Risk Management · Lesson 02 of 15 · Reviewed November 10, 2026
Position sizing translates an explicit scenario into quantity. It does not determine whether the underlying idea is attractive or whether the chosen allowance is personally appropriate. A professional sizing calculation starts with the instrument, entry, planned exit, charges, and available purchase cash, then shows which constraint limits the whole-share result.
This lesson uses fully paid long shares and a fixed round-trip cost assumption. The dedicated exercise makes rounding and cash limits visible and refuses incoherent price ordering. It is a teaching model, not a brokerage buying-power calculation, and its planned loss remains conditional on the entered exit assumption.
1. Choose the scenario before choosing the quantity
A learner may want a round number such as 100 shares, but quantity should not determine the exit reference. If the reference is moved closer solely to make that quantity fit, the analytical hypothesis has changed. Document the entry and invalidation logic before solving for shares.
For a long-share example, planned exit must be below entry. Their difference is the modeled price-loss distance per share. The distance is not a guaranteed loss because an actual fill can occur elsewhere. It is simply the assumption used in the initial calculation.
The related technical-level risk lesson explains how chart references and exposure calculations connect. Here the focus is the quantity calculation itself, including costs and competing limits.
2. Reserve the entered charges in the allowance
Suppose the hypothetical planned-loss allowance is $100 and total fixed round-trip charges are $2. That leaves $98 for the modeled share-price loss. With entry $50 and planned exit $48, the per-share distance is $2. Dividing $98 by $2 gives 49 shares.
This convention includes one entered total cost for a completed round trip. It does not model every broker’s fee schedule. Per-share charges, minimum commissions, exchange fees, financing, and changing slippage can require a more detailed formula. The user should not enter a fixed cost and then assume every real expense has been captured.
If the allowance is less than or equal to the fixed charges, no positive share quantity fits under this model. Zero is a valid result. A calculator should not round upward or ignore costs to create an apparently useful trade.
3. Apply a separate purchase-cash constraint
A loss-based quantity can still require more purchase cash than the exercise has available. At $50 per share, 49 shares require $2,450 in share value. If only $2,000 is reserved for the share purchase, the cash constraint allows 40 whole shares.
The final quantity is the smaller of the loss-based and cash-based limits. In this case it is 40. Planned loss is 40 × $2 + $2, or $82. The unused $18 of allowance is not a target that must be consumed; it is a consequence of the binding cash constraint.
In the worksheet, purchase cash is explicitly reserved for shares only. Round-trip charges are handled separately in the loss allowance. This keeps the teaching arithmetic clear, but it is not a complete settlement, available-funds, or broker-permission model.
4. Round down and show the binding constraint
Whole shares require downward rounding. If the loss calculation permits 49.7 shares, 50 would exceed the entered scenario allowance. Fractional-share availability and execution differ by service and are outside this exercise. The tool uses a consistent whole-share convention.
Display both preliminary limits, not only the final quantity. A learner should know whether loss allowance or purchase cash is binding. That information explains why increasing one input may have no effect until the other constraint stops limiting the result.
For example, increasing allowance from $100 to $120 does not increase the 40-share result while purchase cash remains $2,000 at entry $50. Increasing purchase cash alone to $5,000 allows the loss constraint to bind at 49 shares. A transparent worksheet makes this interaction easy to inspect.
5. Recalculate when the entry assumption changes
An entry at $51 with the same planned exit $48 creates a $3 loss distance rather than $2. With $98 available for price loss, the loss-based quantity falls to 32 whole shares. The later entry changes both the distance and the cash required per share.
Keeping the old quantity while changing the entry can exceed the original allowance. A professional plan recalculates the entire scenario rather than assuming the sizing remains valid because the chart thesis is unchanged. A proposed instruction and an actual fill also need separate records.
Review liquidity and execution costs for why the final entry can differ from a displayed quote. Quantity and execution cannot be evaluated independently when the fill changes the modeled distance.
6. Work through the dedicated sizing exercise
Open the Lesson 2 position-sizing exercise. Enter allowance 100, purchase cash 2000, charges 2, entry 50, and planned exit 48. Predict a 49-share loss limit, 40-share cash limit, final quantity 40, entry value 2000, and planned loss 82.
Change entry to 51 while leaving the exit fixed. The loss-based limit becomes 32 and the cash limit becomes 39, so quantity is 32. Planned loss is $98 including charges. Explain why the unused allowance is a rounding remainder rather than an invitation to round up.
Next set allowance to 1 while charges remain 2. No whole share fits. Try a planned exit equal to entry; the per-share loss distance is zero and does not fit this sizing model. The exercise should reject that input instead of dividing by zero or presenting an unlimited quantity.
7. Recognize the risks the formula does not cap
A planned exit is an assumption about execution. A gap can create a larger per-share loss, and an unfilled protective instruction can leave the holding open. The fact that the initial quantity fits an allowance does not make the allowance a maximum possible loss.
The model also excludes portfolio overlap, correlated positions, leverage, short-sale obligations, derivatives, taxes, and account-specific restrictions. Those are not minor footnotes that more decimal precision can solve. They require separate analysis and, in some cases, different formulas.
The overnight gap lesson holds quantity fixed while changing the exit scenario. That is the appropriate next check after sizing, because it reveals what happens when the key execution assumption deteriorates.
8. Maintain a complete sizing record
Save the original inputs, both quantity limits, selected quantity, cost convention, and calculation time. If an actual order fills partially or at several prices, reconcile the resulting quantity and weighted entry before updating the plan. Do not treat the requested quantity as though it were the confirmed holding.
A revised plan should state whether the change came from price, cash, allowance, cost, or hypothesis. This makes later review more informative than a note saying only that size was adjusted. The same final quantity can arise for different reasons.
A paper example can be useful even when the result is zero or the proposal fails a constraint. The learning objective is to understand the relationship among inputs and limits. A tool that always finds a way to approve an example is less honest than one that explains why it does not fit.
9. Case review: widening the reference after entry
Suppose the original 40-share scenario used entry $50, exit $48, and $2 total charges, producing planned loss $82. After an adverse move, the learner changes the exit reference to $46 without reducing quantity. The revised planned loss is $162. The original allowance did not expand automatically just because the hypothesis became uncomfortable.
The revised scenario should be recorded separately. Moving a reference may be part of a prewritten method, but an unplanned change needs honest labeling. It cannot be presented as proof that the original sizing controlled the later exposure.
For practice, compare three revisions: a worse entry, a wider exit, and higher charges. Change only one at a time and identify which limit binds. This develops an intuitive understanding of the formula while preserving the distinction between a calculated scenario and a personal recommendation.
Review challenge: two constraints respond differently
Use allowance $75, charges $3, entry $24, planned exit $22.50, and purchase cash $1,000. The price-loss distance is $1.50. The loss-based limit is 48 shares, while purchase cash permits only 41 whole shares. Final quantity is 41, share value $984, and planned loss $64.50 including the fixed charge.
Increase purchase cash to $2,000 while keeping every other input unchanged. The loss constraint now binds at 48 shares and planned loss reaches $75. Increasing cash did not change the selected allowance or price distance. It simply removed the earlier constraint.
Next return purchase cash to $1,000 and widen the planned exit to $21. The loss-based quantity becomes 24, below the cash-based 41. Explain the shift before calculating. A professional sizing record should show both preliminary limits so the final quantity never appears to be an unexplained recommendation.
Finally, ask which values came from a hypothesis and which came from a funding convention. A lower exit reference changes the scenario; more available purchase cash changes a resource constraint. Neither is a reason to overwrite the other. Preserving the distinction makes later review useful when actual fills or account values differ from the original plan.
A complete practice record: assumptions, calculation, and review
Start the exercise by copying its inputs into a short record before pressing Calculate. Identify every unit and denominator: dollars, shares, percentages, price units, or a count of completed observations. Write the valuation time and clarify whether the values are fictional, historical, or confirmed transactions. The defaults in this course are fictional teaching examples. Their purpose is to make the arithmetic reproducible, not to recommend a position, percentage, boundary, or financing arrangement for a particular person.
Name the assumption that has the greatest effect on the answer. In one exercise it may be an exit fill; in another it may be the portfolio value, a shared shock, a cost, or the definition of the risk unit. A precise result can be highly sensitive to one uncertain input. State that sensitivity in plain language rather than allowing a clean screen to imply certainty. The calculator can enforce numerical consistency, but it cannot verify that the source data or chosen policy fits a real account.
Predict the result of one controlled change before calculating again. Keep every other input fixed. Explain whether the change affects a numerator, denominator, quantity constraint, cost, or scenario branch. Then compare the displayed result with your prediction. If they differ, return to the definition and arithmetic before inventing a market explanation. This method teaches the relationship among the inputs and prevents experimentation from becoming a search for a reassuring output.
Test a boundary case deliberately. Ask what happens when no whole share fits, a denominator becomes zero, a list is incomplete, a quantity exceeds the holding, or a scenario no longer matches the required price ordering. A validation message is useful evidence about the model’s scope. Do not replace a rejected value with an unrelated number simply to obtain an answer. First identify the violated assumption and decide whether this exercise is the appropriate model for the question.
Keep intended actions separate from confirmed states. A submitted order is not a completed fill, a cancellation request is not necessarily a canceled instruction, and a chart reference is not an available transaction price. For a paper exercise, state the hypothetical execution assumption. For a completed transaction record, use actual quantities, prices, charges, and status. Reconcile partial fills and remaining instructions so the ledger describes the exposure that exists rather than the exposure that was intended.
Write both the ordinary scenario and an adverse alternative when the model permits it. Preserve the original quantity while testing a worse outcome unless the purpose is explicitly to design a new plan. Label any revised plan with its own time and assumptions. A stress case is one selected possibility; it is not automatically the worst conceivable outcome or an estimate of probability. Missing information should remain labeled as missing rather than being converted into a zero or a favorable assumption.
Review the result on two separate dimensions. The first is outcome: what net dollars or normalized result occurred under the stated convention? The second is process: were the original definitions, constraints, and reconciliation steps followed? A favorable outcome does not prove a deviation was sound, and a loss does not prove that correct arithmetic was wrong. This separation helps a beginner identify a specific improvement instead of responding to every result with a new rule.
Finish with a concise explanation containing the observation, calculation, interpretation, and limitation. Another reader should be able to reproduce the important numbers without guessing what the fields mean. Preserve the original record, later revisions, and unfavorable examples. If extending the exercise into a historical or forward paper study, define the eligible sample and review horizon before collecting outcomes. A selected group of attractive examples cannot establish the reliability of a process. The strongest learning result is a clearer, auditable decision routine, including a clear reason when an example remains unresolved or does not fit the entered constraints.
Sources and model scope
Primary investor-education background supplies additional context. The numerical cases, graphics, and worksheets here are original fictional teaching examples. Every calculation depends on its stated convention; no worksheet determines personal suitability, guarantees execution, or establishes future returns.