AAGR is the arithmetic average of annual growth rates; it describes the yearly observations but does not reproduce cumulative investment growth.
Average annual growth rate (AAGR) is the arithmetic average of a series of annual percentage growth rates. It summarizes the average yearly change, giving each included year equal weight.
AAGR is not the constant compound rate that links a starting value to an ending value. It can be positive when wealth declines, or zero when an investment loses money. For endpoint growth, compare it with compound annual growth rate, or CAGR.
For n annual growth rates g_1 through g_n:
For a positive business metric, such as comparable annual revenue:
Here, the numerator is the current year’s value and the denominator is the preceding year’s value. Four annual observations produce three year-over-year changes.
For an investment account, raw balance changes only represent returns when external cash flows and the treatment of income have been addressed.
Suppose a hypothetical business reports these comparable annual revenues. There are no changes in currency, accounting basis, or business scope.
| Annual observation | Revenue | Growth from previous year |
|---|---|---|
| Base year | $10 million | Not applicable |
| Year 1 | $15 million | 50.00% |
| Year 2 | $18 million | 20.00% |
| Year 3 | $22 million | 22.22% |
Keep full precision for the third growth rate until the final calculation:
The comparable CAGR is:
Total revenue growth is 120%. Dividing that total by three gives 40%, which is neither AAGR nor CAGR for this series.
| Measure | Result | Question answered |
|---|---|---|
| Total growth | 120.00% | How much did revenue increase from the base year? |
| AAGR | 30.74% | What was the arithmetic average of the three annual growth rates? |
| CAGR | 30.06% | What constant compound annual rate reproduces the endpoints? |
AAGR is not merely a less precise CAGR. It is a different statistic. FINRA’s explanation of annualized returns emphasizes that compounding matters when converting a multiyear investment gain into an equivalent annual rate. FINRA: Calculating Your Investment Returns.
Suppose an investment starts at $100, earns 50% in year 1, and loses 50% in year 2, with no external cash flows.
The value rises to $150 and then falls to $75. The AAGR is zero:
But cumulative return is -25%, and CAGR is approximately -13.40%:
The loss applies to a larger balance than the initial gain did. Adding the percentage rates therefore fails to describe the change in wealth.
For the same equal-length periods and strictly positive growth factors, the arithmetic mean of annual growth rates is at least as large as the geometric compound rate. They are equal when all annual rates are identical.
AAGR can summarize a set of observed yearly changes, such as comparable revenue growth, or support discussion of the average annual result alongside the individual observations.
It should not replace compound growth when describing what happened to an amount invested through successive years. GIPS guidance identifies annualized investment performance as a geometric, not arithmetic, calculation. GIPS: Standards Handbook for Firms.
AAGR also does not supply the probability of a future outcome. Using an observed average in a forecast requires assumptions about whether the past observations remain relevant.
Mixing time intervals. A six-month rate and a full-year rate are not two comparable annual observations. State the measurement periods rather than averaging them blindly.
Counting a deposit as growth earned. Calculate cash-flow-aware investment returns before producing a performance summary. Time-weighted return and money-weighted return address different aspects of cash-flow timing.
Ignoring the base. A small positive base can produce a very large percentage change. Zero denominators make a year’s growth rate undefined; negative earnings or loss-to-profit transitions need explanation in amounts rather than a mechanically averaged percentage.
Hiding dispersion. AAGR alone does not show volatility, drawdowns, or whether one unusual year dominates the result. Show the underlying rates and investigate changes in business scope or accounting.
Treating a historical mean as promised growth. Neither AAGR nor CAGR establishes future performance or compensates for differences in risk, fees, and income treatment. Investor.gov: Reading Fund Performance.
The examples explain growth measurement and are not personalized investment or business advice.