Compound annual growth rate, or CAGR, is a term used when investment advisors tout their market savvy and funds promote their returns. But what does it really show? This article will define CAGR and discuss its good and bad points.

CAGR Defined
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; it indicates 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 1999 and by year-end your investment was worth \$3,000, a 200% return. The next year, the market corrected, and you lost 50% and ended up with \$1,500 at year-end 2000.

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What was the return on your investment for the period? Using the 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.

To calculate the CAGR you take the nth root of the total return, where "n" is the number of years you held the investment. In this example, you take the square root (because your investment was for two years) of 50% (the total return for the period) and get a CAGR of 22.5%. Table 1 illustrates the annual returns, CAGR, and average annual return of this hypothetical portfolio. The lower portion of the table illustrates how applying the CAGR gives the number that equates the ending value of the initial investment.

 Table 1: How CAGR Works

Figure 1 is a graphical representation of Table 1 and illustrates the smoothing effect of the CAGR. Notice how the lines vary but the ending value is the same.

 Figure 1: CAGR Example

The Good
CAGR is the best formula for evaluating how different investments have performed over time. 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.

When using the CAGR, it is important to remember two things: the CAGR does not reflect investment risk, and you must use the same time periods.

Investment returns are volatile, meaning they can vary significantly from one year to another, and 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.

Investment results vary depending on the time periods. For example,company ABC 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 you were smart enough to buy its stock at \$5 and one year later sell it at \$22 for a 340% gain. But if one more year later the price was \$5 and you still have it in your portfolio, you would be even. If you bought ABC in year 1 at \$22 and still had it in Year 2, you would have lost 77% of your equity value (from \$22 to \$5).

To demonstrate both CAGR and volatility risk, let's look at three investment alternatives: a solid blue chip, a risky tech company and the five-year Treasury bond. We will examine the CAGR and average growth rate for each investment (adjusted for dividends and splits) for five years. We will then compare the volatility of these investments by using a statistic called the standard deviation.

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.

The annual returns, CAGR, average annual return, and standard deviation (StDev) of each of the three investments are summarized in Table 2. We will assume that the investments were made at the end of 1996 and that the five-year bond was held to maturity. The market priced the five-year bond to yield 6.21% at the end of 1996, and we show the annual accrued amounts, not the bond's price. The stock prices are those of the end of the respective years.

 Table 2: Return Comparison

Because we have treated the five-year bond like a savings account (ignoring the market price of the bond), 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 zero also 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's. The CAGR for Blue Chip was slightly less than 20%, but was lower than the average annual return of 23.5%. Because of this difference, the standard deviation was 0.32.

High Tech outperformed Blue Chip by posting a CAGR of 65.7%, but this investment was also more risky because the stock's price fluctuated more than Blue Chip's. This volatility is shown by the high standard deviation of 3.07.

The following graphs compare the year-end prices to the CAGR and illustrate two things. First, the graphs show how the CAGR for each investment relates to the actual year-end values. For the bond, there is no difference (so we didn't display its graph for the CAGR comparison) because the actual returns do not vary from the CAGR. Second, the difference between the actual value and the CAGR value illustrates investment risk.

 Figure 2: Year-End Stock Prices
 Figure 3: Blue Chip CAGR
 Figure 4: High Tech CAGR

In order to compare the performance and risk characteristics between investment alternatives, investors can use a risk-adjusted CAGR. A simple method for calculating a risk-adjusted CAGR is to multiply the CAGR by one minus the standard deviation. If the standard deviation (risk) is zero, the risk-adjusted CAGR is unaffected. The larger the standard deviation, the lower the risk-adjusted CAGR. For example, here is 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 65.70%)

This analysis shows two things:

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

While historical performance is not a 100% indicator of future results, it does provide the investor with some valuable information.

The Ugly
Things get ugly when the CAGR 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. Ads 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.

The Bottom Line
The CAGR 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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