The average says zero. Your balance says otherwise.
A 20% gain followed by a 20% loss does not leave you where you started. Learn why averaging percentage returns can give a different answer from measuring how your account actually compounded.
Updated 14 Nov 2026 · Original educational material · Hypothetical examples, not live market data
Why does +20% followed by −20% lose money?
Start with $100. A +20% gain brings the balance to $120. A subsequent −20% loss is calculated on the new $120 balance, taking away $24. You finish at $96.
The arithmetic average of the two returns is (20% − 20%) ÷ 2 = 0%. But the two actual investment periods together reduced the account by 4%. Both calculations are correct; they answer different questions.
Two averages, two meanings.
The arithmetic mean adds periodic returns and divides by the number of periods. It is the average one-period return in your observed sample or return model.
The geometric mean asks a different question: what constant per-period return would create the same compounded result? When periodic returns fluctuate, their geometric mean is generally lower than the arithmetic mean, provided the growth factors are positive.
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Zero average return. A 7.84% loss of capital.
The hypothetical returns are +20%, −20%, +20% and −20%. Their arithmetic average is 0.0%, but multiplying their four growth factors gives 1.20 × 0.80 × 1.20 × 0.80 = 0.9216.
| Interval | Return | Account value |
|---|---|---|
| Start | — | $100.00 |
| 1 | +20% | $120.00 |
| 2 | −20% | $96.00 |
| 3 | +20% | $115.20 |
| 4 | −20% | $92.16 |
That equivalent constant geometric return is approximately −2.02% per period, because four consecutive factors of about 0.9798 produce the same final 0.9216 multiplier. The arithmetic and geometric calculations cannot be substituted for each other.
Why do large fluctuations create a growth drag?
A percentage loss reduces the base on which later gains compound. A 50% drawdown requires a 100% recovery; a gain of 50% followed by a loss of 50% leaves only 75% of starting capital. This is sometimes called volatility drag or variance drag, although the exact relationship depends on the return process.
Two strategies can report similar arithmetic average returns but have different long-run compounded paths if their return variability, timing, costs or exposure differ. This is why comparing annualized sample averages without defining the compounding convention can mislead.
When is each return measure useful?
Arithmetic mean is useful for describing average one-period returns and for some one-period expected-return models. Geometric mean describes realized compounded growth over a sequence of observations, for the defined period, without external contributions or withdrawals.
If money is added or withdrawn, the account balance alone cannot tell you an investment return. Time-weighted return and money-weighted return (IRR) address different cash-flow questions. A constant DCA growth assumption is also not the same as measuring historical geometric returns from a particular price series.
When comparing figures, check the period length, fees, return currency, treatment of distributions and whether a mean is arithmetic, geometric, annualized or merely cumulative.
Three common errors.
“+20% and −20% cancel.”
They act on different balances, leaving $96 from $100, not $100.
“Average return equals CAGR.”
Arithmetic average and a compound growth rate use different formulas and may diverge.
“A projected rate is historical performance.”
An assumed DCA or portfolio growth rate is only a scenario input unless backed by verified observations.
Frequently asked questions.
Why is the geometric return lower?
Variable gains and losses multiply across changing balances. For positive investment growth factors, geometric mean is no greater than arithmetic mean.
Is geometric mean the same as CAGR?
CAGR is a geometric compound growth rate expressed per year. A geometric mean of weekly or trade-by-trade returns is not annual until transformed using appropriate timing conventions.
What if the investment goes to zero?
A full loss makes the terminal wealth zero and recovery without additional capital impossible. The usual log-return representation is undefined at a zero growth factor.
Does volatility drag mean every volatile asset loses value?
No. It describes the compounding relationship, not a prediction that an asset's total return must be negative. Positive trends can dominate the drag.
What if I add cash every month?
Contributions change account value independently of investment performance. Use an explicitly specified time-weighted or money-weighted methodology to evaluate the returns.