CAGR – What Is It And Why Is It Relevant For Trading Strategies? (Performance Analysis)
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
Example Case
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 differ