Three ways to model account growth
- Fixed % — every trade returns the same percentage of the current balance. This is textbook compounding and the easiest to reason about, but no real strategy produces identical returns every trade.
- Fixed cash — every trade makes the same amount of money. Growth is a straight line, which is what happens when you trade a fixed size regardless of account balance.
- Win rate — fixed-fractional risk: each trade risks a percentage of current equity, winners pay a multiple of that risk and losers cost one unit. Outcomes follow a random sequence, so this model shows streaks, drawdowns and the spread of possible results.
Compound growth formula
For the win-rate model, each trade multiplies the balance by (1 + f × R) on a win or (1 − f) on a loss, where f is the fraction risked and R the average win in units of risk. The expected compound growth per trade is:
This geometric rate — not the arithmetic average return — is what determines where the account ends up.
Why average return is not growth rate
Lose 50% and then gain 50%, and the arithmetic average return is 0% — yet the account is down 25%. Losses and gains don't cancel because each one is applied to a different base. The more volatile the returns, the bigger the gap between the arithmetic average and the compound growth rate. This gap is called volatility drag.
It is why oversized risk can ruin a profitable strategy. A system that wins 50% of the time at 1.2R has positive expectancy (+0.1R per trade). Risk 1% per trade and it compounds upwards. Risk 60% per trade and the expected compound growth is negative — the calculator flags this case explicitly. Position size is not just about surviving a loss; it determines whether an edge compounds at all.
How losses and drawdowns affect compounding
Recovering from a drawdown requires a larger gain than the loss itself:
| Drawdown | Gain needed to recover |
|---|---|
| 10% | 11.1% |
| 20% | 25.0% |
| 30% | 42.9% |
| 50% | 100.0% |
| 75% | 300.0% |
The simulation reports the maximum peak-to-trough drawdown of each path. In win-rate mode, the median and worst drawdowns across all simulated sequences show how rough the ride can be even when the long-run statistics are favourable.
Assumptions behind the simulation
- Returns, win rate and average win stay constant for every trade. In real markets they drift.
- Each trade is independent. Real trades can cluster (several losers in a choppy market).
- Monte Carlo results come from 400 random sequences generated from a reproducible seed. Share the URL and the other person sees the same paths.
- Deposits and withdrawals are applied after every N trades and excluded from trading P/L and drawdown.
- The balance cannot go below zero; a path that hits zero stays there.