Abnormal return, also known as an excess return or abnormal profit, refers to the excess return of investment above or below the expected return. It is a measure of the performance of an investment or portfolio relative to what would have been expected based on the level of risk and overall market conditions.

In finance, the expected return of an investment is the return that is predicted based on factors such as the level of risk associated with the investment, the overall market conditions, and the historical returns of similar investments. The expected return is often used as a benchmark against which the actual performance of an investment can be measured.

For example, if an investment is expected to return 10% per year based on the level of risk and the market conditions, and it actually returns 15% per year, the abnormal return would be 5%. This excess return may be due to a variety of factors, such as unexpected changes in market conditions or the performance of the investment exceeding expectations.

Positive abnormal returns indicate that the investment has performed better than expected, while negative abnormal returns indicate that the investment has performed worse than expected. Abnormal returns can be calculated by subtracting the expected return from the actual return on the investment.

Abnormal returns are often used in academic studies and by financial analysts to evaluate the performance of an investment or portfolio. They can also be used to assess the performance of investment managers or fund managers, as the abnormal return of a particular investment or portfolio can be compared to the expected return to determine whether the investment manager or fund manager has added value through their investment decisions.

## What Are the Factors That Can Affect Abnormal Returns?

There are a number of factors that can affect abnormal returns, including market conditions, the performance of the investment or portfolio, and changes in the level of risk associated with the investment. For example, if an investment is expected to return 10% per year based on the level of risk and the market conditions, but the market conditions change unexpectedly and the investment returns 15% per year, the abnormal return would be 5%.

In addition to being used to evaluate the performance of individual investments or portfolios, abnormal returns can also be used to compare the performance of different investments or portfolios. By comparing the abnormal returns of two or more investments or portfolios, it is possible to determine which one has performed better relative to the expected return.

## What Are The Statistical Techniques That Can Be Used To Test For Abnormal Returns?

There are a number of statistical techniques that can be used to test for abnormal returns in finance. These techniques are used to evaluate the performance of an investment or portfolio relative to what would have been expected based on the level of risk and overall market conditions.

One common technique for testing for abnormal returns is the t-test. The t-test is a statistical test that is used to determine whether the mean of a sample is significantly different from a hypothesized value. In the context of testing for abnormal returns, the t-test can be used to determine whether the mean return of an investment or portfolio is significantly different from the expected return.

Another technique for testing for abnormal returns is the Fama-MacBeth regression analysis. This technique involves regressing the abnormal returns of an investment or portfolio on a set of explanatory variables, such as the level of risk or the overall market conditions. If the coefficients on the explanatory variables are significantly different from zero, it indicates that the abnormal returns are related to the explanatory variables and are not simply due to random chance.

The third technique for testing for abnormal returns is the market model regression analysis. This technique involves regressing the returns of an investment or portfolio on the returns of a benchmark index, such as the S&P 500. The residuals from this regression analysis represent the abnormal returns of the investment or portfolio. If the abnormal returns are significantly different from zero, it indicates that the investment or portfolio has achieved abnormal returns.