Average Return Calculator
Find the arithmetic average and geometric mean return on any investment, and see why the two numbers differ and which one actually reflects what happened to your money.
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Enter your values above to see the results.
Tips & Notes
- ✓Always use geometric mean (CAGR) when evaluating actual investment performance — arithmetic average consistently overstates what compounding actually produced.
- ✓A -50% loss requires a +100% gain to recover, not +50% — this asymmetry means downside volatility is more destructive than upside volatility is beneficial.
- ✓Reducing portfolio volatility through diversification improves geometric returns even without changing arithmetic returns — this is mathematically provable, not just intuition.
- ✓When fund managers report average returns, verify whether they are reporting arithmetic or geometric — arithmetic average is almost always higher and more impressive looking.
- ✓The gap between arithmetic and geometric mean grows with volatility — highly volatile individual stocks often show this gap most dramatically in marketing materials.
- ✓Sequence of returns matters: the same set of annual returns produces different final values depending on the order they occur, particularly for portfolios with withdrawals.
Common Mistakes
- ✗Trusting arithmetic average return figures in investment marketing without converting to geometric mean — arithmetic average reliably overstates actual compound performance.
- ✗Assuming a +50% year followed by a -50% year breaks even — the result is -25% on original capital, because percentage losses and gains are applied to different base amounts.
- ✗Not accounting for volatility drag when projecting long-term returns — using a 10% arithmetic average instead of the 8.5% geometric equivalent overstates 30-year final value by 60%.
- ✗Comparing arithmetic averages across investments with different volatility profiles — the higher-volatility investment will show a larger arithmetic-to-geometric gap.
- ✗Ignoring the sequence of returns risk for retirement portfolios — early large losses are catastrophic for portfolios experiencing withdrawals even when long-term average returns are healthy.
- ✗Calculating average return without weighting for portfolio size — a 20% return on $10,000 and a 5% return on $100,000 should not receive equal weight in the average.
Average Return Calculator Overview
The average return on an investment sounds simple — add up the annual returns and divide by the number of years. But this arithmetic average consistently overstates actual investment performance. The geometric mean, also called the compound annual growth rate (CAGR), is the number that actually describes what happened to your money.
Understanding the difference between these two figures is one of the most important concepts in investment analysis, and one of the most commonly misunderstood.
What each field means:
- Initial Investment — starting portfolio value or the amount originally invested
- Annual Returns — the return percentage for each year of the holding period; can be positive or negative
- Holding Period — total years of the investment; determines how many annual returns are entered
What your results mean:
- Arithmetic Average Return — simple mean of all annual return percentages; overstates actual performance when returns vary
- Geometric Mean Return (CAGR) — the true annualized return that produced the actual final value from the starting value
- Final Portfolio Value — the actual ending value based on compounded returns year by year
- Total Gain — dollar difference between starting and ending value
Example — $10,000 invested over 4 years with volatile returns:
Year 1: +50% portfolio grows to $15,000 Year 2: -33% portfolio falls to $10,050 Year 3: +25% portfolio grows to $12,563 Year 4: -20% portfolio falls to $10,050 Arithmetic average: (50 - 33 + 25 - 20) / 4 = 5.5% per year Geometric mean (CAGR): ($10,050 / $10,000)^(1/4) - 1 = 0.12% per year The 5.5% arithmetic average is wildly misleading — the actual annual return was 0.12%. Volatility destroys the average: a 50% gain requires a 100% gain to recover a 50% loss.
EX: Why a -50% loss requires a +100% gain to break even $10,000 gains 50% in year 1: $15,000 $15,000 loses 50% in year 2: $7,500 Arithmetic average: (50% - 50%) / 2 = 0% (appears to break even) Actual result: $7,500 (lost 25% of original investment) Geometric mean: ($7,500 / $10,000)^(1/2) - 1 = -13.4% per year The arithmetic average said 0%. The geometric mean said -13.4%. Only one is correct.
Arithmetic vs geometric mean — the volatility gap:
| Return Sequence | Arithmetic Avg | Geometric Mean | Gap |
|---|---|---|---|
| +10%, +10%, +10% | 10.0% | 10.0% | 0% (no volatility) |
| +20%, 0%, +20% | 13.3% | 12.6% | 0.7% |
| +30%, -10%, +30% | 16.7% | 14.9% | 1.8% |
| +50%, -30%, +50% | 23.3% | 17.6% | 5.7% |
Volatility drag — how variance reduces compound returns:
| Annual Variance | Arithmetic Return | Geometric Return | Drag |
|---|---|---|---|
| Low (bonds) | 5.0% | ~4.9% | ~0.1% |
| Moderate (balanced) | 8.0% | ~7.4% | ~0.6% |
| High (equities) | 10.0% | ~8.5% | ~1.5% |
| Very high (single stocks) | 15.0% | ~11.0% | ~4.0% |
Volatility is mathematically destructive to compound returns — a phenomenon called volatility drag. The higher the variance in annual returns, the larger the gap between the arithmetic average (which investment marketers often quote) and the geometric mean (which tells you what actually happened to your money). This is one of the strongest mathematical arguments for diversification: reducing volatility in a portfolio improves compound returns even when it does not change the arithmetic average.
Frequently Asked Questions
Arithmetic mean adds all annual return percentages and divides by the number of years. Geometric mean compounds the returns year over year and finds the equivalent steady annual rate. If returns were +20% and -20% over two years: arithmetic mean is 0%, suggesting no gain or loss. But $10,000 becomes $12,000 after year one (+20%) and then $9,600 after year two (-20% of $12,000). The geometric mean is -2.0% per year — the actual experience. Arithmetic mean is only accurate when annual returns are identical. In all real investment scenarios, geometric mean is the correct measure of actual performance.
The mathematics of percentage changes creates an asymmetry — a percentage loss and an equal percentage gain applied to different base amounts do not cancel out. A 50% loss from $10,000 leaves $5,000. A subsequent 50% gain returns only to $7,500, not $10,000. The arithmetic average of +50% and -50% is zero, but the actual result is -25%. This gap between arithmetic average and geometric mean is called volatility drag and grows larger as return variance increases. Reducing portfolio volatility through diversification reduces this drag and improves compound returns, even when it does not increase the arithmetic average return.
CAGR (Compound Annual Growth Rate) is identical to the geometric mean return — it is the single steady annual rate that would produce the same starting-to-ending value as the actual sequence of returns. If $10,000 grew to $19,500 over 7 years: CAGR = ($19,500/$10,000)^(1/7) - 1 = 10.0%. The arithmetic average of the actual annual returns might be 11-12% — higher than the CAGR — due to volatility drag. CAGR is the performance number that actually corresponds to what an investor experienced in their portfolio.
The geometric mean return is calculated as: (Final Value / Initial Value)^(1/n) - 1, where n is the number of years. Alternatively, if you have individual annual returns r1, r2, r3...: Geometric Mean = [(1+r1) x (1+r2) x (1+r3) x ... x (1+rn)]^(1/n) - 1. For example, with returns of +30%, -10%, +20%: [(1.30) x (0.90) x (1.20)]^(1/3) - 1 = (1.4040)^(0.333) - 1 = 12.0% per year. Compare this to the arithmetic average of (30-10+20)/3 = 13.3% — the geometric mean is lower due to volatility.
No — the geometric mean is the same regardless of the order annual returns occur. A sequence of +30%, -10%, +20% and a sequence of +20%, +30%, -10% produce exactly the same geometric mean and exactly the same final portfolio value, assuming no withdrawals or contributions. However, sequence of returns matters enormously for portfolios with ongoing withdrawals. A retiree experiencing large losses in early years while withdrawing funds faces a very different outcome than one who experiences the same returns in reverse order, even though the geometric mean over the full period is identical.
Always request the geometric mean return (CAGR) rather than the arithmetic average. Ask for the return net of all fees — expense ratios, transaction costs, and advisory fees. Compare against the appropriate benchmark over the same period — an equity fund should compare against an equity index, not against bonds or cash. Look at rolling returns over multiple periods (1-year, 3-year, 5-year, 10-year) rather than a single favorable period. Verify the Sharpe ratio or similar risk-adjusted metric alongside raw returns — a fund that achieves 10% with high volatility is less impressive than one achieving 9% with low volatility.