The compound annual growth rate (CAGR) is the rate of return (RoR) that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each period of the investment’s life span.
The compounded annual growth rate (CAGR) is one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.
It measures a smoothed rate of return.
Investors can compare the CAGR of two or more alternatives to evaluate how well one stock performed against other stocks in a peer group or a market index.
CAGR is thus a good way to evaluate how different investments have performed over time, or against a benchmark.
The CAGR does not, however, reflect investment risk.
\begin{aligned}&CAGR= \left ( \frac{EV}{BV} \right ) ^{\frac{1}{n}}-1\times 100\\&\textbf{where:}\\&EV = \text{Ending value}\\&BV = \text{Beginning value}\\&n = \text{Number of years}\end{aligned}CAGR=(BVEV)n1−1×100where:EV=Ending valueBV=Beginning valuen=Number of years
To calculate the CAGR of an investment:
Divide the value of an investment at the end of the period by its value at the beginning of that period.
Raise the result to an exponent of one divided by the number of years.
Subtract one from the subsequent result.
Multiply by 100 to convert the answer into a percentage.
The compound annual growth rate isn’t a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown at the same rate every year and the profits were reinvested at the end of each year.
In reality, this sort of performance is unlikely. However, the CAGR can be used to smooth returns so that they may be more easily understood compared to alternative methods.
Imagine you invested $10,000 in a portfolio with the returns outlined below:
From Jan. 1, 2018, to Jan. 1, 2019, your portfolio grew to $13,000 (or 30% in year one).
On Jan. 1, 2020, the portfolio was $14,000 (or 7.69% from January 2019 to January 2020).
On Jan. 1, 2021, the portfolio ended with $19,000 (or 35.71% from January 2020 to January 2021).
We can see that on an annual basis, the year-to-year growth rates of the investment portfolio were quite different as shown in the parentheses.
On the other hand, the compound annual growth rate smooths the investment’s performance and ignores the fact that 2018 and 2020 were vastly different from 2019. The CAGR over that period was 23.86% and can be calculated as follows:
CAGR=\left(\frac{\$19,000}{\$10,000}\right )^{\frac{1}{3}}-1\times100=23.86\%CAGR=($10,000$19,000)31−1×100=23.86%
The CAGR of 23.86% over the three-year investment period can help an investor compare alternatives for their capital or make forecasts of future values. For example, imagine an investor is comparing the performance of two uncorrelated investments.
In any given year during the period, one investment may be rising while the other falls. This could be the case when comparing high-yield bonds to stocks, or a real estate investment to emerging markets. Using CAGR would smooth the annual return over the period so the two alternatives would be easier to compare.
As another example, let’s say an investor bought 55 shares of Amazon.com (AMZN) stock in December 2017 at $1,180 per share, for a total investment of $64,900. After three years, in December 2020, the stock has risen to $3,200 per share, and the investor’s investment is now worth $176,000.1 What is the CAGR?
Using the CAGR formula, we know that we need the:
Ending Balance: $176,000
Beginning Balance: $64,900
Number of Years: 3
So to calculate the CAGR for this simple example, we would enter that data into the formula as follows: [($176,000 / $64,900) ^ (1/3)] - 1 = 39.5%.