## What is Abnormal Return?

Abnormal Return refers to the difference between the return of a particular asset or portfolio and its expected return. It measures the performance of an asset or portfolio relative to market or benchmark returns, either exceeding or falling short of expectations. Abnormal returns can be used to assess the effectiveness of investment strategies, the relative performance of securities, and risk-adjusted returns. They are crucial for investors, fund managers, and researchers.

In finance, abnormal returns are often employed to evaluate the performance of an investment strategy or portfolio. Expected returns are estimated based on market risk and expected rates of return. If the actual return of an asset or portfolio exceeds the expected return, it is termed as a positive abnormal return. Conversely, if the actual return is lower than the expected return, it is known as a negative abnormal return.

There are various methods to calculate abnormal returns, with the most common being subtracting market or benchmark returns. Different statistical models, such as the Market Model or the Capital Asset Pricing Model (CAPM), can be used for specific calculations.

## Characteristics of Abnormal Return

The characteristics of abnormal returns can vary depending on the market environment, time frame, and research methods. Here are some common characteristics of abnormal returns in financial markets:

- Relativity: Abnormal returns are comparative measures against market or benchmark returns, evaluating the performance of an asset or portfolio relative to its expected return. Thus, it requires comparing actual returns with a reference standard.
- Short-Term Nature: Abnormal returns are generally calculated and assessed over short periods, reflecting the performance that exceeds or falls short of expectations during a specific time frame.
- Chance: Abnormal returns might include some randomness. Variations in investment returns are influenced by market volatility, unforeseen events, and several other factors. A single abnormal return doesn't necessarily indicate genuine investment capability or long-term strategy advantage.
- Risk Adjustment: To evaluate abnormal returns more comprehensively, they are usually risk-adjusted. Common methods include using risk adjustment models like the Capital Asset Pricing Model (CAPM) to measure excess returns relative to risk.
- Informational Content: To some extent, abnormal returns reflect the market's response to specific events or information, providing clues about company performance, industry changes, or macroeconomic shifts. They are often indicators for studying market efficiency and information dissemination.

## Causes of Abnormal Return

Understanding the causes of abnormal returns is crucial for investment decisions and risk management. Here are some common reasons for abnormal returns:

- Corporate Events and Announcements: Important company announcements, earnings reports, mergers and acquisitions, product innovations, or bankruptcies may attract market attention and reactions, leading to abnormal returns.
- Market Factors: Macroeconomic data, industry changes, market sentiment, interest rate fluctuations, and political events may affect the returns of the entire market or specific asset classes, contributing to abnormal returns.
- Information Asymmetry: Some investors might gain returns exceeding market expectations through better or more accurate information. This information asymmetry could come from insider sources, professional analysts' reports, or non-public information.
- Trading Strategies and Techniques: Using specific investment strategies, trading techniques, or models such as technical analysis, fundamental analysis, quantitative models, or arbitrage strategies can also result in returns exceeding market expectations.
- Market Inefficiencies: If irrational behavior, price distortions, or investor sentiment fluctuations exist in the market, it might lead to abnormal returns. Investors can exploit market inefficiencies to seek excess return opportunities.

## Calculation Methods and Examples of Abnormal Return

Various statistical models can be used to calculate abnormal returns, with the Market Model and Capital Asset Pricing Model (CAPM) being the most common. These models estimate expected returns and compare actual returns to expected returns to determine abnormal returns. Here are the basic steps for calculating abnormal returns using the Market Model and CAPM:

**Calculating Abnormal Returns Using the Market Model**

Select an index or asset representing the overall market performance as the benchmark return.

- Use historical data to calculate the mean and standard deviation of benchmark returns.
- For a specific asset or portfolio, calculate its actual returns over the same period.
- Use the Market Model formula to calculate the expected return rate, usually a linear regression model: Actual Return Rate = α + β × Market Return Rate.
- Abnormal return is equal to the actual return rate minus the expected return rate.

**Calculating Abnormal Returns Using the Capital Asset Pricing Model (CAPM)**

CAPM is based on the theoretical framework of the Capital Asset Pricing Model, using the relationship between market risk and asset-specific risk to estimate expected returns.

- Use the CAPM formula to calculate the expected return rate: Expected Return Rate = Risk-Free Rate + β × (Market Return Rate - Risk-Free Rate).
- The risk-free rate is the rate of return on an investment with no risk, typically using Treasury rates.
- β (Beta Coefficient) indicates the sensitivity of an asset or portfolio to market-wide risk.

**Examples**

- Assume a stock's actual return rate is 12%, and the market return rate is 8%. The expected return rate calculated using the Market Model is 10%. Therefore, the stock's abnormal return is 12% - 10% = 2%.
- Assume the expected return rate is calculated using the CAPM model as 9%, the risk-free rate is 3%, and the market return rate is 8%. Therefore, the stock's abnormal return is 12% - 9% = 3%.