Volatility Drag

The Math

An arithmetic average simply sums a series of returns and divides by the count — it treats +50% and −50% as canceling out. Compounding does not work that way: a portfolio that gains 50% one year and loses 50% the next is not flat, it is down 25%, because the loss is taken on a larger base than the gain was earned on. The standard approximation is geometric mean ≈ arithmetic mean − σ²/2, where σ is the volatility of the return series. The higher the variance, the wider the gap between the average return an investor might quote and the compound return their account actually shows — the drag is not a fee or a cost, it is a direct mathematical consequence of compounding through variable returns.

The Asymmetry of Losses

Because losses and gains are not symmetric under compounding, recovery math gets harder the deeper the drawdown goes. A 10% loss needs an 11% gain to recover. A 50% loss needs a 100% gain. A 90% loss needs a 900% gain. This is why drawdown size, not just average return, is the number that determines whether a strategy actually compounds wealth over time — two series with identical average returns but different volatility will produce meaningfully different ending values, and the more volatile one is always the loser.

Why It Matters for Position Sizing

Volatility drag is the mathematical reason position sizing is not a matter of conviction. Oversizing a position raises the return-to-risk math past its optimum — the same edge, run at too large a stake, compounds slower, not faster, because the added variance eats more than the added return contributes. The Kelly criterion is the formal answer to exactly this trade-off: it sizes a bet at the point where compound growth is maximized, which is always well short of the point where average return alone looks highest. Sharpe ratio is the everyday shorthand for the same idea — return per unit of volatility, because volatility is what the compounding math actually penalizes.