Definition
– Average Annual Growth Rate (AAGR) is the arithmetic mean of a series of periodic growth rates, expressed as a percentage. It measures the simple average rate at which a value (an investment, a company metric, or an economic indicator) changed per period, without accounting for compounding.
Key formula
– AAGR = (GR1 + GR2 + … + GRn) / n
– where GRi = growth rate in period i (expressed as a decimal or percentage)
– n = number of periods
How to compute AAGR — step‑by‑step
1. Choose equal-length periods (years, quarters, months).
2. Calculate each period’s growth rate: growth = (ending value / beginning value) − 1.
3. Convert each growth to percent if desired.
4. Sum the period growth rates.
5. Divide the sum by the number of periods: that result is the AAGR.
Short checklist — when to use AAGR and practical checks
– Use AAGR when you want a simple, easily understood average of period-to-period rates.
– Ensure all periods are the same length.
– Check for large outliers or a period of extreme loss/gain — AAGR can be distorted.
– Remember AAGR ignores compounding; if you need a compounded measure of return use CAGR (see below).
– Decide whether to compute growth from period‑end to next period‑end (typical) or use average prices if that better fits your analysis.
Worked numeric example (investment over four years)
– Year-end values:
– Start (beginning of Year 1): $100,000
– End Year 1: $120,000
– End Year 2: $135,000
– End Year 3: $160,000
– End Year 4: $200,000
1. Compute year-over-year growth rates:
– Year 1: (120,000 / 100,000) − 1 = 0.20 → 20.00%
– Year 2: (135,000 / 120,000) − 1 = 0.125 → 12.50%
– Year 3: (160,000 / 135,000) − 1 ≈ 0.18519 → 18.52%
– Year 4: (200,000 / 160,000) − 1 = 0.25 → 25.00%
2. Sum the rates and divide by 4:
– AAGR = (20.00% + 12.50% + 18.52% + 25.00%) / 4 ≈ 19.00%
Compare with CAGR (compound annual rate)
– CAGR formula: CAGR = (Ending value / Beginning value)^(1 / number of years) − 1
– Using the same example: CAGR = (200,000 / 100,000)^(1/4) − 1 = 2^(0.25) − 1 ≈ 18.92%
– Interpretation: AAGR (19.00%) ≈ CAGR (18.92%) here, but AAGR can differ materially when returns vary widely or include large negative periods.
What AAGR tells you
– AAGR gives the simple average of year‑to‑year growth rates and is useful for quick comparisons or to summarize a set of periodic percent changes.
– It is commonly used for headline comparisons of revenue, earnings, GDP growth, or periodic investment returns.
Limitations and cautions
– No compounding: AAGR does not represent the actual compounded growth over multiple periods.
– Sensitive to volatility: extreme positive or negative periods can skew the mean.
– Misleading for cumulative returns: the arithmetic average of percent changes can overstate (or understate) the true geometric return.
– Use CAGR or geometric mean when you need the compound rate that links beginning and ending values.
When to prefer CAGR
– Use CAGR when you want the single steady rate that, if applied each period, would grow the beginning value to the ending value (i.e., it accounts for compounding).
Short tip
– Present both AAGR and CAGR when communicating performance: AAGR shows average yearly swing; CAGR shows actual compounded trend.
Sources
– Investopedia — Average Annual Growth Rate (AAGR): https://www.investopedia.com/terms/a/aagr.asp
– U.S. Bureau of Economic Analysis (BEA) — national economic data and GDP: https://www.bea.gov/
– U.S. Securities and Exchange Commission — investor education resources: https://www.investor.gov/
– International Monetary Fund (IMF) — data and methodology on economic indicators: https://www.imf.org/
Educational disclaimer
This explanation is for educational purposes only and does not constitute personalized investment advice. Always verify data and consider consulting a qualified financial professional before making investment decisions.