Average Annual Growth Rate (AAGR): Definition and Calculation

What Is Average Annual Growth Rate (AAGR)?

Average annual growth rate (AAGR) is the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis. It represents the arithmetic mean of a series of growth rates, is expressed as a percentage, and doesn't factor in compounding.

AAGR is a widely used metric. Among other things, it is commonly used to analyze a country's gross domestic product (GDP), a company's revenues or profits, and the performance of an investment, such as a mutual fund or stock.

Formula for Average Annual Growth Rate (AAGR)

$\begin{aligned} &AAGR = \frac{GR_A + GR_B + \dotso + GR_n}{N} \\ &\textbf{where:}\\ &GR_A=\text{Growth rate in period A}\\ &GR_B=\text{Growth rate in period B}\\ &GR_n=\text{Growth rate in period }n\\ &N=\text{Number of payments}\\ \end{aligned}$​AAGR=NGRA​+GRB​+…+GRn​​where:GRA​=Growth rate in period AGRB​=Growth rate in period BGRn​=Growth rate in period nN=Number of payments​

Understanding the Average Annual Growth Rate (AAGR)

AAGR helps determine long-term trends. It is a metric that’s commonly used to assess the performance of investments, businesses, and economies over several years.

AAGR tells us the mean annualized rate of growth of the subject. It is calculated by adding the individual growth rates together and then dividing the resulting figure by the total number of time periods. AAGR is easy to calculate, smooths out fluctuations, and facilitates comparison across different datasets and timeframes.

AAGR is used to analyze various financial metrics, including a company’s revenue, profit, and market share, economic indicators such as GDP and employment rates, and investment returns. AAGR can be calculated for any investment, but it will not include any measure of the investment's overall risk, as measured by its price volatility. Furthermore, the AAGR does not account for periodic compounding.

AAGR Examples

The AAGR measures the average rate of return or growth over a series of equally spaced time periods. Here are two examples.

Financial Investment

Assume an investment has the following values over the course of four years:

• Beginning value = $100,000
• End of year 1 value = $120,000
• End of year 2 value = $135,000
• End of year 3 value = $160,000
• End of year 4 value = $200,000

The formula to determine the percentage growth for each year is:

$\text{Simple percentage growth or return} = \frac{\text{ending value}}{\text{beginning value}} - 1$Simple percentage growth or return=beginning valueending value​−1

Thus, the growth rates for each of the years are as follows:

• Year 1 growth = $120,000 / $100,000 - 1 = 20%
• Year 2 growth = $135,000 / $120,000 - 1 = 12.5%
• Year 3 growth = $160,000 / $135,000 - 1 = 18.5%
• Year 4 growth = $200,000 / $160,000 - 1 = 25%

The AAGR is calculated as the sum of each year's growth rate divided by the number of years:

$AAGR = \frac{20 \% + 12.5 \% + 18.5 \% + 25 \%}{4} = 19\%$AAGR=420%+12.5%+18.5%+25%​=19%

In financial and accounting settings, the beginning and ending prices are usually used. Some analysts may prefer to use average prices when calculating the AAGR depending on what is being analyzed.

Gross Domestic Product (GDP) Growth

As another example, consider the five-year real GDP growth of the United States over the last five years.

The U.S. real GDP growth rates for 2019 through 2023 were 2.5%, -2.2%, 5.8%, 1.9%, and 2.5%, respectively. Thus, the AAGR of U.S. real GDP over the last five years has been 2.1%, or (2.5% - 2.2% + 5.8% + 1.9% + 2.5%) /5.

AAGR vs. Compound Annual Growth Rate (CAGR)

AAGR is a linear measure that does not account for the effects of compounding. The above financial investment example showed that growth over four years averaged 19% per year. The AAGR is useful for showing trends; however, it can be misleading to analysts because it does not accurately depict changing financials. In some instances, it can overestimate the growth of an investment.

For example, consider an end-of-year value for year five of $100,000 for the AAGR example above. The percentage growth rate for year five is -50%. The resulting AAGR would be 5.2%; however, it is evident from the beginning value of year one and the ending value of year five, the performance yields a 0% return. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR).

The CAGR smooths out an investment's returns or diminishes the effect of the volatility of periodic returns. 

Formula for CAGR

$CAGR = \frac{\text{Ending Balance}}{\text{Beginning Balance}}^{\frac{1}{\text{\# Years}}} - 1$CAGR=Beginning BalanceEnding Balance​# Years1​−1

Using the above example for years one through four, the CAGR equals:

$CAGR = \frac{\$200,000}{\$100,000}^{\frac{1}{4}}- 1 = 18.92\%$CAGR=$100,000$200,000​41​−1=18.92%

For the first four years, the AAGR and CAGR are close to one another. However, if year five were to be factored into the CAGR equation (-50%), the result would end up being 0%, which sharply contrasts the result from the AAGR of 5.2%.

Limitations of the AAGR

AAGR is a simple average of periodic annual returns. Though useful, this growth measure also contains flaws, which are important to be aware of.

Issues include its sensitivity to outliers and fluctuations and giving the impression of a constant rate of growth over the observation period, which may not be the case. Another drawback of using AAGR to examine investment opportunities is that it does not take account of risk. One investment may have a slightly higher AAGR but be much more volatile and risky.

The Bottom Line

The average annual growth rate (AAGR) provides the arithmetic mean of a series of growth rates and is commonly used in finance as an indicator of performance and a comparative tool. With a simple calculation, AAGR lets you see the average annualized return of a subject over multiple years. However, its simplicity also carries drawbacks and makes relying solely on this measure to make decisions a bad idea.