Geometric Mean Return Calculator: Measure Investment Performance Accurately

How to use the tool

• Type your returns in decimals, separated by commas. Example 1: 0.12, -0.05, 0.03. Example 2: 0.08, 0, 0.07, -0.02.
• Press “Calculate.” The script multiplies each (1 + r), takes the n-th root, then subtracts 1.
• Read the result as a percentage; it represents your average compound growth per period.

Formula used

$$GMR = \left(\prod_{i=1}^{n}(1+r_i)\right)^{1/n} – 1$$

Worked examples

• Example 1: 0.12, -0.05, 0.03 → Product = 1.12 × 0.95 × 1.03 = 1.09592. Cube root = 1.0311. GMR = 3.11 %.
• Example 2: 0.08, 0, 0.07, -0.02 → Product = 1.132488. Fourth root = 1.0316. GMR = 3.16 %.

Quick-Facts

• Geometric mean never exceeds arithmetic mean for unequal returns (CFA Institute, 2020).
• “CAGR is simply a geometric mean over time” (Investopedia, https://www.investopedia.com/terms/c/cagr.asp).
• If any period is -100 %, the product becomes zero and GMR = -100 % (Morningstar, 2022).
• Accepts daily, monthly, or annual data because the root adjusts for period length (CFA Curriculum, 2023).

FAQ

What is the geometric mean return?

Geometric mean return is the nth-root of the compounded growth factors minus 1, giving the exact average rate earned per period (CFA Institute, 2020).

Why is it better than the arithmetic mean?

Arithmetic mean ignores compounding, so it overstates performance when returns vary. Geometric mean captures volatility effects, one reason CFA texts call it “the only correct average for multi-period returns” (CFA Curriculum, 2023).

Can the result be negative?

Yes. When the compounded product is below 1, the root also falls below 1, yielding a negative percentage that signals a net loss (Morningstar Guide, 2022).

Does mixing daily and monthly data distort the output?

Mixing frequencies distorts results because each root assumes equal-length periods. Convert all returns to the same interval first (Vanguard Research, 2021).

What happens if one period is -100 %?

The product becomes zero, so the geometric mean is -100 %; recovery is impossible because the investment value hit zero (Investopedia, https://www.investopedia.com/articles/08/arithmetic-geometric-mean.asp).

Is geometric mean the same as CAGR?

CAGR is the geometric mean of a single investment’s total growth over several periods, so both metrics equal each other when cash flows are absent (Investopedia, link above).

How many periods produce a reliable estimate?

Studies suggest at least five periods reduce random error for volatile assets (Dimson et al., 2022).

Does the tool adjust for cash flows?

No. Geometric mean is time-weighted and ignores external cash flows; use money-weighted return (IRR) if deposits or withdrawals occur (GIPS Standards, 2020).