Chapter 10 · Variance and Drawdown
Why can a positive-expectancy strategy still lose several times in a row?
- Skills to practice
- Probabilistic decisionsControl losses
- Read first
- Chapter 8 · Expected value
- 3D simulation
- None
Market scene
Zhe gives a computer one rule: 40% chance to win two units, otherwise lose one. A unit is 1% of current capital, with no fees, for 200 trades.
He runs 100 outcome sequences, seeds 1–100. Median final capital is 1.55 times initial, but 1 path ends below initial. Each path's largest decline from its own peak differs too; median is 11.5%.
Why are experiences so different under the same rule?
Your decision
After eight consecutive losses, what will you do?
Observe the result
| Question | Answer under these assumptions |
|---|---|
| Eight specified trades all lose | About 1.7% |
| An eight-loss streak anywhere in 200 | About 75.0% |
| Losing endings in default 100 paths | 1 |
| Median maximum drawdown in default 100 paths | 11.5% |
An uncomfortable stretch does not prove the logic wrong; enduring discomfort does not prove it still valid.
The mechanism
Fix 40% wins, payoff two, loss one, risk 1% of current capital, and 200 independent trades. A win multiplies capital by 1.02; a loss by 0.99. Paths start at 1 and follow outcome order.
- Same probabilities
- Different win/loss sequences
- Resize from remaining capital
- Different equity paths
- Record each peak
- Measure declines from peaks
Streak starts slide. Overlapping windows are not independent probabilities to add directly. The model tracks current consecutive losses and calculates first hitting chances trade by trade.
Drawdown compares prior peaks; final losses compare initial capital. These are different. A 20% loss needs 25% recovery; a 50% loss needs 100%. Recovery's starting base is smaller.
What it is called
Real markets
Chapter 3 shows identical closes with different processes. Endpoint-only analysis may claim profits unavailable after intrapath risk triggers.
Declines in Chapter 18 trigger further selling. More independent draws cannot repair omitted feedback.
Chapter 4 shows exhausted follow-on fuel. Investigate vanished conditions during losing streaks rather than calling everything bad luck.
Hands-on
One assumption: 40% win rate, +2R on wins and −1R on losses. Resize to current equity for 200 trades, excluding costs. Starting capital = 1; reaching 0.5 or lower marks a threshold breach, but the plotted path continues.
Path1: ending equity2.09 ×, maximum drawdown7.8%; longest losing streak7 trades;No threshold breach。
Seed1–100; fixed parameters and seeds are reproducible. The exact probability of at least eight consecutive losses in 200 trades is approximately75.0%. These paths exclude probability drift, serial correlation and price gaps, so they cannot estimate a safe position size in real markets.
Course versionV1-docs; sourcelab:equity-paths；Chapter 10 / TRD-PROB-004
Records parameters and results at the click only; does not mean the experiment passed.View snapshot to save
- Keep 1% risk; inspect different final balances, drawdowns, and longest streaks.
- Generate another 100 paths, recording seed ranges and explaining changed summaries.
- Return to the same seeds and raise risk only; inspect dispersion and threshold touches.
- Write tolerance, peak definitions, pauses, and post-stop checks. Synthetic draws only; no live trades.
Change one variable
Three depths
- FoundationWhy can a positive-expectancy strategy lose several times consecutively?Chapter 10
- AdvancedHow can Monte Carlo simulate a strategy's possible drawdown distribution?Advanced A · Probability and statistics
- InstitutionalHow should maximum-drawdown limits enter risk budgets, and how should size decrease after a trigger?Institutional
Inspect possible paths before deciding whether you can follow risk rules. Record final profit, maximum drawdown, and threshold touches separately.
Monte Carlo needs a generating process. This experiment assumes independence and fixed parameters; historical resampling needs dependence, lengths, and extremes. Separate model distributions from outside-model stress; see Advanced A.
Continue the project: compare block-sampled and independent drawdowns.
Budgets specify peaks, frequency, reduction size, pauses, and restart owners. Budget breaches trigger action without statistical proof of invalidation. Record discipline separately from research conclusions.
Continue the project: replay drawdown triggers, reductions, and restarts.
Questions to take away
Chapter self-test
The first is eight specified losses; the second is at least one eight-loss streak anywhere in 200. They ask different questions.
No. A path may reach a high peak, fall substantially, and still end above inception.
No. One default path in 100 loses. An independent model guarantees even less about real markets.
Half the capital remains and must double. Gain and loss percentages use different bases.
One idea to take away
Positive expectancy describes an average edge, not guaranteed profits over finite trades. Short-term results deviate from the average; an edge can still suffer drawdowns.
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