# How to Calculate Cumulative Abnormal Return

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The term abnormal return is used to describe an unexpected profit or loss on an investment over a designated period of time. It measures the difference between a benchmark performance (such as a market index like the S&P 500) and the performance of an individual stock. It can also measure the difference between actual performance and a stock's predicted CAPM (capital asset pricing model) return. The writers for the Corporate Finance Institute explain that CAPM uses the risk-free market rate and values representing the risk premium associated with an investment. Either way, it represents how the profit or loss on an individual investment compares to a benchmark value.

## Calculating Cumulative Abnormal Returns

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The formula for looking at abnormal returns is easy: (actual return) - (expected / benchmark return) = abnormal return. Abnormal returns can be positive or negative. For example, if the benchmark return of the stock was ​10 percent​, and Stock A had a return of ​13 percent​, the abnormal return is ​3 percent​. However, if Stock A has a return of ​7 percent​, the abnormal return is ​-3 percent​. As you can see, the value of abnormal return helps determine whether Stock A outperformed or underperformed based on the benchmark return. Usually, a higher abnormal return is better; however, due to the shorter periods these calculations often examine, it's best to track values over a longer time to make sure the market response to Stock A is sustainable.

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The Corporate Finance Institute team also explains cumulative abnormal returns. These look at abnormal returns over a number of consecutive periods. For example, if you're looking at four periods where abnormal returns were ​3, 2, 3 and 5 percent​, your cumulative abnormal return over those four periods is the sum of those, or ​15 percent​. Alternately, if your abnormal returns were ​3, -4, 2 and -1 percent​, your cumulative abnormal return is ​0 percent​.

## Using Cumulative Abnormal Returns

Abnormal returns (and cumulative abnormal returns) are usually calculated over short-term periods, such as a few days or a few weeks. This is because compounding daily abnormal returns can produce bias in the results. They're usually used to examine the way a stock's value changes after a business event. Events can be positive things like dividend statements, earning announcements, mergers or buyouts; they can also represent negative occurrences like lawsuits, loss announcements and even fraud. Events can have effects that stabilize within a few days or carry on for weeks based on their significance to the company's image.

The key here is that abnormal stock returns are based on an index representing the average market performance during that time period, per writers for Nasdaq. This means that any market movements or fluctuations that occur market-wide are corrected for. So if you're tracking Stock A over a three-week period, and during that time the stock market rises dramatically due to some sort of systematic influence, using the abnormal return formula will allow you to eliminate any change in Stock A's value based on that market increase. If, over that period, cumulative abnormal return is close to zero, any changes in Stock A's value came from market index changes, rather than fluctuations due to Company A's actions.