Trading compounding calculator

What does compounding do to a trading account?

Compounding means each period's gain or loss is a percentage of the balance at that moment, not of the starting sum. Gains grow the base for the next period and losses shrink it.

The default inputs start with $10,000, gain 2% in a gaining week and lose 1.5% in a losing week, with 60% of 52 weeks gaining. That is 31 gaining weeks and 21 losing ones, and the account ends at $13,451.36, an average change of 0.572% a week. Had all 52 weeks gained 2%, the balance would be $28,003.28, which is the dashed line in the chart.

A steady percentage per period is an assumption for the arithmetic. Real trading results differ from one period to the next, cluster in streaks and can be negative for long stretches. The calculator shows what a set of fixed numbers produces, nothing more.

What is the formula for compounding with losing periods?

With no money added or withdrawn: end balance = start x (1 + g)^W x (1 - l)^L, where g is the gain in a gaining period, l the loss in a losing period, W the number of gaining periods and L the number of losing ones.

The calculator sets W = the number of periods x the share that gain, rounded down, and L = the rest. For the default: W = 52 x 60% = 31.2, rounded down to 31, and L = 21. So 10,000 x 1.02^31 x 0.985^21 = $13,451.36.

The average change per period is the growth factor raised to 1 / the number of periods, minus 1: 1.3451^(1/52) - 1 = 0.572% a week. That geometric figure is the steady rate that would reach the same end balance. Averaging the percentages instead, (31 x 2% - 21 x 1.5%) / 52 = 0.587%, overstates it, and 0.587% a week for 52 weeks would end near $13,554 rather than $13,451.

How the calculator places the losing periods

The losing periods are spread as evenly as whole periods allow, in a fixed order you can predict. Period k is a gain when the running count of gains, k x the share that gain, rounded down, goes up by one. Otherwise it is a loss.

• At 60%: loss, gain, loss, gain, gain, then the same five again.
• At 50%: loss, gain, loss, gain, alternating throughout.
• At 70%: loss, gain, gain, loss, gain, gain, loss, gain, gain, gain in every ten.

With nothing added or withdrawn, the order makes no difference to the end balance, because multiplication gives the same answer in any order. Five 5% losses and five 5% gains turn $10,000 into $9,875.62 whichever come first. Once a fixed amount leaves the account every period, order matters: withdrawing $500 after each of the same ten periods ends at $4,225.62 if the losses come first and $5,475.62 if the gains do. The schedule under the result shows the run period by period, so you can see the order used.

Why gaining and losing the same percentage loses money

After a loss, the next gain works on a smaller balance; after a gain, the next loss works on a larger one. Either way, equal percentages up and down do not cancel. Set the gain and the loss both to 1.5% with half the periods gaining, and 52 weeks of the default account ends at $9,941.66, below the $10,000 start, although the win rate is 50% and the percentages match.

The effect grows with the size of the moves. At 2% up and 2% down over 100 periods, $10,000 ends at $9,801.95. Each pair of one gain and one loss multiplies the account by 1.02 x 0.98 = 0.9996, and that small shortfall compounds as well. The drawdown recovery calculator shows the same arithmetic for a single larger fall.

How the share of gaining periods moves the end balance

On the default inputs, 2% gains and 1.5% losses over 52 weeks, each 10 points of win rate changes the end balance by more than $2,000:

At 40% the account shrinks even though each gain is larger than each loss. The bar chart under the result redraws this for your own inputs. To see whether a win rate and a payoff produce a positive average per trade in the first place, use the trading expectancy calculator.

Compounding with regular additions or withdrawals

Choose to add or withdraw a fixed amount each period. It moves at the end of the period, after that period's gain or loss.

• Adding $100 a week to the default account ends at $19,551.94. Of that, $5,200 is money paid in and $4,351.94 comes from the gains and losses.
• Withdrawing $100 a week ends at $7,350.78 after $5,200 is taken out. The gains and losses add $2,550.78, less than without withdrawals because they work on a smaller balance, and the largest fall from a high is 26.95%.
• Withdrawing $400 a week empties the account in week 27, after $10,679.16 has been withdrawn in total. A withdrawal never takes the balance below zero, and an empty account has nothing left to compound.

The third line in the chart tracks the starting balance plus or minus the money moved, so you can see how much of the curve is your own money.

Worked examples in pounds and dirhams

• Pounds, adding each month. £5,000 to start, a 1.5% gain in a gaining month, a 1% loss in a losing month, 55% of 24 months gaining and £200 added each month. That is 13 gaining months and 11 losing ones, ending at £10,473.61: £4,800 paid in and £673.61 from gains and losses. With every month gaining, the same deposits would reach £12,874.22.
• Dirhams, withdrawing each month. AED 40,000 to start, a 3% gain, a 2% loss, half of 36 months gaining and AED 1,000 withdrawn each month. The account ends at AED 7,725.64 after AED 36,000 is withdrawn, so gains and losses added AED 3,725.64. Measured from its high, the balance falls 80.69% along the way, almost all of it from the withdrawals.

The arithmetic is the same in all 24 currencies on the selector, and amounts are never converted between them.

How to work out trading compounding in Excel

With no money added or withdrawn, the closed form fits one cell: =10000*1.02^31*0.985^21 returns 13,451.36, the default result. Replace the counts with your own gaining and losing periods.

For a gain in every period, Microsoft documents FV(rate, nper, pmt, [pv], [type]), with money paid out entered as a negative number: =FV(0.02,52,0,-10000) returns 28,003.28. A fixed addition goes in the pmt argument as a negative number, but FV applies one rate to every period, so for a mix of gains and losses with additions or withdrawals, build one row per period: balance = previous balance x (1 + that period's percentage) + the amount added, or minus the amount withdrawn.

Common mistakes, and what the calculator leaves out

• Treating a percentage per period as a plan. A figure like 2% a week is an input to arithmetic. Nothing on this page suggests any account can produce it.
• Averaging percentages. Use the geometric average, as the result does, not the plain average of gains and losses.
• Ignoring the losing periods. On the default inputs, leaving them out more than doubles the end balance, $28,003.28 against $13,451.36.
• Forgetting the order once money moves. With withdrawals, early losses cost more than late ones.

The calculator leaves out costs, tax, financing charges, changes in position size, and returns that vary from period to period. Its losing periods all lose the same fixed amount, and real ones do not.

Glossary

Compounding: applying each period's percentage to the current balance. Gaining period: a period that ends up by the gain entered. Losing period: a period that ends down by the loss entered. Share of periods that gain: gaining periods as a share of all periods. Geometric average change: the single steady rate per period that reaches the same end balance. Largest fall from a high: the deepest drop from any earlier high point in the run, as a percentage of that high.

Frequently asked questions

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