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Investment
Compound returns are multiplicative, so a single large loss outweighs several good years. That asymmetry sets the case for risk control.
By FreeCalculators Editorial · Published 2026-09-01 · Updated 2026-09-04 · 4 min read · 911 words
Compound returns multiply rather than add, which means a single large loss does more damage than an equally large gain does good. A portfolio that gains 50% and then loses 50% is down 25%, not flat. That asymmetry is why avoiding deep drawdowns contributes more to long-run wealth than capturing the strongest upside years, and it is arithmetic rather than opinion.
Multiply 1.50 by 0.50 and you get 0.75. Reverse the order and you still get 0.75. The loss is applied to a larger base than the gain was, so it removes more absolute value. Extend this across a long sequence and the effect compounds: the geometric mean of a volatile series is always lower than its arithmetic mean, and the gap widens with volatility.
This is the mathematical case for diversification. Reducing the depth of your worst years raises your compound return even if it lowers your average one.
| Return sequence | Arithmetic mean | Compound result over 2 years | Effective annual |
|---|---|---|---|
| +50%, -50% | 0% | -25.0% | -13.4% |
| +30%, -30% | 0% | -9.0% | -4.6% |
| +20%, -20% | 0% | -4.0% | -2.0% |
| +10%, -10% | 0% | -1.0% | -0.5% |
| +8%, +6% | 7% | +14.5% | +7.0% |
| +25%, -12% | 6.5% | +10.0% | +4.9% |
It does not mean move to cash. Cash caps drawdowns near zero in nominal terms and guarantees a slow real loss to inflation, which over thirty years is a larger cumulative erosion than most equity drawdowns. Avoiding volatility entirely trades one certain loss for the risk of another.
What it does mean is that reducing the depth of your worst outcomes is worth giving up some of your best. That is exactly the trade a diversified portfolio makes, and the arithmetic above is why it can improve compound returns rather than merely smoothing them.
Two portfolios, twenty years, same average (2026)
Portfolio A: higher average, deeper falls Sixteen years at +14% Four years at -28% Arithmetic mean +5.6% $100,000 compounds to $296,000 Effective annual +5.6% Portfolio B: lower average, shallower falls Sixteen years at +11% Four years at -12% Arithmetic mean +6.4% $100,000 compounds to $370,000 Effective annual +6.8% B has a lower ceiling in good years and ends 25% ahead, because its bad years cost far less. Shallower losses beat higher averages.
Portfolio A had bigger winning years and lost the race. The four bad years cost it more than the twelve extra points a year of upside earned, because each loss applied to a compounded base.
The practical steps are unglamorous: diversify across asset classes that do not fall together, rebalance on a schedule, keep near-term spending out of volatile assets, and size your equity weighting to a drawdown you could hold. None of that requires predicting anything.
What it does require is leaving the money alone. Bureau of Labor Statistics data on the long-run rise in consumer prices shows why a portfolio held entirely in cash is not a safe harbour over decades, so the answer to loss asymmetry is a better mix rather than an exit. The goal is a portfolio whose worst year you can sit through, not one that never has a bad year.
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This guide was written and reviewed by FreeCalculators Editorial, drawing on published formulas, official government sources, and real calculator outputs from our 4 calculators in this category. Every claim is sourced; every formula is auditable. Read our review policy.