What Is Average Annual Growth Rate (AAGR)?

The average annual growth rate (AAGR) reports the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis. It doesn’t take compounding into account.

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)

The average annual growth rate helps determine long-term trends. It applies to almost any kind of financial measure including growth rates of profits, revenue, cash flow, expenses, etc. to provide the investors with an idea about the direction wherein the company is headed. The ratio tells you your average annual return.

The average annual growth rate is a calculation of the arithmetic mean of a series of growth rates. 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 is a standard for measuring average returns of investments over several time periods on an annualized basis. You’ll find this figure on brokerage statements and in a mutual fund’s prospectus. It is essentially the simple average of a series of periodic return growth rates.

One thing to keep in mind is that the periods used should all be of equal length—for instance, years, months, or weeks—and not to mix periods of different duration.

AAGR Example

The AAGR measures the average rate of return or growth over a series of equally spaced time periods. As an example, 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.

As another example, consider the five-year real gross domestic product (GDP) growth for the United States over the last five years. The U.S. real GDP growth rates for 2017 through 2021 were 2.3%, 2.9%, 2.3%, -3.4%, and 5.7%, respectively. Thus, the AAGR of U.S. real GDP over the last five years has been 1.96%, or (2.3% + 2.9% + 2.3% + -3.4% + 5.7%) / 5.

AAGR vs. Compound Annual Growth Rate

AAGR is a linear measure that does not account for the effects of compounding. The above example shows that the investment grew an average of 19% per year. The average annual growth rate 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 5 of $100,000 for the AAGR example above. The percentage growth rate for year 5 is -50%. The resulting AAGR would be 5.2%; however, it is evident from the beginning value of year 1 and the ending value of year 5, 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 1 through 4, 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 5 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

Because AAGR is a simple average of periodic annual returns, the measure does not include any measure of the overall risk involved in the investment, as calculated by the volatility of its price. For instance, if a portfolio grows by a net of 15% one year and 25% in the next year, the average annual growth rate would be calculated to be 20%.

To this end, the fluctuations occurring in the investment’s return rate between the beginning of the first year and the end of the year are not counted in the calculations thus leading to some errors in the measurement.

A second issue is that as a simple average it does not care about the timing of returns. For instance, in our example above, a stark 50% decline in year 5 only has a modest impact on total average annual growth. However, timing is important, and so CAGR may be more useful in understanding how time-chained rates of growth matter.

What Is the Average Annual Return (AAR)?

The average annual return (AAR) is a percentage used when reporting the historical return, such as the three-, five-, and 10-year average returns of a mutual fund. The average annual return is stated net of a fund’s operating expense ratio. Additionally, it does not include sales charges, if applicable, or portfolio transaction brokerage commissions.

In its simplest terms, the average annual return (AAR) measures the money made or lost by a mutual fund over a given period. Investors considering a mutual fund investment will often review the AAR and compare it with other similar mutual funds as part of their mutual fund investment strategy.

Understanding the Average Annual Return (AAR)

When you are selecting a mutual fund, the average annual return is a helpful guide for measuring a fund’s long-term performance. However, investors should also look at a fund’s yearly performance to fully appreciate the consistency of its annual total returns.

For example, a five-year average annual return of 10% looks attractive. However, if the yearly returns (those that produced the average annual return) were +40%, +30%, -10%, +5% and -15% (50 / 5 = 10%), performance over the past three years warrants examination of the fund’s management and investment strategy.

Components of an Average Annual Return (AAR)

There are three components that contribute to the average annual return (AAR) of an equity mutual fund: share price appreciation, capital gains, and dividends.

Share Price Appreciation

Share price appreciation results from unrealized gains or losses in the underlying stocks held in a portfolio. As the share price of a stock fluctuates over a year, it proportionately contributes to or detracts from the AAR of the fund that maintains a holding in the issue.

For example, the American Funds AMCAP Fund’s top holding is Netflix (NFLX), which represents 3.7% of the portfolio’s net assets as of Feb. 29, 2020. Netflix is one of 199 equities in the AMCAP fund. Fund managers can add or subtract assets from the fund or change the proportions of each holding as needed to meet the fund’s performance objectives. The fund’s combined assets have contributed to the portfolio’s 10-year AAR of 11.58% through Feb. 29, 2020.

Capital Gains Distributions

Capital gains distributions paid from a mutual fund result from the generation of income or sale of stocks from which a manager realizes a profit in a growth portfolio. Shareholders can opt to receive the distributions in cash or reinvest them in the fund. Capital gains are the realized portion of AAR. The distribution, which reduces share price by the dollar amount paid out, represents a taxable gain for shareholders.

A fund can have a negative AAR and still make taxable distributions. The Wells Fargo Discovery Fund paid a capital gain of $2.59 on Dec. 11, 2015, despite the fund having an AAR of negative 1.48%.

Dividends

Quarterly dividends paid from company earnings contribute to a mutual fund’s AAR and also reduce the value of a portfolio’s net asset value (NAV). Like capital gains, dividend income received from the portfolio can be reinvested or taken in cash.

Large-cap stock funds with positive earnings typically pay dividends to individual and institutional shareholders. These quarterly distributions comprise the dividend yield component of a mutual fund’s AAR. The T. Rowe Price Dividend Growth Fund has a trailing 12-month yield of 1.36%, a contributing factor to the fund’s three-year AAR of 15.65% through Feb. 29, 2020.

Special Considerations

Calculating an average annual return is much simpler than the average annual rate of return, which uses a geometric average instead of a regular mean. The formula is: [(1+r₁) x (1+r₂) x (1+r₃) x … x (1+r_i)] ^(1/n) – 1, where r is the annual rate of return and n is the number of years in the period.

The average annual return is sometimes considered less useful for giving a picture of the performance of a fund because returns compound rather than combine. Investors must pay attention when looking at mutual funds to compare the same types of returns for each fund.