Position sizing
Learning objectives
- Convert a dollar risk budget into contracts for any NQ, ES, MNQ or MES trade, with slippage in the stop.
- Explain why the 1% rule is a fixed-fractional house policy, not a measured optimum.
- State what fractional Kelly keeps (half about 75%, quarter about 44% of the growth rate) and why Kelly computed on an estimated edge oversizes.
- Explain why fill quality at a larger size is something you measure on your own fills, and why same-direction index trades count as one bet.
09:45 ET (21:45 ICT, winter). A trader says “I trade 2 NQ.” That is a habit, not a risk policy. On a 10-point stop, 2 NQ risks $400; on a 25-point stop, $1,000. Same “2 NQ”, two and a half times the risk, and the trader never chose it.
Position sizing decides whether a normal losing streak costs you tuition or the account. This lesson answers one question you ask before every trade: given this stop, how many contracts?
Key terms
Position sizing (định cỡ vị thế): choosing the number of contracts so that the loss at your stop equals a dollar amount you fixed in advance Definition.
Fixed fractional (tỷ lệ cố định): the dollar budget is a fixed share of the account, for example 1% Definition. RSK1.05 in the Risk course owns the full formula; this lesson applies it to entries.
Term you need: Kelly criterion (tiêu chí Kelly). The bet size that maximises the long-run growth rate of an account, given a known win rate and payoff. RSK1.06 covers it in full; here you need only what fractions of it keep.
The formula, in this order
A $50 budget, a 5-point ES stop: which contract fits?
Definitioncontracts = floor(risk $ ÷ ((stop points + slippage) × $ per point)) Definition
Work it left to right, never backwards:
- Risk $ comes from your account rule (next section).
- Stop points come from structure (M6.08). Add slippage: one tick each way is 0.5 points on all four contracts. Add your round-trip fees per contract too.
- $ per point comes from the contract (M0.05): NQ $20, ES $50, MNQ $2, MES $5.
The formula picks the contract. If the count on NQ is zero, the trade is an MNQ trade or no trade.
The 1% rule is a policy
Our house rule: risk at most 1% of the account per trade while you are learning House rule. It is a fixed-fractional policy chosen for survival, not a size anyone measured as optimal.
On a $5,000 account, 1% is $50. A 10-point NQ stop costs (10 + 0.5) × $20 = $210 per contract, so one NQ does not fit. On MNQ the same stop costs $21, and floor(50 ÷ 21) = 2 MNQ ($42 at risk). Same chart, same stop; the budget picked the instrument.
Kelly, in one paragraph
Kelly is the size that maximises long-run growth, and full Kelly is brutal to live with: in Thorp’s continuous model a full-Kelly bettor has a 50% chance of seeing the account halve at some point Model. Fractions of it give up less growth than you might expect, but not as little as people say: half Kelly keeps about 75% of the growth rate, quarter Kelly only about 44% Definition. A popular shortcut, “half or quarter Kelly keeps most of the growth”, is right for half and wrong for quarter. The bigger problem is the input. Kelly assumes you know your edge, and you only estimate it: a 1:1 trade won 53% of the time after costs puts full Kelly at 6% of the account, but a 53% win rate from 50 trades has an interval of roughly 39% to 67%, and at 50% or below Kelly says bet nothing Definition. Kelly computed on a noisy estimate oversizes. The 1% rule is not “Kelly in disguise”; for small edges it is usually far below Kelly, which is the point. RSK1.06 has the growth curve and the uncertainty band.
Size changes the fill
Market-impact models such as Almgren and Chriss (2000) describe a trade-off for large orders: trading fast costs impact, trading slow costs timing risk Model. They were built for institutional orders far larger than a retail ticket, so take the direction, not the numbers.
For you the question is narrower: do your fills get worse as you add contracts, and when? One public practitioner study on NQ found that the price move per contract of net order-flow imbalance varies strongly by time of day and by regime PlausibleOne trader's study. That is one practitioner’s pre-registered study, its intervals are not clustered by session, and it caps at Plausible. It suggests your cost per contract is not a constant: the same size can fill cleanly at 11:00 ET and badly in the seconds after an 08:30 ET release.
How much retail slippage on NQ grows with size is not yet measured in our lab. Measure your own: log the fill against the price you saw, by size and time of day (MKT2.03), and re-check expectancy after each size step (M7.10).
Correlated positions count as one bet
A long NQ and a long ES are two bets on overlapping baskets of large-cap stocks. Until you know how they co-move (RSK1.07; our lab has not yet measured the NQ–ES correlation), count them as one: add the dollar risk of same-direction index trades and keep the total inside one trade’s budget House rule.
Risk note. A stop is not a guarantee. A stop order becomes a market order when it is touched, and in a fast market (a release, the Globex reopen) it can fill beyond your price Definition. Size so that a fill several ticks past the stop still sits inside your daily loss limit.
Worked example
Illustrative prices, no real session. Account $5,000, house rule 1% = $50 per trade. ES breakout long, entry 6,012.00, structure stop 6,007.00: 5 points, plus 0.5 points of slippage = 5.5 points.
- ES: 5.5 × $50 = $275 per contract. floor(50 ÷ 275) = 0. The plan is fine; the instrument is wrong for the account.
- MES: 5.5 × $5 = $27.50 per contract. floor(50 ÷ 27.50) = 1 MES, $27.50 at risk.
A second MES would bring the risk to $55, over budget, so it stays at one. Same setup, same stop, same R multiple; the contract absorbed the constraint. If your journal’s numbers suggest more, size increases are earned through logged expectancy over a fixed sample (M7.10), one step at a time House rule, never from the account balance or a feeling.
Prop-firm note. Prop accounts add a contract cap per account size on top of this formula; you trade the lower of the two numbers. Topstep’s dated caps are taught in the Prop Firm course (PROP4.03).
Common mistakes
Common mistake: Sizing by “what I usually trade” while the stop varies per setup. A fixed 2-contract habit with stops from 5 to 25 points makes your dollar risk swing fivefold, while your expectancy maths (M6.08) assumed constant risk. Fix the dollars, derive the contracts, every trade.
Common mistake: Treating a Kelly number from your journal as a known edge. Thirty trades at 57% on a 1:1 bracket put full Kelly at 14% of the account per trade. The interval on that win rate runs from about 39% to 75%, and its low end says bet nothing. An estimate is not the edge Kelly assumes.
Common mistake: Leaving slippage out of the stop. On a tight 4-point MNQ stop, one tick each way adds 12.5% to the dollar risk; on a budget that just fits, that is the difference between two contracts and one.
Drill: re-size your last ten trades
Take your last ten journaled trades (sim is fine).
- For each, write the stop in points, add 0.5 points of slippage, and compute the per-contract dollar risk on the instrument you traded.
- Apply the formula with a budget of 1% of your account and write the contract count it gives.
- Compare it with the size you actually traded. Count how many trades were oversized, and by how much.
Solution
There is no single answer; check your arithmetic. Example: $10,000 account, budget $100, an MNQ trade with a 15-point stop. Per contract: (15 + 0.5) × $2 = $31. floor(100 ÷ 31) = 3 MNQ ($93 at risk). If you traded 5 MNQ, you risked $155, 1.55% of the account. If your sizes followed habit or confidence rather than the stop, compute the count before you place the order.
Recap
- Contracts = floor(risk $ ÷ ((stop + slippage) × $ per point)); risk $ from your budget, stop from structure, in that order, every trade.
- The 1% rule is a fixed-fractional house policy for survival, not a measured optimum and not “Kelly in disguise”.
- Half Kelly keeps about 75% of full Kelly’s growth rate, quarter Kelly about 44%; Kelly computed on an estimated edge oversizes.
- Fill cost per contract is not a constant; measure your own fills before and after each size step.
- Same-direction NQ and ES positions count as one bet against one budget.
Further reading
- Understanding the Kelly Criterion (Edward Thorp): the maths, why full Kelly is maximally aggressive, and the drawdown odds at fractions of it.
- Using the Kelly Criterion for Investing (Ziemba & MacLean): worked examples of how violent full-Kelly betting gets, and the case for fractional Kelly.
- Optimal Execution of Portfolio Transactions (Almgren & Chriss): the impact versus timing-risk trade-off for large orders.
- Order Flow, Measured: a public practitioner study on NQ, including how impact per contract varies by time and regime.
- Our lab: the fractional-Kelly growth shares (75% at half, about 44% at quarter) are arithmetic we checked; retail slippage by size on NQ and the NQ–ES correlation are not yet measured.
Connects to: M6.08 (the stop that defines the risk) → M6.10 (the re-entry rules that protect it). RSK1.05 and RSK1.06 in the Risk course own the sizing formula and Kelly.
Educational content only. Not financial advice. Futures trading involves substantial risk of loss.
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