Expected Value in Options Trading - Weighing Every Outcome
Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026
In this lesson
Calculate the expected value of an options position from a set of outcomes and probabilities, and explain why a trade priced at the model's fair value has an expected value of about zero before costs.
Expected value (EV) is the probability-weighted average result of a trade: each possible outcome times its chance of happening, added up. It answers the question the risk-to-reward ratio and the probability of profit each answer only half of: across all the ways this trade can end, what does it make or lose on average?
How do you calculate expected value?
Expected value is the sum, over every outcome, of the outcome's result times its probability.
- List the outcomes. For an option at expiration, group stock prices into zones with the same kind of result.
- Give each zone a probability. The probabilities must add up to 100%.
- Multiply and add. Each zone's result times its probability, summed.
- Subtract costs. Commissions, fees and the cost of crossing the bid-ask spread come straight off the total.
The probabilities can come from your own view of the stock or from a pricing model. Both are shown below, because the difference between them is the whole point.
Worked example
A trader's own estimate for the XYZ 50/55 bull call spread, 30 days
XYZ is at $50 with 30 days left. The 50/55 bull call spread costs a $1.48 debit: it loses $148 at or below $50 and makes $352 at or above $55. Suppose a trader with a bullish view estimates the zones below. The trader also expects prices that land between the strikes to cluster just above $50, near $52, where the spread makes about $50; spread evenly across the zone, the average would be about +$102 instead.
- Expected value before costs: $123.20 + $12.50 - $59.20 = $76.50 per spread.
- After costs: if crossing the bid-ask spread costs $0.05 a share on each of the two legs, that is $10 per spread, leaving $66.50, before commissions.
The math is easy. The probabilities and the middle-zone average are the hard part, and they are this trader's opinion, invented here to show the arithmetic, not a measurement.
Illustrative and hypothetical. The ticker and prices are invented for teaching, and the figures exclude commissions, fees, margin interest and taxes, which reduce real results. Past or hypothetical outcomes do not indicate future results.
Why does the max-profit, max-loss shortcut give the wrong answer?
A common shortcut is probability of profit times the maximum profit, minus the rest times the maximum loss. It treats every win as the biggest win and every loss as the biggest loss. Using the model's probabilities at 30% volatility and a 4.5% rate, to one decimal place:
- Bull call spread: 36.7% x $352 - 63.3% x $148 = about +$36, which looks like an edge.
- 48/45 bull put spread: 73.3% x $61 - 26.7% x $239 = about -$19, which looks like a loser.
Neither is right. Many outcomes land between the extremes, and the shortcut ignores them.
The max-profit, max-loss shortcut versus the full calculation
50/55 bull call spread
48/45 bull put spread
What is the expected value when you use the model's own probabilities?
Do the full calculation for the 48/45 bull put spread, which collects a $0.61 credit, using the three zones from the probability of profit lesson:
The total is about $0. That is not a coincidence. The premiums came from the same model that produced the probabilities, and a model price is, by construction, the price at which the trade is fair under that model's risk-neutral probabilities. Every model-priced spread in this module, all 30 days to expiration, comes out within $1 of zero per spread before costs, whether it is a debit or a credit spread, high POP or low. That is a property of the model, not a measurement of real-world odds.
Expected value of the bull put spread, zone by zone
Contribution to expected value
What does that mean for real trades?
- High probability is not an edge. The bull put spread wins about 73% of the time under the model, and its expected value is still about zero. Its small, frequent wins are paid for by rarer, larger losses.
- A good ratio is not an edge either. The bull call spread's 2.38 : 1 reward to risk is balanced by its 37% chance of profit.
- An edge is a disagreement with the market. Positive expected value needs your probabilities to be better than the ones built into the price, as in the trader's estimate above. That view can simply be wrong, and the market's prices already reflect many other traders' views.
- Costs come out every time. Starting from about zero, commissions, fees and bid-ask slippage push a model-priced trade's expected value below zero.
- Expected value is an average, not a promise. Even a genuinely positive-EV trade can lose on any one occasion, which is why each trade's maximum loss still has to fit your risk budget.
Check your understanding
A trade makes $200 with 60% probability and loses $250 with 40% probability. What is its expected value before costs?
Show answer
0.6 x $200 - 0.4 x $250 = $120 - $100 = $20 per trade.
Why is the expected value of a model-priced spread close to zero?
Show answer
Because its premiums are the model's fair values, and the probabilities come from the same model. Under the model, what you pay or collect matches the probability-weighted payoff, so the average result is about zero before costs.
Why does 'POP times max profit minus the rest times max loss' misstate expected value?
Show answer
It assumes every winning trade makes the maximum and every losing trade loses the maximum, ignoring the outcomes between the strikes, where results are partial.
Key takeaways
- Expected value is each outcome's result times its probability, added up, minus costs.
- The max-profit, max-loss shortcut ignores partial outcomes and can make a trade look better or worse than it is.
- Under the model that sets the premiums, a fairly priced trade has an expected value of about zero before costs, at any probability of profit.
- A positive expected value needs probabilities better than the market's, and an edge large enough to cover costs.
Common questions
What is expected value in options trading?
It is the average result you would expect per trade if you could repeat the same trade many times under the same odds: each possible outcome times its probability, added up. A positive expected value means the trade comes out ahead on average under those odds; it says nothing about any single trade.
How do you calculate the expected value of an option?
List the possible results at expiration, assign each a probability that adds up to 100%, multiply each result by its probability and add the products. Then subtract fees and the cost of crossing the bid-ask spread.
Can an options trade with a high probability of profit have negative expected value?
Yes. If the rare losses are large enough, they can outweigh many small wins. A trade that wins 73% of the time can still lose money on average once its larger losses and its costs are counted.
Do options have positive expected value?
Under the pricing model that sets the premium, a fairly priced option starts with an expected value of about zero before costs, for the buyer and the seller alike. A positive expected value needs your probabilities to be better than the market's, and that edge has to be larger than your costs.