CAR

If you’ve ever found yourself wondering how a big event—like a merger, a new product launch, or an earnings report—really impacts a company’s stock price, you’re not alone. There’s a lot of noise in the market, and it can be tricky to pinpoint what’s actually going on. This is where Cumulative Abnormal Return (CAR) comes into play. Let’s explore CAR in a more relatable way and why it’s something investors often keep an eye on.

What is Cumulative Abnormal Return?


Cumulative Abnormal Return, commonly known as CAR, refers to the sum of abnormal returns over a specific period. In simpler terms, it helps measure the actual impact of a specific event—like a merger, earnings announcement, or regulatory change—on a company’s stock price, compared to what was expected based on the market's overall movement.

The formula for CAR is quite straightforward:

CAR=∑(ARt)
​
Where AR_t is the abnormal return at time "t". The abnormal return (AR) itself is the difference between the actual return and the expected return of the stock.

How to Calculate Cumulative Abnormal Return?


Calculating CAR involves several steps, and while the process might seem technical, it's fairly straightforward once you break it down. Here's how to do it step by step:

1. Choose the Event Window:
First, define the event window. This is the time period during which you'll analyze the stock's performance relative to an event (like a merger, earnings report, or product launch). The event window often includes a few days before and after the event, such as [-2, +2], where day 0 is the day of the event.

Example: If a company announces a new product on June 1 (day 0), you could examine stock returns from May 30 to June 3 (a 5-day event window).

2. Estimate the Expected Return:
The next step is to calculate the expected return of the stock, which is the return you would have expected without the event happening. The most common methods include:
  • Market Model: This involves using the Capital Asset Pricing Model (CAPM) or a simple market index (like the S&P 500) to predict what the stock's return would have been based on overall market movements.
  • Historical Average Return: You can also use the historical average return of the stock during a “normal” period to estimate the expected return.
Formula for expected return using CAPM:

Expected Return = α + β × Market Return
  • α (alpha): Intercept from the regression model (essentially the stock’s independent return).
  • β (beta): Sensitivity of the stock’s returns to market returns (found through historical data).

3. Calculate the Actual Return:
Calculate the actual return of the stock during the event window. The return for each day is typically calculated as:

Actual Returnt=Pricet−Pricet−1Pricet−1\text{Actual Return}_t = \frac{\text{Price}_t - \text{Price}_{t-1}}{\text{Price}_{t-1}}

Where:

  • Price_t is the stock’s closing price on day t.
  • Price_{t-1} is the stock’s closing price on the previous day.

4. Find the Abnormal Return (AR):
Once you have the expected and actual returns, the next step is to calculate the abnormal return for each day. The abnormal return is simply the difference between the actual return and the expected return:

Abnormal Returnt=Actual Returnt−Expected Returnt

5. Calculate Cumulative Abnormal Return (CAR):
Now, to calculate the Cumulative Abnormal Return (CAR), you add up the abnormal returns over the event window. If your event window is from day -2 to day +2, you would sum the abnormal returns for those 5 days:

CAR=∑t=−2t=+2Abnormal Returnt\text{CAR} = \sum_{t=-2}^{t=+2} \text{Abnormal Return}_t

This gives you the total abnormal return that occurred due to the event over the selected time period.

Example Calculation:

Let’s assume the following for a stock:
  • The expected returns based on a market model are 1% for each day of the event window.
  • The actual returns over the 5-day window are as follows:

Day

Actual Return

Expected Return

Abnormal Return

-2

1.5%

1.0%

0.5%

-1

2.0%

1.0%

1.0%

0

5.0%

1.0%

4.0%

+1

1.0%

1.0%

0.0%

+2

1.5%

1.0%

0.5%

Step 1: Calculate the abnormal return for each day:
  • For Day -2: 1.5% - 1.0% = 0.5%
  • For Day -1: 2.0% - 1.0% = 1.0%
  • For Day 0: 5.0% - 1.0% = 4.0%
  • For Day +1: 1.0% - 1.0% = 0.0%
  • For Day +2: 1.5% - 1.0% = 0.5%

Step 2: Sum the abnormal returns over the event window to calculate CAR:

CAR = 0.5% + 1.0% + 4.0% + 0.0% + 0.5% =6 .0%

In this example, the Cumulative Abnormal Return (CAR) is 6.0%, meaning the stock outperformed expectations by 6% over the event window.

How are Assets Related to Cumulative Abnormal Return?


Assets play a significant role in influencing Cumulative Abnormal Return because they reflect a company's underlying value and performance potential. Here's how assets and CAR are connected:

1. Assets Reflect a Company's Value
Think of assets as the building blocks of a company’s value. When a business owns a lot of valuable stuff—like a huge inventory of products, or cutting-edge technology—investors pay attention. They see these assets as potential drivers of future growth. Now, when an event happens, like a new product launch or a big acquisition, investors start asking, “Will this event make the company’s assets more valuable?” If they think the answer is “yes,” they’re likely to push the stock price up, leading to a positive CAR (which means the stock performs better than expected). But if the event makes investors worry that the company’s assets won’t be as valuable as before—like if a new competitor enters the market—they might react by selling the stock, which leads to a negative CAR.

2. Asset Growth and Profitability
Imagine a company that's rapidly growing its assets—buying more land, developing new products, or investing in new technology. That’s usually a good sign for investors. It means the company is gearing up to grow, and its stock price might climb as a result. So, if an event happens that suggests the company’s assets will be even more valuable in the future (like they just acquired a huge new market), investors may react positively, leading to a positive CAR. On the flip side, if the event raises concerns—like they bought an asset that turns out to be a bad investment—it could lead to a negative CAR.

3. Risk and Asset Management
Just like managing your own finances, companies need to manage their assets wisely. If they’re managing their assets well—selling off unneeded properties or investing in high-return projects—investors are likely to feel confident about the company’s future. This confidence can translate into a positive CAR. But if an event reveals that a company is mismanaging its assets (like taking on too much debt or investing in failing projects), investors may get nervous and sell off the stock, which leads to a negative CAR.

4. Tangible vs. Intangible Assets Matter
Not all assets are the same. Some are tangible—like real estate, factories, or equipment. These are the things you can touch and see. Then there are intangible assets—like patents, brand value, or even a strong reputation. While tangible assets give investors a sense of security, intangible assets can sometimes offer even greater returns. For example, if a company announces a new patent that’s expected to revolutionize its industry, that’s an intangible asset with huge potential. Investors might get excited and drive the stock price up, resulting in a positive CAR.

5. Asset Structure and Financing Decisions
Finally, how a company pays for its assets matters. Some companies might use debt (loans), while others might use equity (money raised from investors). If an event shows that a company is using its assets and finances wisely—like paying off debt or reinvesting profits into valuable assets—investors might react with optimism, leading to a positive CAR. On the other hand, if a company is loading up on debt to buy assets and investors worry about their ability to repay, the event might trigger a negative CAR.

Importance of Cumulative Abnormal Return


  1. Measures Event Impact: CAR helps you see how much a specific event, like a product launch or earnings report, actually moves a company's stock price compared to what was expected. It strips away the noise and focuses on the impact of the event itself.
  2. Gives Insight into Investor Reactions: It’s like a snapshot of how investors feel about the event—are they excited, nervous, or indifferent? CAR helps you understand their reaction in real time.
  3. Useful Performance Check: If you want to know if a merger, acquisition, or big announcement was a hit or a miss, CAR can show you if the market liked it by comparing the actual stock performance to what would’ve happened without the event.
  4. A Tool for Event Studies: CAR is commonly used in financial research to track how different events affect a company’s value. It’s a go-to tool for analyzing the market’s reaction to all sorts of corporate actions.
  5. Helps in Decision-Making: Whether you're an investor or a company exec, CAR gives you crucial insights that can guide your decisions—like whether to invest more, hold tight, or pull back.

Limitations of Cumulative Abnormal Return


  1. Assumes Market Trends Stay Stable: CAR works under the assumption that a stock's past performance can predict its expected returns, but markets can be unpredictable, especially during turbulent times.
  2. Short-Term Focus: CAR often looks at short-term changes in stock prices, which might not give you the full picture of how the event will affect the company in the long run.
  3. Doesn’t Account for Other Factors: Sometimes, external events like a sudden market crash or global economic changes can skew the CAR results, making it hard to figure out how much of the stock movement is actually due to the event you're studying.
  4. Depends on the Right Model: The accuracy of CAR relies on the model you use to estimate expected returns (like the CAPM model), and if the model doesn’t reflect the current market well, your results might be off.
  5. Timing Can Be Tricky: Deciding on the right "event window" is key. If you pick the wrong time frame to measure CAR, you might miss the real impact or overestimate how much the event affected the stock price.