Compound Annual Growth Rate: What You Should Know

What Is the CAGR?

The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a period longer than one year. It's one of the most accurate ways to calculate and determine returns for individual assets, investment portfolios, and anything that can rise or fall in value over time.

CAGR is a term often used when investment advisors tout their market savvy and when funds promote their returns. 

Understanding the CAGR

The CAGR is a mathematical formula that provides a smoothed rate of return. It results in a pro forma number that tells you what an investment yields on an annually compounded basis. It indicates to investors what they really have at the end of the investment period.

Assume you invested $1,000 at the beginning of 2022 and your investment was worth $3,000 by year's end, a 200% return. The market corrected the next year and you lost 50%, ending up with $1,500 at the end of 2023.

Using average annual return doesn't provide the return on your investment for the period. The average annual return on this investment was 75% (the average of a 200% gain and a 50% loss) but the result was $1,500, not $3,065, in this two-year period: $1,000 for two years at an annual rate of 75%. You have to calculate the CAGR to determine what your annual return was for the period.

How to Calculate the CAGR 

Take the nth root of the total return to calculate the CAGR where n is the number of years you held the investment. This calculation is the geometric mean. Take the square root of 50% (the total return for the period) in this example because your investment was for two years. You obtain a CAGR of 22.5%.

This table illustrates the annual returns, CAGR, and the average annual return of this hypothetical portfolio. It illustrates the smoothing effect of the CAGR. Notice how the lines vary but the ending value is the same.

CAGR is the best formula for evaluating how different investments have performed over time. It helps fix the limitations of the arithmetic average return. Investors can compare the CAGR to evaluate how well one stock performed against other stocks in a peer group or against a market index. The CAGR can also be used to compare the historical returns of stocks to bonds or a savings account.

CAGR and Risk

It's important to remember two things when using the CAGR:

1. It doesn't reflect investment risk.
2. You must use the same time periods.

Investment returns are volatile. They can vary significantly from one year to the next but CAGR doesn't reflect volatility. It's a pro forma number that provides a "smoothed" annual yield so it can give the illusion that there's a steady growth rate even when the value of the underlying investment can vary significantly. This volatility or investment risk is important to consider when making investment decisions.

Investment results vary depending on the time periods. Company ABC's stock had the following price trend over three years:

This could be viewed as a great investment if you were smart enough to buy the stock at $5 and one year later sell it at $22 but you would be even if the price was $5 one year later and you still hold it in your portfolio. You would have lost 77% of your equity value (from $22 to $5) if you bought ABC in Year 1 at $22 and still had it in Year 2.

Look at three investment alternatives to demonstrate both CAGR and volatility risk: a solid blue chip, a risky tech company, and a five-year Treasury bond. We'll examine the CAGR and average growth rate for each investment, adjusted for dividends and splits, for five years. We'll then compare the volatility of these investments by using a statistic known as the standard deviation. Standard deviation is a statistic that measures how annual returns might vary from the expected return.

The standard deviation of a savings account is zero because the annual rate is the expected rate of return assuming you don't deposit or withdraw any money. A stock's price can vary significantly from its average return, causing a higher standard deviation. The standard deviation of a stock is generally greater than the savings account or a bond that's held to maturity.

The annual returns, CAGR, average annual return, and standard deviation (StDev) of each of the three investments are summarized in this table. We assume that the five-year bond was held to maturity. The market priced the five-year bond to yield 6.21% at the end of the first year and we show the annual accrued amounts, not the bond's price. The stock prices are those at the end of the respective years.

We've treated the five-year bond in the same way as a savings account, ignoring the market price of the bond, so the average annual return is equal to the CAGR. The risk of not achieving the expected return was zero because the expected return was locked in. The standard deviation is also zero because the CAGR was the same as the annual returns.

Blue-chip shares were more volatile than the five-year bond but not as much as the high-tech group. The CAGR for blue chip was slightly less than 20% but it was lower than the average annual return of 23.5%. The standard deviation was 0.32 due to this difference.

High tech outperformed blue chip by posting a CAGR of 65.7% but this investment was also riskier because the stock's price fluctuated more than the blue chip prices. This volatility is shown by the high standard deviation of 3.07.

These graphs compare the year-end prices to the CAGR and they illustrate two things. First, they show how the CAGR for each investment relates to the actual year-end values. There's no difference for the bond because the actual returns don't vary from the CAGR so we didn't display its graph for the CAGR comparison.

Second, the difference between the actual value and the CAGR value illustrates investment risk.

Investors can use a risk-adjusted CAGR to compare the performance and risk characteristics between investment alternatives. A simple method for calculating a risk-adjusted CAGR is to multiply the CAGR by one minus the standard deviation. The risk-adjusted CAGR is unaffected if the standard deviation (risk) is zero. The larger the standard deviation, the lower the risk-adjusted CAGR.

Here's the risk-adjusted CAGR comparison for the bond, the blue chip, and the high-tech stock:

• Bond: 6.21%
• Blue Chip: 13.6% (instead of 19.96%)
• High Tech: -136% (instead of 65.7%)

This analysis shows two findings:

• The bond holds no investment risk but the return is below that of stocks.
• Blue chip appears to be preferable to a high-tech stock. The high-tech stock's CAGR was much greater than the blue chip's CAGR (65.7% versus 19.9%) but its risk-adjusted CAGR is lower than the blue chip's risk-adjusted CAGR because high-tech shares were more volatile.

The CAGR isn't ideal if it's used to promote investment results without incorporating the risk factor. Mutual fund companies emphasize their CAGRs from different periods to encourage investment in their funds but they rarely incorporate a risk adjustment.

Read the fine print to understand the time period that applies. Advertisements can tout a fund's 20% CAGR in bold type but the period used may be from the peak of the last bubble and this has no bearing on the most recent performance.

The Bottom Line

The CAGR is a good and valuable tool to evaluate investment options but it doesn't tell the whole story. Investors can analyze investment alternatives by comparing their CAGRs from identical time periods. They should also evaluate the relative investment risk. This requires the use of another measure such as standard deviation.

The comments, opinions, and analyses expressed on Investopedia are for informational purposes online. Read our warranty and liability disclaimer for more info.