Risk math • Simple stock examples
Position sizing by dollar risk: calculate a ceiling, then test the constraints.
For a simple long or short stock example, divide a user-selected dollar-risk budget by the absolute distance between the planned entry and thesis invalidation, then round down to whole shares. The result is a theoretical ceiling—not a recommendation, trade approval, or promise that realized loss will stay inside the budget.
Direct answer
Maximum theoretical whole shares = floor(dollar-risk budget ÷ |entry − invalidation|)
Define the setup's observable invalidation before calculating size. If the distance is zero, missing, or wider than the entire budget for one share, stop: the formula has no usable positive result. If it produces a positive ceiling, reduce or reject it when capital, liquidity, spread, gap, portfolio, margin, or execution constraints demand a lower number.
Decision map
What each sizing check answers—and what it cannot
Transparent arithmetic
Three synthetic stock examples
The simple long arithmetic is $50.00 − $49.20 = $0.80 per share, then $80 ÷ $0.80 = 100 whole shares. That is the ceiling before every other constraint—not permission to use 100 shares.
Simple short: round down
Entry $75.00, invalidation $76.20, distance $1.20, budget $100. The quotient is 83.33, so the theoretical ceiling is 83 shares, representing $99.60 of simplified planned distance risk before costs and execution differences.
One share exceeds the budget: zero
Entry $20.00, invalidation $14.00, distance $6.00, budget $5. The quotient is below one whole share, so the formula returns 0 shares. Moving invalidation merely to force a preferred size reverses the risk-first sequence.
These are synthetic arithmetic examples, not current market data, order instructions, performance records, recommendations, or statements that any price level is appropriate.
Inputs in the correct order
- Define thesis invalidation.Choose an observable failure from the setup logic—not from the share count you want. Read how to define invalidation.
- Estimate the entry condition.Use the planned condition and current source context. A moving market can make the actual entry different.
- Calculate absolute risk per share.Use the absolute entry-to-invalidation distance for these simple stock examples. Options, futures, leveraged, short, and other products can carry different or nonlinear risks.
- Set the dollar-risk budget independently.The user chooses the hypothetical budget in light of their circumstances and total exposure. Lumiere does not prescribe a universal dollar amount or account percentage.
- Round down to whole shares.Never round up beyond the simplified ceiling. A missing, zero, non-finite, or one-share-too-wide input stops the calculation.
- Apply the lower real-world constraints.Capital, buying power, spread, liquidity, gaps, fees, concentration, data quality, and broker rules can make the defensible result lower or zero.
Why realized loss can exceed the paper formula
Gap and slippage
Price may move through the planned level before an order can execute. The SEC notes that a triggered stop becomes a market order and can execute significantly away from the stop price in a fast market.
Stop-limit non-execution
A limit can constrain execution price, but the order may remain unexecuted if the market moves beyond it.
Liquidity and spread
Displayed prices, available size, spread, and market impact can make the assumed entry or exit unrealistic.
Fees and financing
Commissions, exchange fees, borrow costs, and margin interest can increase the economic loss beyond simplified price-distance arithmetic.
Portfolio concentration
FINRA describes concentration as a source of amplified losses and notes that correlated holdings can create overlapping exposure.
Systems and data
Stale or incomplete data, halts, connectivity failures, broker rules, and platform outages can interrupt or change the plan.
IBKR handoff
Run broker checks after the written ceiling—not instead of it
IBKR's Check Margin view can show order details, commissions, and potential margin impact before transmission. Check Risk can compare current and what-if portfolio-relative P&L for one or more proposed orders. Those broker-native previews add account context; they do not define the trader's thesis invalidation, guarantee a fill, or turn the theoretical share ceiling into a recommendation.
Execution source: SEC Investor Bulletin: Stop, Stop-Limit, and Trailing Stop Orders, reviewed August 4, 2026.
Portfolio source: FINRA: Concentrate on Concentration Risk, reviewed August 4, 2026.
Broker margin source: IBKR TWS: Check Margin Pre-Order, reviewed August 4, 2026.
Broker portfolio source: IBKR TWS: Check Risk Pre Order, reviewed August 4, 2026.
Use the lowest coherent ceiling—and preserve zero as an answer
The dollar-risk result answers one narrow question about a simplified distance. The position considered in a review should never exceed that ceiling and may need to be lower because of capital, broker, liquidity, portfolio, or data constraints. If the setup cannot support a clear invalidation, one whole share exceeds the budget, or current context is unreliable, zero is a complete result.
Use the full pre-trade checklist to keep source, thesis, invalidation, risk, execution limits, and the no-trade condition together.
Practice the sequence