mutualfunds
– Aswath Damodaran, NYU Stern — teaching material on risk, return, and valuation: http://pages.stern.nyu.edu/~adamodar/
Educational disclaimer
This explainer is for educational purposes only. It is not personalized investment advice and does not recommend specific securities or predict future returns. Always verify inputs and consider consulting a qualified professional before making investment decisions.