Understanding the CAGR Formula
Compound Annual Growth Rate represents the constant annual rate of return that would take an investment from its beginning balance to its ending balance, under the assumption that profits are reinvested each year.
The Mathematical Equation
Total Return (%) = ((Ending Value − Beginning Value) ÷ Beginning Value) × 100
Simple Annual Return (%) = Total Return (%) ÷ n
Where n represents the duration in years. Because CAGR is a geometric progression, it accounts for the compounding effect where returns generate their own returns in subsequent years.
Why Simple Average Return Misleads
The arithmetic mean return can severely distort actual investor outcomes when asset prices fluctuate.
The Volatility Trap
Imagine buying $10,000 of stock. In year one, it gains 100%, rising to $20,000. In year two, it drops 50%, falling back to $10,000.
Arithmetic Average: (100% − 50%) ÷ 2 = +25.0% per year.
Actual CAGR: ($10,000 ÷ $10,000)(1/2) − 1 = 0.0% per year.
The arithmetic average claims you made 25% a year, even though your pocket balance did not gain a single penny. CAGR tells the honest truth: your net annualized growth rate was exactly zero.
Comparing Investments Across Unequal Horizons
Comparing a 3-year mutual fund return of 45% against a 7-year real estate return of 85% is difficult without annualizing both figures.
Fund A (45% in 3 years)
CAGR = (1.45)(1/3) − 1 = 13.18% per year.
Asset B (85% in 7 years)
CAGR = (1.85)(1/7) − 1 = 9.19% per year.