# Cumulative abnormal returns

Cumulative abnormal returns (CARs) is an investment performance metric that measures the total return of a security over a specific period of time relative to the expected return. It is calculated by subtracting the expected return of the security from the actual return and adding up the differences across the specified period. CARs is a useful tool for managers because it can help to identify undervalued and overvalued investments, and can be used to measure the performance of a portfolio relative to a particular benchmark. CARs is often used to evaluate the performance of a security or portfolio over a longer period of time, such as a year, since it takes into account the compounded period-over-period effects of any mispricing.

## Example of cumulative abnormal returns

• Suppose an investor owns shares in a company that has performed well in the past year, with a return of 10%. If the expected return for the same period was 8%, then the CAR for the stock would be 2%. This means that the stock outperformed expectations by 2%, which indicates that the stock was undervalued and could be a good investment.
• A portfolio manager might use CARs to compare the performance of their portfolio to a particular benchmark, such as the S&P 500. If their portfolio returned 10% while the S&P 500 returned 8%, then the CAR for the portfolio would be 2%. This would indicate that the portfolio outperformed the benchmark by 2% and could be a good choice for investors.
• Another example of CARs is in mergers and acquisitions. If a company acquires another company, the target company's stockholders may receive a premium above the current market price. The CAR is the difference between the premium and the expected return of the stock, which can be used to measure the success of the transaction.

## Formula of cumulative abnormal returns

The formula for calculating cumulative abnormal returns (CARs) is:

CARs = [(Current Price - Initial Price) / Initial Price] + [(Return on Market - Return on Security) / Return on Security]

Where:

Current Price = Current stock price of the security
Initial Price = Initial stock price of the security
Return on Market = Return on the benchmark over the same period
Return on Security = Return on the security over the same period

The formula is used to measure the performance of a security or portfolio relative to a particular benchmark. It does this by taking into account both the initial and current price of the security, as well as the return on the benchmark and the return on the security over the same period. This allows investors to compare the performance of their security or portfolio to the benchmark and identify any mispricing. CARs can be used to measure the performance of a security or portfolio over a longer period of time, such as a year, since it takes into account the compounded period-over-period effects of any mispricing.

## When to use cumulative abnormal returns

Cumulative abnormal returns (CARs) can be used to measure the performance of a security or portfolio over a longer period of time, such as a year. It can be used to:

• Detect mispricing of a security or portfolio relative to the market,
• Identify undervalued or overvalued investments,
• Assess the performance of a portfolio relative to a particular benchmark,
• Measure the effect of news events on the security’s return,
• Determine whether a portfolio is taking on too much risk for its size, and
• Compare the performance of different portfolios.

## Types of cumulative abnormal returns

Cumulative abnormal returns (CARs) is a useful investment performance metric that measures the total return of a security over a specified period of time relative to the expected return. There are three types of CARs that are commonly used by managers to measure the performance of a security or portfolio relative to a particular benchmark:

• Abnormal return: This is the difference between the actual and expected return of a security over a specified period of time.
• Cumulative abnormal return: This is the sum of all the abnormal returns over the specified period of time.
• Average abnormal return: This is the average of all the abnormal returns over the specified period of time.

## Advantages of cumulative abnormal returns

The advantages of cumulative abnormal returns (CARs) include:

• Improved accuracy in measuring performance: CARs allow for a more accurate evaluation of performance since it takes into account the compounded period-over-period effects of any mispricing.
• Increased visibility of undervalued and overvalued investments: By observing the CARs of a security or portfolio over a period of time, managers can identify which investments may be undervalued or overvalued.
• Easy comparison of performance: CARs enable managers to easily compare the performance of a security or portfolio to that of a benchmark, which can help to inform decisions about buying and selling.
• Ability to measure long-term performance: CARs are often used to evaluate the performance of a security or portfolio over a longer period of time, such as a year, which can provide valuable insight into the underlying performance of the asset.

## Limitations of cumulative abnormal returns

Cumulative abnormal returns (CARs) can be a useful tool for managers to identify undervalued and overvalued investments, and to measure the performance of a portfolio relative to a particular benchmark. However, there are a few limitations associated with CARs that must be taken into consideration. These include:

• CARs are based on historical data and, as such, may not be reflective of future performance. Therefore, they may not be an accurate predictor of future returns.
• CARs do not take into account any external factors or market events that may have affected the security’s performance.
• CARs do not account for any structural changes in the market or the security itself, such as changes in risk exposure or liquidity.
• CARs can be difficult to interpret for short-term investments since the effects of mispricing may not be as significant over a shorter period of time.
• CARs do not take into account the costs associated with trading a security, such as commissions and spreads, which can erode returns.

 Cumulative abnormal returns — recommended articles Net asset value per share — Investment ratio — Market performance — Market value of equity — Long term investment balance sheet — Risk measures — Financial exposure — Annualized rate — Market growth rate