Compounding Position Size: Fixed Lot vs Fixed Fraction and the Kelly Formula

Compounding position size means recalculating your lot from the current balance instead of using the same lot forever. The account grows and the trade grows; the account shrinks and the trade shrinks. It sounds like a shortcut to fast growth, but the math of multiplying has a trap in it: past a certain level, more risk makes the account grow slower, and it can shrink even while the system still has an edge. This article works through it step by step, from volatility drag to the Kelly formula, and looks at results from our own tests on gold.

Fixed lot vs a fixed % of the account

• Fixed lot: open 0.05 lot on every trade, whatever the balance. Profit or loss per 1R (one unit of risk per trade) stays the same in money, so the account grows in a straight line
• Fixed fractional: risk 1% of the account on every trade. Lot = (balance × risk %) ÷ (Stop loss distance in money per 1 lot). The full method is in Position size from your Stop loss. The account grows exponentially

What people often miss: a fixed lot is not fixed risk. If the Stop loss distance changes, the money at risk per trade changes with it. In our backtests, one system on gold placed its Stop loss at 0.6% of price. As gold rose from about 1,760 to about 4,266 dollars, the Stop loss distance in money per lot grew 2.4 times. The same lot quietly risked more and more money, and with the same % risk budget, the lot you could afford shrank 2.4 times.

Why +50% then −50% doesn’t bring you back

An account grows by multiplying, not adding. Start at 100, gain 50% to reach 150, then lose 50% and you have 75. Reverse the order and you get the same: 100 × 0.5 × 1.5 = 75. The arithmetic mean of +50% and −50% is 0%, but the geometric mean (the rate the account actually grows per round) is √(1.5 × 0.5) − 1 = −13.4%.

Equal gain then loss	After two rounds	Actual growth per round (geometric)
+10% / −10%	−1%	−0.5%
+20% / −20%	−4%	−2.0%
+50% / −50%	−25%	−13.4%

The missing part is called volatility drag. A good approximation is: actual growth ≈ mean − variance ÷ 2. The more you risk per trade, the wider each result swings. Variance grows with the square of the risk %, while the mean grows only in a straight line, so at some point the drag overtakes the profit. That is where the “hump” in the next section comes from, and it is the same reason a 50% loss needs a 100% gain to recover. More in Why many traders risk only 1% per trade.

Example: one system, 200 trades, only the risk % changes

Assume a system whose numbers are known exactly (in real life nobody knows them). It wins 35% of trades, winners make +2R and losers lose −1R.

1. Edge per trade (expectancy) = 0.35 × 2 − 0.65 × 1 = +0.05R, a thin edge like many real systems
2. Build a sequence of 200 trades, 70 wins and 130 losses, in random order (longest losing streak: 8). Starting balance 10,000
3. At 1% risk, a win multiplies the account by 1.02 and a loss by 0.99. Final balance = 10,000 × 1.02⁷⁰ × 0.99¹³⁰ = 10,000 × 3.9996 × 0.2708 = 10,829
4. Repeat for each risk level and measure the deepest drawdown along the way

Risk per trade	Final balance	Max DD (this sequence)	Typical max DD (20,000 random runs)	Chance of ending below start	Chance of a 50% DD
0.5%	10,459	5.9%	8.8%	30.4%	0.0%
1%	10,829	11.5%	17.0%	35.8%	0.0%
2%	11,265	22.1%	32.4%	35.8%	8.7%
2.5%	11,320	27.0%	38.8%	41.5%	21.5%
5%	10,036	48.3%	65.9%	47.3%	85.3%
10%	3,928	76.2%	92.2%	70.0%	100%

The three right-hand columns come from reshuffling the outcomes 20,000 times (200 trades per run, each trade winning with 35% probability). “Typical” is the median. The median final balance matches the second column exactly.

Three things the table shows:

• Past 2.5%, you get less and hurt more. Risking 3% ends at 11,265, the same as 2%, but with a 31.7% drawdown instead of 22.1%. Risking 10% loses 61%, with exactly the same system and the same edge
• The final balance depends only on how many trades win and lose, not the order, because multiplication can be done in any order. The drawdown along the way depends heavily on the order
• A system with an edge can still finish down. With a +0.05R edge, about one in three random 200-trade runs ended below the start even at 0.5% risk. More in Losing streaks are normal

The Kelly formula finds the top of the hump

The Kelly criterion is the fraction to risk per trade that makes an account grow fastest over the long run. For a system whose winners make R times what its losers lose:

f* = W − (1 − W) ÷ R, where W is the win rate and R is average win ÷ average loss

Our example: f* = 0.35 − 0.65 ÷ 2 = 0.35 − 0.325 = 0.025, or 2.5%, exactly the top of the hump in the chart. Here f* is the money lost at the Stop loss as a % of the account, not a lot size.

Two points worth remembering:

• At roughly twice Kelly, growth is zero. In this example that point is about 5.04%, which is why 5% risk ends at 10,036, almost break-even
• Beyond that, the account shrinks over time even though the edge per trade is still positive, because volatility drag beats the mean. If the formula gives a negative number, the system has no edge and shouldn’t be traded at all

Why full Kelly is dangerous, and why people use only part of it

1. The inputs are estimates. Say you believe your system wins 40%. Kelly = 0.40 − 0.60 ÷ 2 = 10%. But the true win rate is 35%, so the true Kelly is 2.5%. Risking 10% on this real system is the last row of the table: 3,928 left from 10,000. A 5-point error in win rate made the calculated figure 4 times the true one. And backtests usually look better than live trading; see Why backtest results differ from live trading.

2. Full Kelly hurts a lot even with correct numbers. At 2.5%, the median deepest drawdown over 200 trades was 38.8%, and 21.5% of random runs saw the account halve at some point.

3. Fractional Kelly gets most of the growth with far less pain. Half Kelly (1.25%) grows at 75% of the full-Kelly rate, but the median deepest drawdown falls to 21.0% and the chance of a 50% drawdown falls to 0.3%. That is why traders who use Kelly typically use a quarter to a half of it, with a hard cap on top.

One more caution: Kelly works one trade at a time. If you hold several trades that move together, your real risk is the sum, not the % per trade. Read Correlation and portfolio risk.

A fixed lot doesn’t always lose to compounding

Same 200-trade sequence, comparing a fixed lot that risks the same as the compounding version’s first trade:

Method	Final balance	Max DD (this sequence)	DD in the worst 5% of random runs
Fixed 100 dollars per trade (1% of start)	11,000	11.3%	33.7%
Compounding 1%	10,829	11.5%	31.3%
Fixed 200 dollars per trade (2% of start)	12,000	21.4%	64.2%
Compounding 2%	11,265	22.1%	53.5%

The fixed lot finishes higher because it earns +0.05R of the starting balance per trade, straight, while compounding pays volatility drag on every trade. Compounding only overtakes after enough trades: in this example about 1,104 trades at 1% risk and about 1,613 at 2%. Its clearer advantage shows in bad runs. Compounding cuts trade size as the account falls, so the drawdown in the unluckiest runs is shallower.

What our backtests showed

Each comparison below uses exactly the same trades, with only the sizing method changed, on gold (XAUUSD) on the 1-minute chart.

• Compounding made more profit but was worse per unit of risk. An 8-candle box breakout system, 3,000-dollar balance, real tick data for 2026 (about the first 7 months), exactly 836 trades in both runs. A fixed 0.01 lot made +809 with a 115-dollar drawdown. Compounding at 2% risk made +1,661 but with a 407-dollar drawdown. Profit per drawdown fell from 7.01 to 4.08, and the Profit factor fell from 1.85 to 1.64 on the very same trades, meaning the bigger trades landed in the losing stretches, since the lot is largest right after a run of wins. In 2022–2025 (ticks generated from 1-minute bars), profit per drawdown was also worse in 3 of 4 years
• Risk-based sizing can make a system look much worse. A system entering at the 61.8 level of the previous swing range, 10,000-dollar balance, 2026 real ticks. A fixed 0.10 lot made +13,322, but sizing at 0.5% risk per trade made only +469. This system’s big winners came from large ranges with wide Stop losses, so risk-based sizing gave the smallest lot to the trades that made the most money. Another system (3,000-dollar balance, 2026 real ticks) risking a fixed 12 dollars per trade raised profit from +2,532 to +2,817, but drawdown rose from 265 to 375, and profit per drawdown fell from 9.6 to 7.5
• Stepping up after losses lost to simply raising the lot. The same breakout system, base lot 0.05, 2026 real ticks. Adding 0.01 lot after every loss until it was won back made 5.7% less than just raising the base lot to the same drawdown. Jumping to 0.10 lot for 5 trades after a loss made 16.7% less. A ladder puts on its biggest size right at the bottom of the hole

Whatever way you grow position size, it first has to beat “just raise the fixed lot” at the same drawdown. More profit from bigger trades doesn’t mean a better method.

These are backtest results. Past results do not predict future results, and they are not returns you should expect. To read profit against drawdown in a report, see The MT5 backtest report explained and Drawdown: equity vs balance.

Step up in stages, or recalculate every trade?

Same sequence at 1% risk: recalculating every trade ends at 10,829 with an 11.5% drawdown; recalculating every 25 trades ends at 10,980 with 11.4%. Across 20,000 random runs, the medians differ by less than 1% for both final balance and drawdown. How often you recalculate is not what decides the result, so choose what you can do consistently.

• Recalculate on a schedule, such as the start of each week or every 25 trades, using the balance at that moment
• Don’t wait on the way down. If the account falls 20% and you keep the old lot, your 1% is now 1 ÷ 0.8 = 1.25% of the current account. Cut the lot as soon as the balance drops a lot
• Always round down. Lots move in 0.01 steps, and a small account can’t hit the % exactly. Round down, not up
• Don’t raise the lot because you just lost. That is the ladder above, and close to Martingale

Adding to a trade that is already in profit is a different topic; see Scaling in, scaling out and partial closes.

Withdrawals

A withdrawal shrinks the base you compound from, so the next trades are smaller, but the money you took out is safe from future drawdowns. Same sequence at 1% risk, withdrawing half of the new profit every 50 trades: the account ends at 10,285 plus 544 withdrawn, 10,830 in total, almost exactly the same as never withdrawing (10,829). With a thin edge, withdrawing by a rule cost almost nothing here.

• Set the rule in advance, such as withdrawing half of the profit at fixed intervals. Don’t withdraw on emotion
• After a withdrawal, recalculate the lot from the new balance straight away
• Measure drawdown and profit from the post-withdrawal balance, or the numbers will be distorted

Common mistakes

• Assuming more risk always means faster growth. Past Kelly you get less, and beyond about twice Kelly the account shrinks
• Using full Kelly from backtest numbers. The figure is usually too high. Use a fraction and a cap
• Judging a compounding method by total profit. Look at profit per drawdown, compared with simply raising a fixed lot at the same drawdown
• Watching drawdown only as a %. As the account grows, drawdown % can look the same while the money lost is several times larger. Check both
• Compounding up but refusing to cut the lot when the account falls. That gives you the downside of both methods. Use the calculator below to see how much gain each level of loss needs to recover