Enter a starting amount, a return per period and the number of periods to see what it compounds to, with optional additions each period. Then add the swings a real strategy has: the same average return compounds to less when returns vary, and leverage makes the gap wider.
Optional, at the end of each period.
The starting amount alone, at a steady return.
The calculator above earns the same return every month. A strategy averages that return with swings around it, and the swings cost growth. Give the size of a typical swing to see the same average compound into less.
Each month returns the average plus or minus this.
Average return 1.00% a month, compound return 0.50% a month. On $10,000.00 over 36 months, steady growth ends at $14,307.69; with swings of ±10.0% the typical result is $11,982.81.
| Leverage | Average | Compound | Typical result |
|---|---|---|---|
| 1x | 1.00% | 0.50% | $11,982.81 |
| 2x | 2.00% | 0.02% | $10,072.25 |
| 3x | 3.00% | −1.47% | $5,876.80 |
| 5x | 5.00% | −7.67% | $565.59 |
In this model the compound return peaks near 1.01x and falls beyond it, even though the average keeps rising.
Each period's return is earned on the balance, including the returns of earlier periods. A starting amount P at a return r per period for n periods, with A added at the end of each period, ends at:
balance = P × (1 + r)^n + A × ((1 + r)^n − 1) / r
time to double = ln 2 / ln(1 + r)The period can be a day, a week, a month or a year; the return must be for that same period. A return of 1% a month is not 12% a year compounded: it is 1.01^12 − 1 = 12.68%.
The formula above assumes the same return every period. A trading strategy never earns that. It has up periods and down periods around its average, and a loss always applies to whatever balance is there. Gain 10% and lose 10% and you are down 1%, because 1.1 × 0.9 = 0.99. The bigger the swings, the bigger the loss, even with the average stuck at 0%:
| Swing | After 2 periods | After 20 periods |
|---|---|---|
| ±5% | $99.75 | $97.53 |
| ±10% | $99.00 | $90.44 |
| ±20% | $96.00 | $66.48 |
The rate your account really compounds at is the geometric return. For two equally likely outcomes, the average μ plus or minus a swing σ, the typical path compounds at:
geometric return = √((1 + μ + σ)(1 + μ − σ)) − 1 ≈ μ − σ² / 2That is the calculation in the swings section. It is a simple model, two outcomes and no fat tails, so read it as the shape of the effect, not a forecast. Real returns have more extreme periods than this, which makes the drag larger, not smaller.
Leverage multiplies the average return and the swings by the same amount, but the drag grows with the square of the swings. So the compound return rises with leverage at first, peaks, and then falls, while the average keeps climbing. Past the peak, more leverage means a lower result; far enough past it, one bad period takes the account. On a perpetual future the exchange closes the position before that, at the price the liquidation calculator gives you. The Kelly criterion calculator works out the same peak from a win rate and a payoff.
Two strategies with the same average return can end far apart. The one with smaller swings keeps more of its average, and it also has shallower drawdowns along the way. That is why a strategy is judged by its Sharpe ratio (return per unit of volatility) and its maximum drawdown alongside its return, not by an average. The Sharpe and Sortino calculator and the max drawdown calculator compute both from a series of returns. A backtest gives you that series from a strategy's real trades, with fees and funding.
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Multiply by one plus the return once for every period: balance = start × (1 + r)^n. With an amount added at the end of each period, add A × ((1 + r)^n − 1) / r. At 1% a month, $10,000 becomes $14,307.69 after 36 months, not the $13,600 that 36 × 1% of simple interest would give.
Set the period to Days, enter the return per day and the number of days. A daily rate compounds fast on paper, so check it against what a strategy really earns: trading returns are never the same every day, and the swings section shows what that does to the result.
Because the loss applies to a bigger balance than the gain did. $100 up 10% is $110, and 10% down from $110 is $99. The average return is 0% but the account lost 1%. This is volatility drag: the compound (geometric) return is below the average (arithmetic) return by roughly half the variance, and it grows with the size of the swings.
The arithmetic return is the plain average of each period's return. The geometric return is the steady rate that would give the same final balance, and it is what your account actually compounds at. They are equal only when every period returns the same; the more returns vary, the further the geometric return falls below the average.
Not past a point. Leverage multiplies the average return and the swings together, and the drag grows with the square of the swings. In the calculator's two-outcome model the compound return peaks at a leverage of μ / (σ² − μ²) and falls after it, and a large enough multiple turns one bad period into a wiped-out account.
By what it compounds to and what it costs on the way: its return over the whole test, its Sharpe ratio (return per unit of volatility) and its maximum drawdown. Two strategies with the same average return can end far apart if one swings much harder. A backtest gives all three from the strategy's real trades, with fees and funding.