How Compounding Works Against You and for You

Compounding means that each percentage return is applied to a capital base already changed by prior results. It amplifies a persistent positive return process and also magnifies the path dependence of losses. Compounding is neutral. It does not create an edge.

Percentage returns do not add directly

Starting with USD 10,000:

• a 10% gain produces USD 11,000;
• a second 10% gain produces USD 12,100;
• total gain is 21%, not 20%.

After a 10% loss, the account has USD 9,000. A 10% gain then produces USD 9,900. The account remains 1% below the starting value.

Loss and recovery

If (d) is the drawdown fraction, the gain required to recover is: d ÷ (1 − d) This is why a 20% loss requires a 25% gain and a 50% loss requires a 100% gain.

Position sizing determines the compounding path

• Fixed-percentage sizing reduces the currency amount at risk after losses and increases it after gains.
• Fixed monetary risk becomes a larger percentage of equity after losses.
• Aggressive fractions increase both growth potential and drawdown.
• Correlated positions can make the effective fraction much larger than the per-trade setting.

Reducing size after a loss slows further percentage decline, but it also reduces the currency gain available for recovery. There is no free recovery mechanism.

Arithmetic vs geometric return

The arithmetic average of periodic returns can be positive while compounded wealth declines. For example, +50% followed by −50% has an arithmetic average of 0%, but capital becomes (1.5 × 0.5 = 0.75), a 25% loss. The gap between arithmetic and geometric outcomes grows with volatility.

Prop-account implications

A prop account may terminate at an intermediate drawdown threshold, so terminal compounded return is not the only objective. A position-sizing policy must keep plausible paths inside daily and maximum-loss rules. The correct compounding base may also differ from nominal account balance. When the usable loss buffer is much smaller, a seemingly modest percentage of nominal equity can consume a large part of the actual risk capacity.