The position sizing formula does not know you just lost

The position sizing formula has three inputs. Your account balance. The fraction of it you accept to lose on one trade. The distance to your stop. Nothing in it asks how your last trade ended. Yet for many traders the trade after a loss is the biggest of the day. The formula did not change. The hands did.

The position sizing formula is the rule that converts a fixed fraction of your account and a stop distance into a trade size: size = (account × risk per trade) / stop distance. It fixes the loss in advance, before the market moves. CME Group's trading course puts the fraction for newer traders at 1% to 3% of the account. Van Tharp called position sizing the "how much" question and wrote that "it is through position sizing, not your trading system, that you meet those objectives." The same source lists 93 position sizing models. Most traders use one, and break it in the same place.

What is the position sizing formula?

Start with the only version you need. Risk amount = account balance × risk fraction. Position size = risk amount / stop distance per unit. On a 50,000 dollar account at 1% risk, the risk amount is 500 dollars. CME Group's worked example uses that account, a stop 50 ticks from entry and a tick worth 10 dollars. One contract risks 50 × 10 = 500 dollars. One contract is the answer. If the tick is worth 5 dollars, the same stop allows two contracts. The stop decides the size. The size never decides the stop.

Two things follow. First, the loss on a correctly sized trade is known before entry. That known loss is your 1R, the unit this blog uses for R-multiples. Second, the formula is memoryless. It takes the current balance, which is lower after a loss, and returns a slightly smaller size. It does not take your mood, your morning or your need to get back to flat.

1% to 3%

risk per trade suggested for newer traders

CME Group, Proper Position Size

500 $

1% of a 50,000 $ account

CME Group worked example

1 contract

with a 50-tick stop at 10 $ per tick

50 × 10 × 1 = 500 $

How do you calculate position size with a stop loss?

Take the same three numbers in this order. Stop first. CME Group writes that the stop belongs "at a logical level, where it will tell you if you're wrong about the direction of the trade," not where routine noise will hit it. Risk fraction second. On a 10,000 euro account at 1%, that is 100 euros. Size last. If your stop sits 20 pips away and one mini lot moves 1 euro per pip, 100 / 20 = 5 mini lots. Move the stop to 40 pips and the size halves to 2.5. Same risk, same 1R, different size.

This is how to calculate position size for any instrument, from a T-bond future to a CFD. ESMA's 27 March 2018 measures capped CFD leverage for retail clients at 30:1 on major currency pairs and 5:1 on individual equities. Those caps limit how large a position can be. They say nothing about how large it should be. The 74% to 89% of retail CFD accounts that ESMA found losing money were not short of leverage.

What happens to position sizing after a loss?

The data come from a trading floor, not a survey. Coval and Shumway (Journal of Finance, 2005) studied 1,082 Chicago Board of Trade T-bond futures traders across more than 5 million transactions in 1998. Traders who lost money in the morning had a 31.2% chance of taking above-average risk in the afternoon. Traders who made money in the morning had a 27% chance. The losers placed more trades, larger trades and carried more inventory. They were about 15% more likely to execute a price-moving trade, and those price moves reversed faster than others.

Source: Coval & Shumway (2005), via CFA Institute Journal Review

These were professionals with a seat and a year of recorded fills. The gap is 4.2 percentage points. It is not dramatic. It points one way. The authors call the traders "highly loss-averse." That term has a number. Tversky and Kahneman's 1992 estimate of the loss-aversion coefficient is 2.25: a loss weighs about 2.25 times a gain of the same size. A trader who just lost 1R is not looking at 1R. The felt deficit is closer to 2.25R, and the quickest way to erase a 2.25R feeling is a trade larger than 1R.

That is position sizing after a loss in one sentence. The formula returns a size for the market. The trader enters a size for the deficit. You can see the difference in the fill, not in the plan. This is also the mechanism behind revenge trading, which this blog has described by its timestamps. Size is the other half of the signature.

Why does fixed fractional position sizing shrink after a loss?

Fixed fractional position sizing means risking the same percentage of the current balance on every trade. The word "current" does the work. After a 1R loss at 1%, the balance is 99% of what it was, and the next risk amount is 1% of that. On a 10,000 euro account, five consecutive 1R losses take the balance to 9,509.90 euros and the risk amount from 100 euros to 95.10 euros. The size falls 4.9% while the trader's urge to recover rises.

Compare the other rule, the one nobody writes down. Double after each loss. The same five losses cost 100 + 200 + 400 + 800 + 1,600 = 3,100 euros, or 31% of the account. Recovery from a 31% hole needs a 45% gain, which this blog covered under drawdown trading meaning. Five losses in a row are not rare. At a 45% win rate the chance of five straight losses in any given window is 5.03%, and the chance of at least one such streak somewhere in 200 trades is 99.4%. A sizing rule that cannot survive five losses will meet them.

Source: Arithmetic, illustrative

The line above is the doubling path. The fixed fractional path is nearly flat: 100, 99, 98.01, 97.03, 96.06. One of those lines ends at 1,600 euros on a single trade. The formula drew the other one.

Does the Kelly criterion say to bet more after a loss?

No. Kelly's 1956 paper in the Bell System Technical Journal, "A New Interpretation of Information Rate," gives the fraction of capital that maximises long-run growth. For an even-money bet, that fraction is the probability of winning minus the probability of losing. The inputs are the edge and the odds. The last outcome is not an input. A 55% edge at even money gives 10% of capital before a loss and 10% of capital after it.

Kelly is an upper bound, not a target. The full fraction produces drawdowns few accounts hold. The point for this article is narrower. The one sizing rule derived from first principles has no term for recent results. Any rule that adds one is adding something the mathematics did not ask for. Trading expectancy is the number that should move your size, and it moves over hundreds of trades, not between 09:31 and 09:48.

What do prop firm rules say about size after a loss?

Prop firms do not trust the formula to hold. They write a ceiling into the contract. FTMO's trading objectives, read on 15 October 2026 on the official page, set a maximum daily loss of 5% of initial capital and a maximum loss of 10% on the 2-step challenge, and 3% daily with a 10% end-of-day trailing maximum on the 1-step version. The daily limit is recalculated at 00:00 CE(S)T from the balance, and the breach test uses equity, so open positions count. FTMO is a trademark of its owner; Socius Trades is not affiliated with FTMO.

Read those numbers against the sizing formula. At 1% risk, a 5% daily limit allows five full losses. At 2.5% risk it allows two. A trader who doubles size after the first loss reaches the daily limit on the second. The rule that ends the challenge is the same rule that ends many retail accounts, with a different enforcement date. Barber and Odean's study of 66,465 households from 1991 to 1996 found that those who traded most earned 11.4% a year against 17.9% for the market. Activity has a cost. Activity at oversized risk has a larger one.

“The formula has no memory. The trader has nothing but memory. Position sizing after a loss is the moment those two meet.”

What your journal would show

Below is what a read-only journal shows on a day like this, using illustrative demo data. Socius Trades imports the executed trades from cTrader or MetaTrader and computes R-multiples from the stop and the size on each fill, so the size drift is visible without you typing anything. The mechanism is a ratio: size on the trade after a loss divided by size on the trade before it.

1. 09:31

   Trade 1, standard size

   Risk 1.0% of balance. Stop hit. Result -1.00R.

2. 09:48

   Trade 2, 17 minutes later

   Risk 2.3% of balance. Same setup, same stop distance, 2.3 times the size. Result -2.30R.

3. 10:05

   Trade 3, 17 minutes later

   Risk 3.1% of balance. Stop widened to fit the size. Result -3.10R.

4. 10:40

   Trade 4, 35 minutes later

   Risk 1.0% of balance. First trade sized by the formula since 09:31. Result 0.80R.

Three numbers tell the story. On this demo account, median risk per trade is 0.9% after a winning trade and 2.4% after a losing one. The average result on trades sized above 1.5% of balance is -0.42R. The average result on trades sized by the formula is 0.12R. The expectancy was positive all along. The sizing after a loss was what made the account negative. The 09:31 loss cost 1R. The two trades that followed cost 5.4R. If you want to see the same ratio on your own history, Socius Trades plans start with a 14-day trial on Essential and read your broker history as it is.

0.9%

median risk per trade after a win

illustrative demo data

2.4%

median risk per trade after a loss

illustrative demo data

-0.42R

average result on trades sized above 1.5%

illustrative demo data

0.12R

average result on formula-sized trades

illustrative demo data

What can you actually do about it?

None of this is a promise. These are rules that remove the moment of choice, because the choice after a loss is the one Coval and Shumway measured.

Write the risk fraction as a number, not a range. "1% to 2%" becomes 2% after a loss. "1%" stays 1%.

Compute the size before the day starts, per instrument, per stop distance. A table on paper or a position calculator does the arithmetic once. At 09:48 you read a number. You do not produce one.

Put a ceiling on the ratio. If the size on any trade exceeds 1.2 times the size on the previous trade, the journal should show it and you should have a written reason for it, dated before the trade.

Treat the daily loss limit as a sizing rule, not a stopping rule. If your limit is 3% and your risk is 1%, you have three trades. Count them. A prop firm counts them for you. Nobody counts them for a personal account unless the journal does.

Review the ratio weekly, not after each loss. The loss is the worst moment to decide anything about size. The weekly review is when the ratio over 40 or 50 trades says whether the rule held.

The formula will keep returning the same size. The work is to let it.

Trading involves risk of loss. Socius Trades is an analytics tool, not investment advice.