Chapter 4 of 4
Expectancy, drawdowns and testing discipline
Study win rate, payoff size, cost drag, losing sequences and why backtests need out-of-sample evidence.
In this chapter
Win rate is only one component #
Expected P&L per observation can be represented as win probability × average win − loss probability × average loss − average costs. It is an estimate from assumptions or data, not a promised future outcome. A high hit rate can coexist with a negative expectation if occasional losses are large.
Average values can conceal skew, fat tails and dependence between observations. A rule that wins small amounts repeatedly but occasionally has a very large loss requires analysis of the tail, not just a smooth percentage of winning days.
Drawdown follows the path #
Drawdown measures a decline from a prior equity peak. Two experiments can finish at the same total value while producing very different funding pressure and emotional demands along the way. Consecutive losses do not automatically mean an independent process is broken, but they can exceed the available capital.
If losses are correlated, treating each observation as an independent coin toss understates clustering. A longer adverse sequence, a gap or margin increase can force a position to close before a long-run average has any chance to matter.
Test a hypothesis without rewriting history #
Use data and rules that would have been available at each historical point. Allow for failed or delisted securities, unavailable fills, fees and parameter choices. Reserve observations not used to design the rule, then examine stability rather than selecting only the best parameter set.
The more variants tried, the easier it becomes to find a result caused by chance. Keep a research log of the alternatives considered. A backtest is a conditional experiment, not proof that a pattern will work or permission to distribute a trading call.
Decision lab: A high win fraction can coexist with loss #
An illustrative distribution wins 70% of the time for +0.4R and loses 30% for −1.2R. Gross expectancy is 0.28R − 0.36R = −0.08R before costs. Accuracy by itself does not rescue the payoff asymmetry.
Compute net expectancy under larger slippage and a clustered-loss sequence. State which inputs are observed sample estimates and which are assumptions. Compare the capital floor and maximum whole-lot requirement with the worst tested path, without calling the sample’s worst loss a future bound.
Hypothetical worked example
A high hit rate can still lose
An illustrative sample wins 80% of the time with an average gain ₹100. The remaining 20% loses ₹500. Before costs, estimated expectancy is 0.8 × 100 − 0.2 × 500 = −₹20. With ₹10 average cost, it becomes −₹30.
Separately, a fall from a peak ₹1,20,000 to ₹90,000 is a 25% drawdown. Recovering to the peak requires a 33.3% gain from the trough, not 25%.
Neither number predicts the next sample. They show why win rate, net payoff, drawdown and the assumptions behind the record must be read together.
Common mistakes
- Reporting win rate without the average loss and costs.
- Choosing parameters on the full dataset and calling it independent validation.
Can an 80% win rate have negative expectancy?
Make this chapter useful
Can you defend the reasoning?
Before moving on, answer the self-check in your own words and write why each alternative fails. Use the worked example to test that explanation. Then apply it in the module research task; keep the assumptions and the evidence that could change your answer.
Sources and further reading
Further-reading references from the curriculum source list. Contract sizes, expiry calendars, settlement references, margin parameters and tax treatment can change; verify the current operative documents for the actual product. Worked figures are illustrative, not current quotes.
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General financial education. No securities recommendation, assured outcome or personal advice. Read the risk disclosures.