Volatility drag (arithmetic vs geometric return)
Volatility drag is the gap between the arithmetic average of periodic returns and the compound growth rate those returns actually produce. Because a percentage loss requires a larger percentage gain to recover, variable returns compound to less than their average; the gap is approximately half the variance of the returns.
Senzoukria · Glossary · Updated September 2026
At a glance
- Approximation
- Geometric ≈ arithmetic − σ² ÷ 2
- Classic example
- +50% then −50% = ×0.75, a 25% loss
- Recovery needed after a loss L
- L ÷ (1 − L), e.g. 25% after a 20% loss
- Applies to
- Returns compounded on a changing capital base
The mechanism
A gain of 50% followed by a loss of 50% multiplies capital by 1.5 × 0.5 = 0.75. The arithmetic average of the two returns is zero, yet a quarter of the capital is gone. Losses and gains in percent are not symmetric: after a 20% loss, a 25% gain is needed to return to the start, and after a 50% loss, a 100% gain.
For small returns, the compound growth rate is approximately the arithmetic mean minus half the variance. A strategy with an average return of 1% per period and a standard deviation of 10% per period compounds at roughly 1% − (0.10² ÷ 2) = 0.5% per period. At a 14% standard deviation, the drag of about 1% consumes the whole average.
Why sizing and leverage matter
Doubling position size doubles the average return but quadruples the variance, so the drag grows faster than the gain. Beyond a certain size, a strategy with a positive average compounds to a loss. This is the reasoning behind the Kelly criterion and optimal f: the size that maximizes the compound growth rate is finite, and sizes above it reduce long-run growth while increasing drawdowns.
When it applies to a futures record
Volatility drag concerns returns compounded on a capital that changes, as in fixed fractional sizing where each trade risks a percentage of current equity. A backtest that trades a fixed number of contracts and reports dollars accumulates results additively, and its dollar total is not reduced by drag. The drag appears as soon as the results are converted into percentage returns on a capital that is resized after each trade.
In Senzoukria, replay and backtest statistics are computed on dollar results per trade with a fixed quantity per decision, and the automatic backtest does not pass the account equity to the strategy. Compounding, and therefore drag, only enters when you apply a percentage-based sizing rule to those results yourself.
Common mistakes
- Projecting growth from the arithmetic average of monthly returns.
- Increasing leverage to raise the average return without checking the compound rate.
- Comparing a fixed-size dollar backtest with a compounded percentage track record as if they measured the same thing.
Related
In the same section
- Volatility risk premium
- Volatility crush
- Volatility skew
- Volatility cone
- Volatility smile
- VIX
- Volatility surface
- Visible range volume profile
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Frequently asked questions
- Does volatility drag reduce my profit in dollars?
- Not if you trade a fixed number of contracts: the dollars simply add up. It affects percentage returns compounded on a changing capital, which is what happens when size is recalculated from equity after each trade or period.
- How does volatility drag relate to the Kelly criterion?
- Kelly sizing maximizes the compound growth rate, which is the arithmetic return minus the drag. Betting more than the Kelly fraction raises the drag faster than the average return, so growth falls, and far enough above it growth turns negative.