Understanding Average Annual Growth Rate (AAGR): Definition and Formula

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 widely used to evaluate a country's gross domestic product (GDP), a company's revenues or profits, and investment performance, like mutual funds or stocks. Calculating AAGR uses the arithmetic mean of growth rates over a defined time period. AAGR is limited by not accounting for compounding effects, thus necessitating a comparison with other measures like CAGR.

How to Calculate the 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​

Exploring the Importance of 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. Also, AAGR doesn't account for periodic compounding.

Real-World Examples of Average Annual Growth Rate (AAGR)

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 finance, the start and end prices are usually used, but some analysts might use average prices depending on the analysis.

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.

Comparing AAGR and CAGR: Key Differences Explained

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 with the result from the AAGR of 5.2%.

What to Know About the Limitations of the Average Annual Growth Rate (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 downside is that AAGR doesn't consider risk. An investment might show higher AAGR yet be more volatile.

The Bottom Line

AAGR is a widely used financial metric that evaluates performance over time for investments, companies, and economies. A simple and easy calculation, AAGR uses the arithmetic mean of growth rates for a clear overview of past performance.

The limitations of AAGR are in its exclusion of compounding effects and sensitivity to volatility and outliers, which can mislead investors. Due to these limitations, AAGR should be used in conjunction with other metrics, such as CAGR, to obtain a fuller picture of financial growth and investment performance.

It's important to consider investment risk and volatility, as AAGR does not incorporate these factors. Investors should consult with financial professionals and combine AAGR with additional financial tools for comprehensive analysis and informed decision-making.