Chapter 12 · Risk of Ruin
Why can a positive-expectancy strategy still bankrupt someone?
- Skills to practice
- Control lossesProbabilistic decisions
- Read first
- Chapter 11 · Position management
- 3D simulation
- None
Market scene
Zhe stops new trades once teaching capital falls to half its initial amount. The rule stays 40% wins of two units, otherwise loss one, independently repeated 200 times without costs.
Across the same 1,000 seeds, changing only risk fraction gives no threshold hits at 1%, 111 at 5%, 436 at 10%, and 972 at 30%.
Per-trade weighted means remain positive. Why does trying to earn faster make losing the right to continue more likely?
Your decision
Choose how to explain the report rather than the prettiest number.
Observe the result
| Risk per trade | Threshold-touch fraction among 1,000 paths | Median maximum drawdown |
|---|---|---|
| 1% | 0.0% | 12.4% |
| 5% | 11.1% | 51.2% |
| 10% | 43.6% | 79.6% |
| 30% | 97.2% | About 100.0% |
Touches use half initial capital; drawdowns use previous peaks. They cannot replace each other. Approximately 100.0% reflects display rounding, not mathematically zero capital.
The mechanism
Fixed 40% wins, payoff two, loss one, risk proportional to current funds. Seeds 1–1,000 each run 200 trades. Any capital at or below half initial records a touch permanently, even after recovery.
- Larger trade amounts
- Streaks affect capital more
- Remaining capital shrinks
- Advance shutdown line is reached
- Eligibility to continue is lost
Without costs, initial 100,000 and 1% risk leave about 95,099 after five losses and 90,438 after ten. At 10% risk, ten losses leave about 34,868.
Fractions below all capital with bounded losses never reach exactly zero over finite trades. We measure a predefined survival boundary. Gaps, liquidation, and debt beyond capital are separate mechanisms this model cannot exclude. Chapter 18 shows forced exits.
What it is called
Real markets
Chapter 17's liquidated positions cannot participate in flash-crash recovery. Prices returning do not prove holders survived.
Chapter 14 shows size/cancellations affecting fills. Lack of counterparties during reductions may invalidate fixed one-unit losses.
Forced sales in Chapter 18 trigger the next batch. More independent paths cannot substitute for clustered-loss stresses.
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.
- Record default touches, then change only risk to 5% and 10%, saving reports.
- Hold risk and change shutdown line. Inspect stricter-trigger frequency and record horizons/seeds.
- Try blank input and equal entry/stop, then restore valid values. Invalid plans must not produce usable position reports.
- Specify stopping, reviewers, restarting evidence, and omitted independent-model risks. No real money or entry.
Change one variable
Three depths
- FoundationWhy can a positive-expectancy strategy still cause ruin?Chapter 12
- AdvancedHow can simulation estimate a sizing rule's ruin probability and maximum tolerable leverage?Advanced D · Portfolio and risk
- InstitutionalHow do institutions set stop-loss, liquidation, and Kill Switch thresholds to avoid irreversible loss?Institutional
Report capital boundaries, horizons, rules, and assumptions with touch rates. A standalone percentage cannot explain safety.
Compare risk fractions, drifting probabilities, dependence, and extreme losses. Meet predefined tolerance before growth. Tolerable leverage also needs margin, liquidity, and financing, not direct inference from stops. See Advanced D.
Continue the project: define ruin floors and omitted mechanisms.
Institutional stops, liquidation lines, and Kill Switches distinguish blocking entries, de-risking, cancellation, and controlled exits. Record trigger/restart authority and unavailable-feed/system handling. A statistical threshold is not implemented control.
Continue the project: rehearse post-stop positions and approvals.
Questions to take away
Chapter self-test
436 of 1,000 paths over 200 trades under specified distribution and seeds 1–1,000 touched half initial capital or lower. It predicts no arbitrary future account.
No. Finite simulations miss rare events and generators may misrepresent markets.
Advance discipline required stopping new trades. Continued paths aid understanding, not rule-compliant performance claims.
No. Higher lines are easier to touch; every lower-line hit already crossed them.
One idea to take away
Excessive size lets bad luck push equity beyond the boundary where trading cannot continue. Define survival constraints before expected returns.
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Why can a positive-expectancy strategy still cause ruin?
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