# Understanding Compound Annual Growth Rate (CAGR)

Posted on Tuesday, September 11th, 2018 by MarketBeat Staff If you had invested \$1,000 to buy stock in a particular company and in two years that investment was worth \$1,400, simple math would tell you that your investment had increased by 40%.

1,400 - 1,000 = 400
400/1000  = 40%

You might think that 40% growth over two years means that you gained 20% each year. But your financial advisor shows you that it’s not that simple – your investment actually went on a wild ride:

 Initial investment \$1,000 End of the first year \$750 End of the second year \$1,400

In this case, you had a 25% loss your first year (\$1,000 went down to \$750) and a nearly 87% gain your second year (\$750 rose to \$1,400). Let’s average those returns.

87 - 25 = 62

62/2 = 31%

But when you leave your financial advisor’s office, something doesn’t sit right with you. You see a gain of 40%, but your advisor says you are getting a 31% average annual return. If you were actually getting 31% annually, the value of your investment should be much higher.

A different, and for some investors, more useful, metric is Compound Annual Growth Rate (CAGR). This article will discuss what CAGR is and how it is calculated. The article will also discuss the importance of compounding to investment performance and why it’s so important to avoid negative returns. Finally, the article will review the limitation of CAGR and why it’s important to take those limitations into account when using CAGR to compare one investment with another.

What is Compound Annual Growth Rate (CAGR)?

The compound annual growth rate is a value that represents the arithmetic mean of an investment’s annual growth rate over a specified period of time. The formula for calculating CAGR requires a period of time longer than one year.

CAGR is similar to viewing a moving average on a stock chart. A moving average is a smooth line that is plotted over day-to-day stock price changes to give investors a better view of the overall trend of a stock. In the same way, CAGR is a way of smoothing out the fluctuations of a stock to show what an investment is really earning over a period of time.

Let’s go back to our example:

 Initial investment \$1,000 End of the first year \$750 End of the second year \$1,400

As we showed in the introduction, the average annual return on this investment is 31%. But as we said before, if the stock was, in fact, growing at 31% each year, the value of your investment would be \$1,310 at the end of the first year and \$1,716.10 at the end of the second ((1000*1.31)*1.31 = 1,716.10). Since the investment was actually down at the end of the first year and up at the end of the second, the 31% number does not accurately depict the growth rate for this investment.

So to get a better understanding of what the actual annual return was for this stock, an investor will need to calculate the CAGR.

How to calculate the CAGR

To calculate the CAGR, you will need to know three numbers:

1. The investment’s starting value
2. The investment’s ending value for the time period being measured
3. The number of years being measured

The formula for calculating CAGR is a little daunting, but basically, it goes like this:

You divide the investment's ending value by its starting value. You then take the "nth" root of the total return, where "n" is the number of years. From that number, you subtract 1 and then convert to a percent.

Here’s the good news: there are many online tools that will calculate CAGR for you just by entering the values that we listed above. So looking at our example:

1. Investment’s starting value = 1,000
2. Investment’s ending value = 1,400
3. Number of years = 2

The CAGR comes out to 18.32%.

So now we have a clearer idea of the rate of growth of our investment that accurately reflects how much our investment has grown on average.

Compounding is the key to understanding CAGR

Based on our simple example, we have come up with three very different numbers. An investment that increased from \$1,000 to \$1,400 over two years is showing a gain of 40%, or 20% per year. But averaging the first year’s growth rate and the second year’s growth rate gives us an annual return of 31%. However, the CAGR was just 18.32. All numbers are true when taken into context, but the reason why CAGR is the most accurate representation of the overall growth of the investment is because it takes compounding into account.

CAGR represents the growth of an investment over a period of years when you add the CAGR growth to the original value every year. This is the principle of compound interest. In our example, in the first year if you had achieved 18.32 percent growth the value of your \$1,000 investment would have been \$1,183.20. Subsequently, by compounding that growth, the next year an 18.32 percent increase would result in a value of \$1,400 (1,183.20 x .1832) = 216.76 + 1,183.20 = \$1,399.96.

So you can see how CAGR smooths out the volatility of the stock’s performance and provides a more realistic idea of how the stock may perform in the future.

Why negative returns dilute the benefits of compounding

Warren Buffett's first rule of investing is "don't lose money". That is at the core of understanding the benefit and the trap of compounding. When an investment loses money, it takes a much larger return over time for the investment to reach the desired average.

You can look at any sport that uses statistics for an example. If you're a batter and you get 1 hit in your first 10 at-bats of a season, your batting average is .100. In order to get your batting average up to .300 by the time you reached 30 at-bats, you would have to get at least 9 hits in your next 20 at-bats. That calculates to a batting average of .450 over those 20 at bats. You can see how much more difficult that would become the more at-bats you have.

Now look back to our example:

 Initial investment \$1,000 End of the first year \$750 End of the second year \$1,400

Because the investment lost value that first year, it took an incredible rally the second year for the investment to achieve that gain. What if the chart looked like this?

 Initial investment \$1,000 End of the first year \$1,300 End of the second year \$1,400

In this case, the CAGR would remain unchanged. However, the average annual return (18.9%) would be much closer to the CAGR because the gap between the year one and year two averages was not as extreme. But let’s look at another example:

 Initial investment \$1,000 End of the first year \$1,200 End of the second year \$1000

In this case, the CAGR would be 0%. However, the average annual return would be 4% because the percentage gain you made in year one was less than the percentage loss in year two. However, as an investor, the only number that really matters is the \$0 gain in your investment.

Here is a more “real world” example

 Initial investment \$100,000 End of the first year \$140,000 End of the second year \$168,000 End of the third year \$108,000

The average annual return would be 6.67%. However, the CAGR would be just 0.27%. Ouch! That’s the negative effect of compounding on steroids. And it’s why it’s imperative for investors to minimize these negative effects on their portfolio.

The limitations of CAGR and how to avoid them

CAGR measures the performance of an investment over a period of years. It represents how much an investment would grow on a per year basis if it grows at a steady rate. But as all investors know, no investment moves in a strict linear path at all times. That’s the limitation of CAGR.  It does not measure what happened to a stock in a particular year. So in our example, the CAGR “smoothed out” the 25% decline in the first year as well the nearly 87% gain in the second year. Investors should use other forms of fundamental analysis and/or statistical analysis to get a more accurate sense of the future direction of an asset in their portfolio.

The second limitation is that time frame that is being represented. To illustrate this, let's go back to our batting average example. As sports fans, we live in the tyranny of the now. We like to look at one-week or one-month increments to assess a player’s performance. But there are many factors that can contribute to a player having a week or a month of performance that is an outlier to the norm. To get a better picture of statistical probability, you have to look at the average over a longer period of time.

It’s the same way with CAGR. It can be affected enormously by the time period being analyzed. It can be helpful to calculate the CAGR over different time periods to see if there is a statistical difference. Like anything that has to do with statistics, an example may help explain this better.

Let’s say you had a 100,000 investment that lost money in the first two years you owned it, but then showed significant growth for the next three years.

 Initial investment \$100,000 End of the first year \$90,000 End of the second year \$80,000 End of the third year \$95,000 End of the fourth year \$107,000 End of 15, year \$115,000

If you just looked at the CAGR for the last three years, the CAGR would be 12.86% because it is not reflecting any of the negative returns. However, if you were to add in the first two years to get its five-year average, the CAGR would be much more modest, just 2.83%. It’s an investor’s responsibility to interpret CAGR to understand which of those scenarios is the anomaly.

How to use CAGR to compare investments

One of the most common ways CAGR is used is to compare investments. For the reasons we just listed, such as the smoothing out of volatility and the differences in CAGR when measured over different time periods, it’s important when you’re using CAGR to compare investments to make sure that you are comparing like with like. A growth stock may have the same CAGR as a blue-chip stock, but this doesn’t tell us anything about what kind of volatility to expect. Also, if you compare the CAGR of one stock over a two-year period and the CAGR of another over a four-year period, you may be not getting an accurate reflection of how the two investments compare.

The bottom line on CAGR

Compounding has been called “the greatest mathematical discovery of all time.” Every investor knows the importance of generating compounding interest to helping them achieve the financial independence they desire. CAGR can be a more accurate reflection of the way an investment performs because it smooths out the volatility that may not be a true representation of a stock’s performance both positively and negatively. At the same time, CAGR provides a stark reminder to investors about the importance of avoiding negative returns in their portfolio because of the time and above average returns that are required to make up for just one year of negative performance.

Investors using CAGR should be sure to use other methods of fundamental analysis and technical analysis to better assess the long-term or even the short-term direction of a stock. Likewise, when comparing one investment with another, it's important to make sure you're comparing like with like, not only in terms of the investment type but with regard to the investment timeframe.

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