## What Is an Abnormal Return?

An abnormal return describes the unusually large profits or losses generated by a given investment or portfolio over a specified period. The performance diverges from the investments' expected, or anticipated, rate of return (RoR)—the estimated risk-adjusted return based on an asset pricing model, or using a long-run historical average or multiple valuation techniques.

Returns that are abnormal may simply be anomalous or they may point to something more nefarious such as fraud or manipulation. Abnormal returns should not be confused with "alpha" or excess returns earned by actively managed investments.

### Key Takeaways

- An abnormal return is one that deviates from an investment's expected return.
- The presence of abnormal returns, which can be either positive or negative in direction, helps investors determine risk-adjusted performance.
- Abnormal returns can be produced by chance, due to some external or unforeseen event, or as the result of bad actors.
- A cumulative abnormal return (CAR) is the sum total of all abnormal returns and can be used to measure the effect lawsuits, buyouts, and other events have on stock prices.

## Understanding Abnormal Returns

Abnormal returns are essential in determining a security or portfolio's risk-adjusted performance when compared to the overall market or a benchmark index. Abnormal returns could help to identify a portfolio manager's skill on a risk-adjusted basis. It will also illustrate whether investors received adequate compensation for the amount of investment risk assumed.

An abnormal return can be either positive or negative. The figure is merely a summary of how the actual returns differ from the predicted yield. For example, earning 30% in a mutual fund that is expected to average 10% per year would create a positive abnormal return of 20%. If, on the other hand, in this same example, the actual return was 5%, this would generate a negative abnormal return of 5%.

The abnormal return is calculated by subtracting the expected return from the realized return and may be positive or negative.

## Cumulative Abnormal Return (CAR)

Cumulative abnormal return (CAR) is the total of all abnormal returns. Usually, the calculation of cumulative abnormal return happens over a small window of time, often only days. This short duration is because evidence has shown that compounding daily abnormal returns can create bias in the results.

Cumulative abnormal return (CAR) is used to measure the effect lawsuits, buyouts, and other events have on stock prices and is also useful for determining the accuracy of asset pricing models in predicting the expected performance.

The capital asset pricing model (CAPM) is a framework used to calculate a security or portfolio's expected return based on the risk-free rate of return, beta, and the expected market return. After the calculation of a security or portfolio's expected return, the estimate for the abnormal return is calculated by subtracting the expected return from the realized return.

## Example of Abnormal Returns

An investor holds a portfolio of securities and wishes to calculate the portfolio's abnormal return during the previous year. Assume that the risk-free rate of return is 2% and the benchmark index has an expected return of 15%.

The investor's portfolio returned 25% and had a beta of 1.25 when measured against the benchmark index. Therefore, given the amount of risk assumed, the portfolio should have returned 18.25%, or (2% + 1.25 x (15% - 2%)). Consequently, the abnormal return during the previous year was 6.75% or 25 - 18.25%.

The same calculations can be helpful for a stock holding. For example, stock ABC returned 9% and had a beta of 2, when measured against its benchmark index. Consider that the risk-free rate of return is 5% and the benchmark index has an expected return of 12%. Based on the CAPM, stock ABC has an expected return of 19%. Therefore, stock ABC had an abnormal return of -10% and underperformed the market during this period.