Average Return Calculator
Compare arithmetic average return against the geometric (CAGR) return that actually matters.
About Average Return Calculator
The arithmetic mean of investment returns overstates actual performance whenever returns vary year to year. If a portfolio gains 50% then loses 50%, the arithmetic average is 0% — but you actually lost 25% of your money. The geometric mean (CAGR) accounts for compounding and represents the true annual growth rate. The difference between the two is called volatility drag and equals roughly half the variance of returns.
Formulas
Arithmetic mean return
Arithmetic mean = (r₁ + r₂ + … + rₙ) / n
- r_i
- Return in year i
- n
- Number of years
Geometric mean return (CAGR)
Geometric mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) − 1
- r_i
- Return in year i (as decimal)
- n
- Number of years
CAGR from start/end value
CAGR = (End Value / Start Value)^(1/n) − 1
- V_end
- Ending portfolio value
- V_start
- Starting portfolio value
- n
- Number of years
Worked example
With the default values below, Average Return Calculator returns Geometric Mean Return (CAGR) of 6.2349%. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Input Methodone of Annual returns (comma separated), Start & end value over period
- Annual returns (comma separated)
- Annual Returns (%, comma separated)
- 12, -5, 8, 20, -10, 15, 7
- Starting Portfolio Valueminimum 1 $
- 10,000 $
- Ending Portfolio Valueminimum 0 $
- 25,000 $
- Number of Yearsaccepts 1–100
- 10
Results
- Geometric Mean Return (CAGR)The actual compound annual return — what your money really earned.
- 6.2349%
- Arithmetic Mean ReturnSimple average of annual returns. Always ≥ geometric mean.
- 6.7143%
- Volatility Drag (Arithmetic − Geometric)The return lost purely due to year-to-year variability.
- 0.4794%
- Total Return
- 52.7112%
- Number of Years
- 7
- Portfolio Value ($10k start)
- $15,271.12
Step by step
- 1Number of years= 7
- 2Arithmetic mean= 6.7143%
- 3Geometric mean (CAGR)= 6.2349%
- 4Drag: arithmetic − geometric= 0.4794%Caused by volatility — always ≥ 0 (AM-GM inequality).
- 5Total portfolio return on $10,000= 52.7112%
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or fees or charges into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
- This is an estimate for general information and not professional financial, tax or legal advice. See the full disclaimer for the limits that apply to this kind of calculator.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why is the geometric mean always lower than the arithmetic mean?
This follows from the AM-GM inequality in mathematics. Any time there is variation in returns, the geometric mean will be strictly less than the arithmetic mean. The greater the volatility, the larger the gap. Only when every year has the exact same return are they equal.
Which average should I use for investment planning?
Always use the geometric mean (CAGR) for forecasting what your money will actually grow to. The arithmetic mean is useful for estimating expected return in a single future period, but for multi-year projections the geometric mean is the correct tool.
What is volatility drag?
Volatility drag is the return lost due to the asymmetry of gains and losses. A 50% loss requires a 100% gain to break even. The larger the swings in returns, the more this effect erodes wealth. Diversification and lower-volatility strategies reduce drag.
What if one of my years shows a total loss (−100%)?
A −100% return means the entire investment was wiped out, making the geometric mean undefined (you'd be taking the nth root of zero). This calculator rejects returns at or below −100% because no meaningful multi-year average exists.