### 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 expected rate of return is the estimated return based on an asset pricing model, using a long-term historical average or multiple valuations.

Abnormal returns are also called alpha or excessive returns.

### Why abnormal returns are important

Abnormal returns are essential in determining the risk-adjusted performance of a security or portfolio relative to the overall market or a benchmark. Abnormal returns could help identify the skills of a portfolio manager on a risk-adjusted basis. It will also show whether investors have received adequate compensation for the amount of investment risk assumed.

Abnormal feedback can be positive or negative. The figure is only a summary of the difference between actual and expected returns. For example, earning 30% in a mutual fund which should average 10% per year would create an abnormal positive return of 20%. If, on the other hand, in this same example, the real yield was 5%, this would generate an abnormal negative yield of 5%.

### Cumulative abnormal performance

Cumulative abnormal return (CAR), is the total of all abnormal returns. Usually, the calculation of the cumulative abnormal return occurs over a small window of time, often only a few days. This short duration is explained by the fact that the evidence has shown that the multiplication of abnormal daily returns can create a bias in the results. The abnormal cumulative return (CAR) is used to measure the effect of lawsuits, redemptions and other events on stock prices. The cumulative abnormal return (CAR) is also useful in determining the accuracy of the asset pricing model in forecasting expected performance.

The Fixed Asset Pricing Model (CAPM) is a framework used to calculate the expected return on a security or portfolio based on the risk-free rate of return, beta and expected market return. After calculating the expected return on a security or portfolio, estimating the abnormal return consists of subtracting the expected return from the return achieved. The abnormal return may be positive or negative, depending on the performance of the security or portfolio over the specified period.

Key points to remember

- An abnormal return describes the unusual profits generated by a specific security or portfolio over a period of time.
- Abnormal returns, which can be 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 on share prices.

### Example from the real world

Suppose the risk-free rate of return is 2% and the benchmark has an expected return of 15%. An investor has a portfolio of securities and wants to calculate the abnormal return on his portfolio over the previous year.

The investor’s portfolio returned 25% and a beta of 1.25 when compared to the benchmark. Consequently, given the level of risk assumed, the portfolio should have generated 18.25%, ie (2% + 1.25 x (15% – 2%)). Therefore, the abnormal return in the previous year was 6.75% or 25-18.25%.

The same calculations can be useful for a stock. For example, the ABC stock posted a return of 9% and a beta of 2, when measured against its benchmark. Consider that the risk-free rate of return is 5% and that the benchmark has an expected return of 12%. Based on the fixed asset pricing model (CAPM), the ABC share has an expected return of 19%. As a result, ABC shares posted an abnormal return of -10% and underperformed the market during this period.