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What Is Abnormal Return?

The unanticipated profits (or losses) generated by a security/stock are known as **abnormal returns**, also known as “**excess returns**.” Abnormal returns are defined as the difference between the actual returns that investors earn on an asset and the expected returns that are typically predicted using the Capital asset pricing model (CAPM) equation.

Abnormal returns could simply be anomalous, or they could indicate something more sinister, such as fraud or manipulation. The terms “abnormal returns” and “alpha,” or excess returns earned by actively managed investments, should not be confused.

**Abnormal returns can be either positive or negative.** Positive abnormal returns occur when actual returns exceed expected returns. According to the CAPM equation, negative abnormal returns (or losses) occur when the actual return is lower than expected.

### Important Points

- An abnormal return is one that differs from the expected return on investment.
- Investors can determine risk-adjusted performance by looking for abnormal returns, which can be positive or negative in direction.
- Abnormal returns can occur by chance, as a result of an unforeseen external event, or as a result of bad actors.
- The sum of all abnormal returns is called a
**cumulative abnormal return (CAR)**, and it can be used to calculate the impact of lawsuits, buyouts, and other events on stock prices.

### Understanding Abnormal Returns

When compared to the overall market or a benchmark index, **abnormal returns** are critical in determining a security’s risk-adjusted-performance. On a risk-adjusted basis, abnormal returns could help to identify a portfolio manager’s skill. It will also show whether investors were fairly compensated for the amount of investment risk they took on.

An** abnormal return can be either positive or negative.** The figure is simply a summary of how actual returns compare to the expected yield. For example, earning 30% in a mutual fund that is expected to return 10% annually would result in a **positive abnormal return** of 20%. If, on the other hand, the actual return in this same example was 5%, the result would be a 5% **negative abnormal return**.

Important: The abnormal return is determined by subtracting the expected return from the realized return, and it can be either positive or negative.

## Calculation and Formula of Abnormal Return

The calculation formula for the abnormal returns is as follows:

AR_{it} – abnormal return for firm i on day t

where:

R_{it} – actual return for firm i on day t

E(R_{it}) â€“ expected return for firm i on day t

A common practice is to standardise the abnormal returns with the use of the following formula:

where:

SAR_{it} – standardised abnormal returns

SD_{it} â€“ standard deviation of the abnormal returns

The SD_{it} is calculated with the use of the following formula:

where:

S_{i}^{2} â€“ the residual variance for firm i,

R_{mt} â€“ the return on the stock market index on day t,

R_{m} â€“ the average return from the market portfolio in the estimation period,

T â€“ the numbers of days in the estimation period.

## Cumulative Abnormal Return (CAR)

The **total of all abnormal returns is known as the cumulative abnormal return (CAR).** The calculation of the **cumulative abnormal return** is usually done over a short period of time, often just a few days. Because evidence has shown that compounding daily abnormal returns can cause bias in the results, the duration is kept short.

The **cumulative abnormal return (CAR)** is used to determine the accuracy of asset pricing models in predicting expected performance and to measure the impact of lawsuits, buyouts, and other events on stock prices.

The **capital asset pricing model (CAPM)** is a framework for calculating the expected return of a security or portfolio based on the risk-free rate of return, beta, and expected market return. After calculating the expected return of a security or portfolio, the abnormal return is estimated by subtracting the expected return from the realized return.

## Importance of Abnormal Returns

**Abnormal returns** enable investors to track the performance of a single asset or a portfolio of assets in comparison to a specific benchmark, which is typically determined using the **Capital asset pricing model (CAPM)** equation. By using the market return as a baseline, abnormal returns enable investors to determine the true extent of profits and losses.

The figures are also used to calculate the financial impact of mergers, lawsuits, product launches, organizational changes, and other events that affect a company’s stock price.

### Example of Abnormal Returns

An investor owns a stock portfolio and wants to know what the portfolio’s abnormal return was the previous year. Assume that the risk-free rate of return is 2% and that the benchmark index has a 15 percent expected return.

When compared to the benchmark index, the investor’s portfolio returned 25% and had a beta of 1.25. As a result, the portfolio should have returned 18.25 percent, or (2 percent + 1.25 x (15 percent – 2 percent) given the level of risk assumed. As a result, the abnormal return for the previous year was 6.75 percent, ranging from 25 to 18.25 percent.

The same calculations can be used to determine the value of stockholding. When compared to its benchmark index, stock ABC, for example, returned 9% and had a beta of 2. Consider that the risk-free rate of return is 5%, while the benchmark index has a 12-percent expected return. Stock ABC is expected to return 19 percent according to the CAPM. As a result, stock ABC had an abnormal return of -10% during this time period, underperforming the market.