Risk reward and position sizing

EN source master • P04 — Trading Foundations • needs_review.

Educational boundary: mechanisms and evidence only. No BUY/SELL/HOLD signal, trade recommendation, personalized investment advice, guaranteed setup, price target, expected profit, guaranteed win rate or guaranteed risk/reward outcome. All examples are ILLUSTRATIVE / FICTIONAL; no real money or live trade is required.

Sizing is arithmetic under assumptions. A precise division can still be wrong as a model of realized risk if execution differs, costs are omitted or units are mismatched. This lesson uses supplied fictional capital and budget to teach that distinction. It does not tell a learner how much of their real money to risk.

A risk budget is a chosen loss allowance for a defined hypothetical scenario. Here it is an exercise input, not a recommended fraction of capital. Entry assumption is a nominal fill used in the model. Invalidation assumption is a condition at which the scenario is considered no longer applicable; it does not guarantee an executable exit at that value.

For a simple unlevered cash instrument with one-FU integer increments and CU/FU prices, modeled loss per unit equals the adverse entry price minus adverse exit price plus explicit round-trip fees per unit. Size=floor(budget / modeled loss per unit), followed by any separate cash or unit constraints. This formula is meaningful only when the denominator is positive and all units and contract mechanics agree.

The source sizing education supports budget/per-unit-loss arithmetic. Its percentage guidance is not adopted. The supplied 100CU budget below is arbitrary, not “safe,” optimal, appropriate for beginners or suitable for a real account. Changing the budget or prices creates another exercise, not advice.

Costs need a declared convention. Our fictional fee is fixed 0.10CU per unit on entry and 0.10CU on exit. These are not percentages or real venue fee schedules. Adverse allowances add 0.10 to nominal entry and subtract 0.20 from nominal exit. Since prices here already include those allowances, do not subtract slippage a second time.

“Risk/reward” often compresses a conditional loss and a conditional positive outcome into a ratio. A ratio contains no probability, timing, sample size or distribution. It cannot establish expected profit, win rate or suitability. We compare an alternate terminal state to illustrate the arithmetic; its price is neither a target nor a forecast.

Gap risk remains even if a trigger is recorded. A next executable exit below the modeled invalidation assumption increases loss beyond the budget. Fees and slippage can also be larger than stipulated. A planned budget is not a worst-case cap. Instruments with leverage, options, borrowing, inverse contracts or liquidation require different models and are outside this bounded cash exercise.

Source-to-claim scope

• Budget divided by modeled per-unit loss; source percentage recommendations excluded [S04-SIZING].
• A stop does not guarantee execution at the trigger [S04-STOPS].
• Hypothetical results omit actual risk and can involve hindsight [S04-SIMULATION].

The fixture's arithmetic, bucket alignment, strict swing rule, matching/trigger assumptions, journal convention and rubric are explicitly supplied teaching conventions where applicable; these references do not authenticate fictional values or endorse a venue. US securities and futures sources support bounded vocabulary and limitations, not a claim that their rules apply universally to crypto.

• Risk budget: fictional scenario allowance supplied as an input.
• Entry / invalidation assumptions: nominal modeled prices, not execution promises.
• Sizing: units that fit the conditional budget and other stated constraints.
• Round-trip fees: charges at both entry and exit.
• Gap stress: a separate worse execution scenario.
• Conditional payoff/loss ratio: comparison of specified outcomes, not expected value.

Data status: ILLUSTRATIVE / FICTIONAL. Account 10000CU; modeled budget 100CU; integer FU only; unlevered cash; no real account or asset. Nominal entry 50; nominal invalidation exit 48. Entry allowance+0.10, adverse exit allowance−0.20. Fixed fees 0.10 per unit each side. All prices are supplied exercise constants.

Adverse entry=50.10; adverse modeled exit=47.80. Gross loss per unit=2.30; fees 0.20; total modeled loss=2.50. Size=floor(100/2.50)=40FU. Entry cash required=40×50.10+40×0.10=2008CU, less than fictional account 10000. Nominal notional 2000 differs from actual modeled cash outlay 2008.

Modeled exit proceeds=40×47.80−4=1908CU. Net 1908−2008=−100CU. There is no inference that a real exit will occur at 47.80.

An alternate supplied terminal state, nominal 54, has adverse execution 53.80 under the same exit allowance. Net proceeds=40×53.80−4=2148; net outcome 2148−2008=+140CU. Conditional positive-outcome-to-modeled-loss ratio 140/100=1.4. Without costs a nominal comparison(54−50)/(50−48)=2 would overstate that particular ratio. Neither value is an expected profit or a recommended target. No probabilities or frequency claims are provided.

In a separate gap stress, executed exit is 44 exactly; this execution already specifies the fill, so do not subtract the 0.20 allowance again. Net proceeds 40×44−4=1756; net outcome 1756−2008=−252CU. The modeled budget 100 is exceeded by 152. No guarantee limits the next possible gap to this supplied stress.

The calculation demonstrates sensitivity to execution and costs. It does not establish a safe instrument, guaranteed setup, return distribution or amount a user should allocate. A fictional budget remains hypothetical even if the numerical capital resembles someone's real balance.

Ignoring fees; using price distance without FU/CU units; rounding upward; double-counting allowances in already specified fills; calling the invalidation price a guaranteed exit; importing a real percentage recommendation; and treating a conditional ratio as expected return all change the claim.

Inputs: FIX-P04-07. Tasks: derive per-unit modeled loss, integer size and cash need; calculate the three terminal cash outcomes; explain the cost-free ratio discrepancy; recompute size if the exercise budget is 97CU; and identify which assumption fails under the gap.

Label capital and budget fictional; verify instrument units; define entry and invalidation assumptions; add costs once; round units down; check cash constraint; stress gaps; and keep ratios conditional.

Sizing translates a hypothetical budget into units under a model. Costs and execution assumptions matter; gaps can invalidate the modeled loss. A scenario ratio is arithmetic, not a promise or personal allocation rule.

P04-L07-V01 — evidence panel

Educational question: Why can a correctly sized scenario still exceed its modeled budget?

Dataset: FIX-P04-07; ILLUSTRATIVE; observedAt=null. Mechanism sources: S04-STOPS, S04-SIZING, S04-SIMULATION. Build a formula panel: entry 50+.10; adverse invalidation execution 48−.20; round-trip fee.20; per-unit modeled loss 2.50; floor(100/2.50)=40. Separate columns for conditional exit 47.80, alternate terminal 53.80 and gap 44 with net−100,+140,−252. Label the positive case a conditional comparison, not a target or expected profit.

Caption: All capital, prices and outcomes are fictional; a100CU modeled budget is not a maximum-loss guarantee.

Alt text: Forty units yield modeled loss 100CU, but the supplied gap exit 44 produces loss 252CU.

Layout: 390px stacked labels and accessible equivalent text table; 768px/tablet and desktop verification pending. RTL: RTL layout and native labels for later Arabic adaptation; isolate IDs LTR; preserve chronological direction and numerical price axes. No translation authored. Style: Dark navy with cyan, electric blue and violet; readable contrast and labels independent of color; official ZECOIN branding only. Deterministic chart/SVG/HTML; no fabricated market screenshot.

Status: SPECIFICATION_ONLY; version 1; needs_review. No rendered asset or runtime integration is claimed.

P04-L07-V02 — evidence panel

Educational question: Which conclusions follow from these inputs, and which remain unsupported?

Dataset: FIX-P04-07; ILLUSTRATIVE; observedAt=null. Mechanism sources: S04-STOPS, S04-SIZING, S04-SIMULATION. Bind four labelled rows OBSERVED / INFERRED / UNKNOWN / INSUFFICIENT EVIDENCE to this lesson's evidence table and record locators. Include one calculation or classification and its assumptions. Display missing data and execution limits explicitly; no financial call or forecast badges.

Caption: Illustrative evidence states under the stated data and execution assumptions.

Alt text: A four-state table distinguishes supplied fictional records, conditional calculations, missing information and unsupported claims.

Layout: 390px stacked labels and accessible equivalent text table; 768px/tablet and desktop verification pending. RTL: RTL layout and native labels for later Arabic adaptation; isolate IDs LTR; preserve chronological direction and numerical price axes. No translation authored. Style: Dark navy with cyan, electric blue and violet; readable contrast and labels independent of color; official ZECOIN branding only. Deterministic chart/SVG/HTML; no fabricated market screenshot.

Status: SPECIFICATION_ONLY; version 1; needs_review. No rendered asset or runtime integration is claimed.

NONE. Use the embedded fixture, paper or an offline worksheet. No paid access, live market feed, real funds, wallet connection, account creation, signatures or trades are needed. No production tool capability is added or asserted.

• S04-STOPS — FINRA Regulatory Notice 16-19: https://www.finra.org/rules-guidance/notices/16-19 Supports: Stop-market price uncertainty and stop-limit non-execution risk; US securities context. Checked 2026-09-30; primary page inspected.
• S04-SIZING — CME Proper Position Size: https://www.cmegroup.com/education/courses/trade-and-risk-management/proper-position-size Supports: Budget divided by modeled loss per unit. Source percentage recommendations are not adopted. Checked 2026-09-30; primary page inspected.
• S04-SIMULATION — NFA Rule 2-29: https://www.nfa.futures.org/rulebooksql/rules.aspx?RuleID=RULE+2-29&Section=4 Supports: Hypothetical outcomes omit actual financial risk and can contain hindsight limitations; no claim this rule legally governs Academy. Checked 2026-09-30; primary page inspected.

These references support mechanism definitions only. All fixture values, paths, tickets, capital, fills and calculations are original ILLUSTRATIVE / FICTIONAL teaching material, not source-observed prices, a historical performance series or a recommendation for a current market. Documentation examples and official venue names do not endorse a platform. Dataset FIX-P04-07 is bounded to the embedded records and assumptions; observedAt=null because no real-world observation was collected. Future source review and editorial acceptance remain pending: reviewStatus=needs_review, lastReviewedAt=null.

P04-L08 — Trading journal and simulation. Continue within this program's learning sequence.