## What is the Compound Annual Growth Rate?

Compound annual growth rate, or CAGR, is the mean annual growth rate of an investment over a specified period of time longer than one year. It represents 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 used when investment advisors tout their market savvy and funds promote their returns. But what does it really show?

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

For example, let’s assume you invested \$1,000 at the beginning of 2016 and by year-end your investment was worth \$3,000, a 200% return. The next year, the market corrected, and you lost 50% — ending up with \$1,500 at the end of 2017.

What was the return on your investment for the period? Using average annual return does not work. The average annual return on this investment was 75% (the average of 200% gain and 50 % loss), but in this two-year period you ended up with \$1,500 not \$3,065 (\$1,000 for two years at an annual rate of 75%). To determine what your annual return was for the period, you need to calculate the CAGR.

How CAGR Works

To calculate the CAGR you take the nth root of the total return, where “n” is the number of years you held an investment.

Compound Annual Growth Rate 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 in order 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.

Risk

When using the Compound Annual Growth Rate, it is important to remember two things:

– It does not reflect investment risk.
– You must use the same time periods.

Investment returns are volatile, meaning they can vary significantly from one year to another. However, CAGR does not reflect volatility. CAGR is a pro forma number that provides a “smoothed” annual yield, so it can give the illusion that there is 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.

Standard deviation is a statistic that measures how annual returns might vary from the expected return. Very volatile investments have large standard deviations because their annual returns can vary significantly from their average annual return. Less volatile stocks have smaller standard deviations because their annual returns are closer to their average annual return.

For example, 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). In contrast, a stock’s price can vary significantly from its average return, thus causing a higher standard deviation. The standard deviation of a stock is generally greater than the savings account or a bond held to maturity.

Things get ugly when the Compound Annual Growth Rate is used to promote investment results without incorporating the risk factor. Mutual fund companies emphasize their CAGRs from different time periods in order to get you to invest in their funds, but they rarely incorporate a risk adjustment. It is also important to read the fine print in order to know what time period is being used. Advertisements can tout a fund’s 20% CAGR in bold type, but the time period used may be from the peak of the last bubble, which has no bearing on the most recent performance.

Summary

The Compound Annual Growth Rate is a good and valuable tool to evaluate investment options, but it does not tell the whole story. Investors can analyze investment alternatives by comparing their CAGRs from identical time periods. Investors, however, also need to evaluate the relative investment risk. This requires the use of another measure such as standard deviation.

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