Last Updated on May 18, 2022 by Quantified Trading
What is CAGR?
CAGR is an abbreviation of Compound Annual Growth Rate, and is a common measure of growth that is used to measure the returns on investments over several time periods on an annual basis. It can be used on a range of securities such as mutual funds, shares or bonds but is also used outside the world of trading and investments to track the development of metrics such as customer satisfaction. Unlike many other metrics such as Absolute Return, CAGR accounts for compound interest, meaning that it often produces more accurate results that to some extent take into account the erratic and volatile development of investments.
How to Calculate CAGR
As we’ve mentioned, CAGR is different from many other return metrics in that it takes into account the compounding of the investment. Therefore, the formula is a little more complicated than Absolute range, or average yearly return.
To calculate CAGR you need three values
- The beginning value
- The ending value
- Number of years
CAGR is calculated by dividing the ending value by the beginning value, and then raising that figure to one divided by the number of years in the period. Once this calculation is done, you need to subtract one from the results to get the CAGR of the investment.
Here follows the formula:
(Ending value/Beginning value)^(1/number of years) -1
Let’s say that we have an investment that we invested $1000 dollars in. The following four years it fluctuated as follows:
To calculate the CAGR of this investment during the four year period shown in the table, we first need to find the beginning and end values. Since we started with $1000 and ended with $1250, $1000 will be our beginning value and $1250 our ending value. The number of years in the investment is 4 years. When putting those values into the formula, we get the following:
(1250/1000)^(1/4) – 1 = 0.057
In other words, the CAGR of our investment was 5,7%.
Real-world Case: CAGR of S&P 500
The S&P 500 is one of the most well-known indexes, so why not calculate the CAGR of the S&P 500! Our calculation will be done under the assumption that dividends are reinvested, and that the expense ratio is zero, which actually is the case with some index funds (read our article on index funds to find out more).
We’ll calculate the CAGR in the years from 1871 to 2019. We’ll assume that $1 dollar was invested in 1871.
148 years later, in 2019, that $1 would have grown to $372, 500!
In other words, we have our beginning value ($100), our ending value ($372, 500), and the number of years (148 years). Let’s put these values into the CAGR formula:
(372500/1)^(1/148) – 1 = 0.905
That means that the Cagr of the S&P 500 between 1871 to 2019 was roughly 9%.
If you want to calculate the Cagr of the S&P 500 for a custom period, here you can find a useful calculator.
What Is a Good CAGR?
Since CAGR measures the performance of an investment, there is no definite answer as to what a good CAGR is. Depending on the risk and volatility of the investment, a good CAGR could be anything from a few percent to 20-30%. In more advanced trading, you might even consider that to be low. However, to give some sort of answer, everything that beats or makes around the same return as the S&P 500 is a good return. In other words, a CAGR at around 9% per year is considered to be good. In fact, over 90% of mutual fund managers fail to beat the market indexes!
However, keep in mind that returns vary greatly from period to period. The 9% CAGR figure is an average, which means that there have been periods that have overperformed and others that have underperformed. Instead of keeping a goal of 9% annual return, it’s better to compare one’s own returns to those of the S&P for that very period. In other words, if my money was invested from 2008 to 2010, I should compare my returns to those of the S&P 500 during the years of 2008-2010.
Pros and Cons of the CAGR
CAGR vs Annualized rate of return
CAGR holds several advantages over other methods and is superior to many other common performance metrics, because it takes compounding into account. Using, for example, the average annual return(AAR) to measure the return of an investment, which doesn’t take compounding into account, could provide misleading results.
Here is an example to illustrate what we mean to show why you need to understand why arithmetic and geometric averages differ :
Let’s say that 3 years ago, we invested $100 in an investment. The first year we made a return of 10%, the second year it was negative at – 20% and the third year we made a positive return of 10%.
To calculate how much money we have once the third year has come to an end, we do the following calculation: $100*1.1*0.8*1.10 = $ 96.8
In other words, our return was negative during those three years. Now let’s calculate the Cagr and the average annual return(AAR) of the same investment:
CAGR: (96.8/100)^(1/3) -1 = -0.011
AAR: ((1.1+0,8+1,1)/3) – 1 = 0
While the average rate of return indicates that our investment is back at where it started, the CAGR shows that our investment has shrunk by around 1% per year. The reason why there is a difference is, as mentioned previously, that CAGR takes compounding into account while the average annual return doesn’t. That’s one of the most significant benefits of the CAGR.
CAGR vs Absolute Return
Absolute return is a much simpler way of measuring the total return. Unlike the CAGR, it doesn’t take into account the length of the investment period, which makes it much harder to compare two different investments to each other. For example, an investment that has yielded 30% over the course of 30% years, will have the same absolute return as an investment that yielded 30% in 1 year.
Disadvantages of CAGR
Let’s look at some of the disadvantages of CAGR:
CAGR Ignores Volatility and Risk
One of the most significant limitations of CAGR, is that it ignores volatility and implies that growth was steady and evenly split among all years. The growth of an investment will in most cases consist of large swings both to the upside and the downside. With CAGR, the only input values are the beginning value, the ending value, and the number of periods. Therefore, everything in between is ignored, which could make investors underestimate the risk level of their investment.
CAGR Doesn’t Account for When Investors Add Funds
Again, since CAGR only cares for the beginning value, the ending value, and the number of periods, everything in between is ignored, which also applies to the adding or removal of funds to the account. To be able to use CAGR to measure your returns, you need to not have withdrawn or added any funds. Otherwise, the CAGR reading could become inflated and incorrect.
A Different Approach to Using CAGR
The CAGR formula can also be used to calculate how much of a yearly return is needed to reach a certain amount of money in x-years going forward. For example, if our goal is to have $100 000 worth of investments in 10 years, and we’re starting with $15 000, we could put that into the CAGR formula to calculate the CAGR return needed to reach that goal:
Beginning value: $15 000
Ending Value: $100 000
Number of years: 10
When we put these values into the CAGR formula, we get the following calculation:
(100000/15000)^(1/10) -1 = 0.21
So, according to our CAGR calculation, we need a yearly return of 21% to end with $100 000 after 10 years!
Who Could Benefit From projecting CAGR Into the Future?
The reason why it could be beneficial to calculate the CAGR you need to achieve a specific amount of money, varies. Parents who want to finance their child’s college education may run the calculation to see how much capital they need to invest today.
Making the calculation and seeing how big a return (CAGR) you need to reach your goal, could also impact what type of investment you choose. For example, if you need an investment to grow at 9% per year, you might not want to go with bonds, but with an index fund, since that’s around what indexes have performed historically. Conversely, if your goal requires a much lower CAGR, you might choose to go with bonds that provide lower returns with lower risk levels.
Modifying CAGR For Real World Cases
Because it’s rare that investments are kept in an exact number of years, some adjustments must be made for the CAGR to be correct. For example, an investor who buys a share on May 1th, 2015 and sells it on January 1th, 2018, has kept his investment for 2 years and 10 months.
In cases like these, we will have to calculate the number of years as a fractional value, which is done by dividing the number of days in the investment with the number of days in a year, which is 365. In our example, the number of days is 1030 (approximately). The calculation then goes as follows:
Number of years as fractional value = 1030/365 = 2.82
Then we just perform the CAGR calculation as in previous examples. Let’s assume that the beginning value was $1000 and the ending value $1100:
(1000/1010)^(1/2.82) -1 = 0.034
The CAGR of this investment was 3,4%
Here follow some final tips on how to use the CAGR:
CAGR Tip 1: Past Results Are Not Indicative Of Future Results
As with all metrics, CAGR is describing past results. A good figure is not indicative of future success, and investments should be made carefully. Remember that the CAGR is just another metric to guide you in your investing, and should not be considered to better lead you to pick good investments than any other metric, even if it could be helpful.
CAGR Tip 2: Require Much Data
The more years you’re looking at, the more robust an observation. When looking at metrics of any sort and trying to make an informed decision, a few years won’t suffice in most cases. As has been covered previously in the article, many mutual funds manage to outperform the market during a streak of lucky years. However, in the long run, most won’t. Remember this, and be vigilant of advertisements stating CAGRs that are calculated with only a few years of data. They may very well have started their calculation from an equity low, thus cherry picking their best years, which in no form is a good measurement of a security’s performance.
CAGR Tip 3: Don’t Forget Risk And Volatility
Remember to couple the CAGR with other performance metrics. As we’ve mentioned before, CAGR does not take risk or volatility into account. When investing and trading, volatility and risk is of utmost importance and an experienced trader or investor knows that he or she needs to manage risk properly. An investment with a good CAGR could look good at first sight. However, later it might prove a worse choice because of its risk level.