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The compound annual growth rate (CAGR) is the mean annual growth rate over a period longer than one year. It’s an accurate way to calculate and determine returns for individual assets or investment portfolios.
CAGR is used by investment advisors to tout their market savvy, and by investment funds to promote returns.
Key Takeaways
- The compound annual growth rate (CAGR) provides a pro forma number that tells investors what an investment yields on an annually compounded basis.
- CAGR is the best formula for evaluating performance over time.
- Investors can use a risk-adjusted CAGR to compare performance and risk characteristics between investment alternatives.
What Is CAGR?
The CAGR is a formula that provides a smoothed rate of return. It results in a pro forma number that tells what an investment yields on an annually compounded basis. It indicates to investors what they have at the end of the investment period. CAGR reveals a trend by smoothing out fluctuations.
CAGR is the best formula for evaluating how different investments perform over time. It helps fix the limitations of the arithmetic average return. Investors can compare the CAGR to how well one stock performed against others 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.
Investors may use an industry’s CAGR projections to guide their portfolios. According to BCC Research, the virtual reality technology market is expected to grow from $21.1 billion in 2023 to $66.9 billion by 2028, at a CAGR of 26.0% while the artificial intelligence (AI) in drug discovery market is projected to grow from $1.6 billion in 2023 to $5.7 billion by 2028, at a CAGR of 29.6%.
How To Calculate the CAGR
Assume an individual invested $1,000 at the beginning of 2022 that grew to $3,000 by year’s end, a 200% return. The market corrected the next year, and they lost 50%, ending with $1,500 at the end of 2023. Using average annual return doesn’t provide the return on the 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 these two years: $1,000 for two years at an annual rate of 75%.
Calculate the CAGR to determine the period’s annual return. Take the nth root of the total return to calculate the CAGR, where n is the number of years an investment is held. This calculation is the geometric mean. Take the square root of 50% (the total return for the period) in this example because the investment was for two years. The CAGR equals 22.5%.
This table illustrates annual returns, CAGR, and the average annual return of this hypothetical portfolio. It shows the smoothing effect of the CAGR. The lines vary, but the ending value is the same.
CAGR and Risk
Investment returns are volatile. They can vary significantly from one year to the next, but CAGR doesn’t reflect volatility. It 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 also vary depending on the periods. Company ABC’s stock had the following price trend over three years:
| Year | 0 | 1 | 2 |
| Price | $5 | $22 | $5 |
This could be viewed as a great investment if an investor were smart enough to buy the stock at $5 and one year later sell it at $22. They would even if the price was $5 one year later and they still had it in their portfolio. They would have lost 77% of equity (from $22 to $5) if they bought ABC in Year 1 at $22 and still had it in Year 2.
Fast Fact
A negative CAGR means an investment’s value has decreased over time.
Multiple Investments Example
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. First, examine the CAGR and average growth rate for each investment, adjusted for dividends and splits, for five years. Then, compare the volatility of these investments by using a statistic known as the standard deviation.
Standard deviation measures how annual returns vary from the expected return. The standard deviation of a savings account is zero because the annual rate is the expected rate of return. A stock’s price can vary significantly from its average return, causing a higher standard deviation.
The annual returns, CAGR, average annual return, and standard deviation (StDev) of each of the three investments are summarized in this table. 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 the annual accrued amounts are displayed, not the bond’s price. The stock prices reflect those at the end of the respective years. The five-year bond is treated like a savings account, so the average annual return is equal to the CAGR.
The following graphs compare the year-end prices to the CAGR, and they illustrate 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. The difference between the actual value and the CAGR illustrates investment risk.
Blue-chip shares were more volatile than the five-year bond but not as much as the high-tech group. The CAGR for blue chips 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.
Investors can use a risk-adjusted CAGR to compare the performance and risk characteristics between investment alternatives. Calculate a risk-adjusted CAGR by multiplying 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.
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 the bond holds no investment risk, but the return is below that of stocks. Blue chips are preferable to a high-tech stock. The high-tech stock’s CAGR was much greater than the blue chip’s CAGR (65.7% vs. 19.9%), but its risk-adjusted CAGR is lower than the blue chip’s risk-adjusted CAGR because high-tech shares were more volatile.
What Is a Market Index?
A market index is a pool of securities, all of which fall under the umbrella of a section of the stock market. Each index uses a unique methodology.
How Is Average Annual Return Calculated?
Average annual return (AAR) is a simple mathematical calculation of returns segmented into periods. Add the returns in all the periods and divide them by the number of periods used.
Why Is Risk Important When Calculating CAGR?
The CAGR isn’t ideal if it’s used to promote investment results without incorporating risk. For example, mutual fund companies may emphasize their CAGRs from different periods to encourage investment in their funds, but may not adjust for risk. Investors should understand the period used to evaluate the performance results.
The Bottom Line
The CAGR is a 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.
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