CAGR Formula
The compound annual growth rate is the single constant rate that would grow a beginning value to its ending value over the period. It is the geometric mean return, which correctly accounts for compounding, and it is almost always lower than the arithmetic average return because volatility drags compound growth below the simple mean.
Formula
Copy the exact expression or work through it step by step below.
CAGR = (EndingValue / BeginningValue)^(1 / years) - 1 Variables
EndingValue
Ending value
The portfolio or investment value at the end of the period, after all gains, losses, and reinvested income.
BeginningValue
Beginning value
The starting value at the beginning of the period. The ratio of ending to beginning is the total growth multiple.
years
Number of years
The length of the period in years, which can be fractional. The reciprocal exponent annualizes the total growth into a per-year rate.
Step By Step
- 1
Divide the ending value by the beginning value to get the total growth multiple.
Growing from 10,000 to 18,000 is a multiple of 1.8.
- 2
Raise the multiple to the power of one divided by the number of years.
Over 4 years: 1.8^(1/4) = 1.8^0.25 = 1.1583.
- 3
Subtract 1 to convert the growth factor into a rate.
1.1583 - 1 = 0.1583 = 15.83%.
- 4
Note that CAGR is the geometric mean and will be below the arithmetic mean whenever returns vary.
A path of +50% then -10% has arithmetic mean 20% but CAGR of only 16.2%.
Worked Example
Four-year investment growth
Beginning value
10,000
Ending value
18,000
Years
4
Growth multiple = 18,000 / 10,000 = 1.8. CAGR = 1.8^(1/4) - 1. The fourth root of 1.8: sqrt(1.8) = 1.34164, sqrt(1.34164) = 1.15829. So CAGR = 1.15829 - 1 = 0.15829 = 15.83%.
CAGR of about 15.83%. A constant 15.83% annual return compounds 10,000 to 18,000 over four years. Verify: 10,000 x 1.15829^4 = 10,000 x 1.8 = 18,000. Because real returns vary year to year, this smooth rate hides the actual path, which is exactly why CAGR is paired with drawdown and volatility when describing performance.
Common Variations
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Sources & References
- Investments — Bodie, Kane, Marcus, McGraw-Hill (2018)
- Global Investment Performance Standards (GIPS) — CFA Institute
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