Position Sizing

Reviewed 12 August 2026 · Sourced from arithmetic you can recompute, plus the SEC and FINRA on stop orders, Wilder on volatility and Kelly’s 1956 paper

The decision nobody spends any time on

Two people with $8,000 accounts buy the same stock at $42.50 on the same morning. They read the same writeup. They have the same opinion. The stock falls 30% over the next three weeks, to $29.75.

The first one owned 26 shares and had written down before entering that she was out at $39.50. She lost $78. That is 0.98% of her account, and a 1% gain on what is left puts her back to even.

The second one bought “a full position” — 188 shares, $7,990, essentially the whole account. He lost $2,397, which is 29.96% of the account, and he now needs a 42.8% gain on the $5,603 remaining to get back to where he started.

Same stock. Same entry. Same decline. One outcome is a rounding error and the other is a year of the account's life. The difference is 30.7×, and none of it came from analysis. It came from a number chosen in about four seconds by a person who spent nine hours on the chart.

Position sizing is that number. It is the decision of how much — how many shares, contracts or dollars — and the method that produces the first outcome instead of the second runs backward. Rather than starting from what you can afford and buying that much, you start from what you are prepared to lose and let it tell you the share count.

This page is mostly arithmetic, and every figure on it recomputes exactly — check them. Where a number is a trading convention rather than a calculation, it is labeled as one in the ledger, because most of the numbers people quote about sizing fall in that second group.

Why the size of a loss is not the size of the recovery

Here is the whole reason sizing matters, and it is one line of arithmetic. When you lose money, the gain that undoes it is calculated on a smaller balance. So the percentage you need back is always bigger than the percentage you lost, and the gap widens fast.

Worked across the range, on a $10,000 balance, it looks like this. This table is our own arithmetic, and it is exact.

Read the bottom rows slowly. Losing 90% means needing a tenfold return to break even — not to profit, to break even. And notice that at the top of the table the penalty is almost nothing: a 5% loss costs you a 5.26% gain, a 5% surcharge on the mistake. The curve is nearly flat until roughly 20% and then it leaves the room.

That shape is the entire argument for caring about size, and it is why the sizing conventions cluster at small percentages. It is not that small losses are pleasant. It is that small losses are recoverable with ordinary gains and large ones require extraordinary ones. Nothing in a chart pattern or an earnings model changes this. It is division.

One honest note on the 33.3% row: exactly one-third requires exactly 50%. A 33% loss requires 49.25%. The round numbers people quote are usually the clean fractions.

Where the share count comes from

The calculation has three inputs and one division. Nothing about it is sophisticated, which is part of why it gets skipped.

One. Decide the dollars you are willing to lose on this one position. Not a percentage yet — a dollar figure, because a dollar figure is a thing you can picture. Two. Find the distance from your entry price to the price at which you would no longer be in it. That exit is normally a stop-loss order, and it has to be chosen for a reason that has nothing to do with the size you want. Three. Divide.

The share count falls as the exit widens

This is the part that reads backwards the first time. A wider stop means more room for the trade and fewer shares, because each share now carries more risk. Same $80, same $42.50 entry, four different exits:

Every row risks the same $80. The dollars committed swing by ten times, from $340 to $3,400. Two things follow. First, the relationship between how much you put in and how much you can lose is not fixed — a big position with a tight exit and a small position with a loose one can carry identical risk. Second, the formula alone will happily hand you a position worth 42.5% of the account, which is why practitioners usually cap position value as well as risk. That second cap is a convention with no authority behind it, and it is doing real work.

What you stand to make against what you are risking is a separate ratio with its own page — see risk/reward ratio. Sizing does not care about it. Sizing only reads the downside.

The 1% rule is a convention, not a rule

Everything above needed a risk figure, and the near-universal answer is “1% of the account,” or 2% for people who describe themselves as aggressive. It is in every course, on every broker's education page, and in the marketing of every proprietary trading firm.

It is a convention. Nothing publishes it. No exchange, no regulator and no standard-setting body sets a risk-per-trade limit for a retail account, and this page went looking for who first put the number in print and came back with nothing citable — the trail leads to broker blogs and prop-firm landing pages that cite each other. That does not make it a bad heuristic. It makes it a heuristic, and it should be labeled as one wherever it appears, including on this site.

What is worth doing is taking the convention literally and seeing what it implies, because the implication is more interesting than the number. A string of consecutive losses does not add up the way people assume. Ten losses at 1% each is not a 10% drawdown, because the second 1% is 1% of a smaller balance than the first.

The same arithmetic at wider risk settings is where the convention earns its keep:

Tripling the risk setting from 1% to 3% does not triple the pain of a bad run — it takes the twenty-loss hole from something an 22% gain repairs to something needing 84%, which is the region the recovery table says gets ugly. And twenty consecutive losses is not an exotic scenario for anyone who trades often; it is a bad two months.

Two ways people try to make the number more precise

The base formula treats a $3.00 stop as a $3.00 stop regardless of what the stock is. Two refinements try to do better. One is genuinely useful. The other is famous and mostly not usable, and this page will say so.

Volatility-adjusted sizing

A stock that routinely swings $3 in a day and a stock that swings 40 cents should not get the same stop distance, because a $3.00 stop is a normal Tuesday for one and a meaningful event for the other. The common fix is to set the exit distance from a volatility measure instead of a round number, most often average true range.

ATR comes from J. Welles Wilder Jr.'s 1978 book New Concepts in Technical Trading Systems — the same book that produced RSI. True range for a bar is the greatest of three values: the high minus the low, the absolute value of the high minus the previous close, and the absolute value of the low minus the previous close. Averaging that over a window — 14 bars is the most common length, and that length is convention, not derivation — gives a typical daily travel distance in dollars. ATR measures how far a thing moves, not which way; TradingView's own documentation says the indicator “is not used to indicate the direction of price.”

That is the whole idea: the jumpy stock gets a small position and the placid one gets a large position, and both lose about $80 if they go wrong. The ratio of position sizes is just the inverse ratio of the volatilities.

The Kelly criterion

John L. Kelly Jr. published “A New Interpretation of Information Rate” in the Bell System Technical Journal, volume 35, July 1956, pages 917–926. It was a paper about information theory and a gambler with a noisy private wire, not about markets — stock speculation gets one passing sentence. What it derives is the bet fraction that maximizes the expected logarithm of capital, which is the fraction that maximizes the long-run compound growth rate. Kelly is explicit that the log has nothing to do with a utility function: it is used “merely with the fact that it is the logarithm which is additive in repeated bets and to which the law of large numbers applies.”

Now the honest part. The formula requires your true probability of winning and your true payoff ratio as inputs. A card counter can know those. A discretionary trader looking at a chart cannot — they can produce an estimate from a sample of their own past trades, which is a different object, and Kelly's output is highly sensitive to that estimate. Overstate your edge and the formula tells you to bet more, not less.

And even with perfect inputs, full Kelly is brutal to sit through. In the standard continuous approximation, growth rate is g(f) = μf − σ²f²÷2, which peaks at the Kelly fraction and comes back to zero at exactly twice it — bet double Kelly and your long-run growth rate is nil. Half Kelly, by the same arithmetic, delivers three-quarters of the maximum growth rate with half the exposure, which is why “half Kelly” is the version practitioners talk about. That is a real property of that equation. It is not permission to plug in a win rate you invented.

Six 1% positions can be one 6% position

This is the largest hole in retail risk management and it gets the least airtime, because it cannot be fixed by a better formula.

A trader with the $8,000 account holds six positions. Each was sized to risk 1%, $80 apiece, all documented, all disciplined. Total risk on the sheet: 6 × $80 = $480, which is 6% of the account. He describes that as spread out.

Whether it is spread out depends entirely on whether those six things move together. Two extremes bracket the answer:

• Six genuinely independent bets. If you model risk as a standard deviation, independent risks add in quadrature rather than straight, so the combined figure is the square root of 6 times 1% — about 2.45%. Less than half the headline number. That is a modeling assumption, not a fact about markets, and it is generous.
• Six versions of the same trade. Six regional banks, or six semiconductor names, or six things that all just need rates to fall. When the thesis is wrong it is wrong in all six at once, and the account loses the full 6%. You did not hold six positions. You held one, in six tickers, and paid six commissions for the privilege.

Real portfolios sit somewhere between, and the uncomfortable part is where they sit is not fixed — it moves against you. Longin and Solnik studied this directly in the Journal of Finance (volume 56, number 2, April 2001) and their conclusion is one sentence long: “Correlation increases in bear markets, but not in bull markets.” They also rejected the assumption of multivariate normality for the negative tail while failing to reject it for the positive tail — in plain terms, the tidy statistical model of how things move together holds up reasonably well on the way up and breaks on the way down.

The SEC's own beginners' guide names the mechanism without the math: the point of holding different things is to hold “asset categories with investment returns that move up and down under different market conditions,” and it warns that a single fund “doesn't necessarily provide instant diversification, especially if the fund focuses on only one particular industry sector.” The same warning applies to six hand-picked tickers from one sector, with more force, because you chose them precisely because they had something in common.

Practitioners handle this with a second cap — a limit on total risk open at once, and a limit on risk per sector or per theme. Common figures get quoted; none of them is published by anyone. Treat them as conventions. The technical markets page carries sector breadth across six horizons, which is one way to see how much of the market is currently doing the same thing.

Why this is a psychology term wearing a calculator

Everything on this page is arithmetic, and almost nobody's sizing failures are arithmetic failures. They are decisions made at the moment of entry by a person who is excited, or behind, or certain.

Size is where feelings become dollars. Conviction turns into share count. A run of wins turns into a bigger number without anyone deciding to make it bigger. A run of losses turns into a position sized to make the money back, which is the largest position of the sequence arriving at the worst moment in it. None of that shows up as a mistake in a spreadsheet, because the arithmetic was done correctly on a risk figure that had already been quietly moved.

The reason it lands this way has a documented origin. Loss aversion — the finding that losses register more heavily than equivalent gains, from Kahneman and Tversky's 1979 Econometrica paper on prospect theory — predicts the specific behavior sizing is meant to prevent. If a $500 loss hurts more than a $500 gain pleases, then a position large enough to produce a $500 loss will produce enough discomfort to override the plan that created it. The stop does not fail. The person watching the stop fails, and the size is what determined how much pressure was on them.

Which points at the one genuinely useful thing about this whole topic. Size is the only input in a trade that you control completely. You do not control the price, the news, the fill, the gap, the sector, or whether your thesis was right. You control how many shares. A trader with a mediocre read and a small position survives to keep reading. A trader with an excellent read and a position that terrifies them will close it at the wrong moment and never learn that the read was excellent.

Risk and loss is Stage 3 of the Trading Psychology course. The behavior page carries a five-question pre-trade checklist that asks the sizing question in plain language before the order goes in, free and with no account.

What is sourced here and what is not

Most of this page is arithmetic, which is the rare comfortable case: you do not have to trust it, you can recompute it. The sizing settings are a different matter, and mixing the two together is how a convention starts getting quoted as a rule.

The distinction that matters: the arithmetic is not negotiable and the settings are entirely negotiable. Anyone who presents 1% as a law is overselling, and anyone who dismisses the recovery table as opinion has not done the division.

What trips people up

• Sizing from cash available instead of dollars at risk. “I have $4,000 free, so that is the position” produces a loss set by whatever the stock does next. The formula runs the other direction on purpose.
• Widening the exit to justify more shares. The stop gets moved further away, the risk per share goes up, and the trader keeps the share count anyway. Now the risk is whatever it is. The exit has to be chosen before the size, from the chart, not from the size you wanted.
• Tightening the exit to buy more shares. The mirror error, and more common. A $1.00 stop instead of $3.00 buys 80 shares instead of 26 on the same $80 — and a stop that close to entry gets taken out by ordinary noise, so you get stopped out of a position that was going to work.
• Ignoring position value. The risk math will hand you a position worth 42.5% of the account and report it as 1% of risk. Both statements are true. Only one of them describes what happens on a gap.
• Calling six correlated positions diversification. Six names in one sector risking 1% each is a 6% bet, and correlations tighten exactly when the losses arrive.
• Averaging down. Adding to a losing position changes the size after the fact, which means the number you calculated no longer describes the trade you are in. The risk was recalculated by the market, not by you.
• Treating the stop as a guarantee. The SEC says the stop price is not the guaranteed execution price. Overnight news does not respect your arithmetic.
• Sizing off the high-water mark. Risking 1% of what the account used to be worth means risking more than 1% of what it is worth, at the precise moment that matters.
• Sizing anything off money that is already committed. Rent, groceries and the buffer underneath them are not risk capital at any percentage. Net worth is the number a trading loss actually comes out of, and a position sized against a balance that also has to pay the electric bill is not sized at all.

The figures on this page are checked against the source that publishes them, and dated. Published rates move after the release named above — the linked source always carries the current number. This page explains a term; it does not recommend a product.