## What Is an Abnormal Return?

An abnormal return describes the unusual profits generated by given securities or portfolios over a specified period. The performance is different from the expected, or anticipated, rate of return (RoR) for the investment. The anticipated rate of return is the estimated return based on an asset pricing model, using a long run historical average or multiple valuations.

Abnormal returns are also called alpha or excess returns.

## Why Abnormal Returns Are Important

Abnormal returns are essential in determining a security's 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 which 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%.

## Cumulative Abnormal Return

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 of lawsuits, buyouts, and other events have on stock prices. Cumulative abnormal return (CAR) is also useful for determining the accuracy of asset pricing model 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. The abnormal return may be positive or negative, depending on the performance of the security or portfolio over the specified period.

### Key Takeaways

- An abnormal return describes the unusual profits generated by a specific security or portfolio over a period of time.
- Abnormal returns, which can be either positive or negative, determine risk-adjusted performance.
- A cumulative abnormal return is the total of all abnormal returns.
- CAR is used to measure the effect of lawsuits, buyouts, and other events have on stock prices.

## Real World Example

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

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 to 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 capital asset pricing model (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.