Chapter 11 · Position Sizing
How large should a position be for the same trading idea?
- Skills to practice
- Control losses
- 3D simulation
- None
Market scene
Lin and Zhe plan BTC trades with $100,000 accounts, entry 60,000 and exit 57,000. Assume full fills at planned prices and no costs initially.
Lin would use the whole account. Zhe first budgets $1,000 loss. Each unit loses 3,000 from entry to exit, implying one third of a unit, worth 20,000.
They see the same chart. Why are these already different trades?
Your decision
With direction unchanged, how will you set quantity?
Observe the result
| Action | Quantity | Position value | Loss if stop fills as planned |
|---|---|---|---|
| Exit 57,000, risk 1% | About 0.3333 | $20,000 | $1,000 |
| Full account, exit 57,000 | About 1.6667 | $100,000 | $5,000 |
| Risk 1%, exit 59,700 | About 3.3333 | $200,000 | $1,000 |
The last row depends on executable tighter exits. Equal planned losses do not imply equal financing, fill, or gap risk.
The mechanism
For capital 100,000, entry 60,000, exit 57,000, and risk 1%, calculate the budget then divide by per-unit loss. Never choose quantity first and invent a flattering exit.
- Specify hypothesis invalidation
- Map it to a planned exit
- Set bearable trade budget
- Divide by per-unit loss
- Check value and financing
- Add costs and execution deviations
A volatility-based alternative sizes against daily movements. Account daily target 1% divided by estimated asset daily volatility 3% gives about $33,333. This constrains a scale, not maximum daily loss. Recalculate when estimates change.
Another formula assumes known independent repeated probabilities/payoffs to optimize long-run log growth. At 40% wins and payoff two versus one, risk is 10%. This says nothing about tolerable interim declines or whether real wins are truly 40%.
What it is called
Real markets
Chapter 14's shallow book changes prices with size. Exits consuming multiple levels may lose more than a single-price budget.
Chapter 17 uses small margin to bear full moves. Quantity still needs separate liquidation checks; this linear-stop calculator cannot approve exchange entry.
Chapter 6 compares improvised exits with advance cards. Moving losing stops outward invalidates original sizing.
Hands-on
Use hypothetical numbers only; no registration or orders. Risk percentage is the budget before stop execution; fees are deducted separately. Edits remain in this page's memory. After calculating, explicitly save a local snapshot or copy the report.
Complete the assumptions and calculate. Invalid inputs will not be replaced by old results.
- Verify default one-third quantity, $20,000 exposure, and $1,000 planned loss.
- Change only stop to 59,700 and explain 2× account exposure.
- Restore stop, add 0.05R costs, and inspect cost-inclusive losses/net expectancy. Fees do not vanish inside the old budget.
- Copy a report with hypothesis, invalidation, and unavailable-price handling. No accounts or orders; calculations are not direct sizing recommendations.
Change one variable
Three depths
- FoundationWhat size suits the same trading idea?Chapter 11
- AdvancedHow do Volatility Target and Kelly allocate portfolio risk?Advanced D · Portfolio and risk
- InstitutionalHow can multi-strategy positions be allocated by risk contribution rather than capital?Institutional
Budget loss before sizing under reasonable invalidation. Check costs, exposure, and exits. Decimal precision is not reliable planning.
Portfolio Volatility Target needs covariance, not separate divisions. Kelly needs joint outcomes. Probability errors, drift, and tails change optima; see Advanced D.
Continue the project: compare volatility targets and fractional Kelly.
Contribution-based allocation examines holdings, correlation, concentration, and liquidity jointly. Each strategy risking a small amount does not make total risk simply additive. Approved quantity also meets aggregate budgets and execution capacity.
Continue the project: check capital budgets against risk contributions.
Questions to take away
Chapter self-test
$1,000 risk divided by $3,000 unit loss gives the quantity, worth $20,000.
No. Same budgets raise size/exposure; normal-trigger, gap, cost, and liquidation risks remain.
No. It assumes distributions/growth goals, verifies no probabilities, and guarantees no avoidance of shutdown.
Formula notional halves, about 33,333 to 16,667. This is no maximum-loss guarantee.
One idea to take away
Size determines whether you survive long enough for expectancy to materialize. Set acceptable loss per trade, then calculate quantity backward.
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What size suits the same trading idea?
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