What is net expected value in the example?
Reveal the worked answer
−20 per trade.
45−60−5.
Advanced Options · ADV-28 · Core
Probability of profit versus expected value
Can a high win rate hide a losing trade?
What you will learn and prerequisites
- Explain the mechanism in the lesson question.
- Reproduce the worked comparison and recognize its failure case.
Read first: Read a contract and its premium, Rights, obligations and expiration, Defined payoff risk is not margin, Read the whole multi-leg ticket
Probability of profit measures frequency under a model, not profit size or loss severity. A high win rate can coexist with negative expected value. A low premium credit can finance a frequent gain while leaving rare large losses.
Model probabilities themselves also carry uncertainty.
Understand the mechanism
Expected value weights every outcome by probability and subtracts costs. Tail losses, gaps and changing dependence can be missed by a limited backtest. Margin and funding can force a position closed before an assumed terminal outcome.
Do not convert option Delta into a universal probability of a profitable multi-leg strategy.
Walk through the process
Report win rate alongside average win, average loss, distribution tails, costs and drawdown. Stress adverse assumptions and selection bias. Evaluate enough independent evidence to avoid extrapolating a lucky streak.
A successful recent period is not proof of stationary probabilities.
Model and implementation boundary
These are complete fictional reading examples, not live opportunities. Terminal identities assume the stated common settlement. Multi-expiry values require a surviving-leg model. Costs, assignment and financing can alter realized outcomes; a mathematical bound alone does not guarantee the same operational loss path.
A worked example
Suppose a fictional strategy wins 50 with 90% probability and loses 600 with 10%. Gross expected value is .9×50−.1×600=−15. With five cost per trade it becomes−20.
The graph varies assumed win probability, holding payoffs and costs fixed. It makes clear how much accuracy is needed merely to break even; it does not estimate any real strategy's probability.
Open the calculation without leaving this lesson
Probability of profit versus expected value—worked comparison
Vertical: Net expected value (USD per trade)
Horizontal: Assumed win probability
1. Fictional example
Read the graph as a data table
| Assumed win probability | Fictional example |
|---|---|
| 0.8 | -85 |
| 0.85 | -52.5 |
| 0.9 | -20 |
| 0.92 | -7 |
| 0.94 | 6 |
| 0.96 | 19 |
| 0.98 | 32 |
What would invalidate the reading?
Calling a short-premium trade safe because most historical outcomes won ignores rare severity and implementation costs.
Check your understanding
Try the question before revealing its answer. These are reading checks, not trading certification or a site completion record.
What is the critical failure to avoid?
Reveal the worked answer
Calling a short-premium trade safe because most historical outcomes won ignores rare severity and implementation costs.
Explain this risk before treating the example as a decision rule. A correct calculation does not guarantee a favorable market outcome.
Return to the question: Can a high win rate hide a losing trade? State the observed facts, the assumptions and the failure condition separately.
Sources, assumptions and downloadable script
External references support definitions and conventions. Worked scenarios and prose are original. No current quotes or dealer inventory are claimed.
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