Risk math
Position sizing by dollar risk
Dollar-risk sizing starts with the amount a plan is prepared to lose if the setup fails and divides it by the planned risk per unit. The result is a theoretical maximum—not a promise that the realized loss will stay within that amount.
Formula
Maximum theoretical units = floor(dollar-risk budget ÷ absolute entry-to-invalidation distance)
Calculate the distance first, divide the risk budget by that distance, and round down. Then reduce the result for expected slippage, fees, gaps, spread, liquidity, buying power, correlated exposure, and any broker or product constraints.
Worked example
The calculation is $100 ÷ $0.50 = 200 shares. A risk-first review should still reduce or reject that size when the spread, expected slippage, liquidity, gap risk, commissions, portfolio exposure, or buying-power impact makes the theoretical result unrealistic.
Inputs in the correct order
- Define thesis invalidation.Choose an observable level from the setup logic—not from the share count you want. Read how to define invalidation.
- Estimate entry.Use the planned entry condition and current market context. A rapidly moving market can make the actual entry different.
- Calculate risk per unit.For a simple long equity example, use entry minus invalidation. For a simple short example, use invalidation minus entry. More complex products require different risk analysis.
- Set a dollar-risk budget.The budget must be chosen by the user in light of their circumstances and total exposure. Lumiere does not prescribe a universal amount or percentage.
- Round down and apply constraints.Never round up beyond the calculated theoretical maximum. Then incorporate execution and portfolio risks.
Why realized loss can exceed the formula
Gap and slippage
Price may move through the planned level before an order can execute.
Stop mechanics
A stop order becomes a market order after triggering; a stop-limit may not execute.
Liquidity
Available size and spread can make the expected price unrealistic.
Fees and financing
Commissions, exchange fees, borrow costs, and margin interest can increase loss.
Portfolio concentration
Multiple correlated positions can create more total risk than each standalone calculation suggests.
System and data risk
Stale data, connectivity failures, exchange halts, and broker outages can interrupt the plan.
Margin is a separate constraint
The SEC warns that margin can produce losses greater than the amount initially invested and that a brokerage firm may liquidate securities without consulting the customer when equity is insufficient. IBKR TWS provides a pre-order margin-impact preview, but that tool does not replace understanding the account agreement and current requirements.
Primary source: SEC Investor Bulletin: Understanding Margin Accounts.
Platform source: IBKR TWS: Check Margin Pre-Order.
Use the formula as a ceiling, not a target
The output answers one narrow question: how many units fit a simplified planned-loss budget at the stated distance? It does not establish that a trade is suitable, attractive, liquid, or likely to succeed. When the inputs are uncertain or one unit already exceeds the budget, the defensible size is zero.
Practice safely