Probability of Profit

What is probability of profit?

Probability of profit, or POP, is the probability assigned to a positive result for the complete trade at a selected date. The entry premium, every leg, and the included costs determine which price regions are profitable, and the selected stock-price distribution assigns probability to those regions.

At expiration, use the position’s terminal payoff. For an earlier target date, use its value at that date. Holding to expiration and exiting early are two different trades, each with its own POP.

How is POP calculated?

First calculate the complete position’s profit or loss across stock prices. Find every region where the result is positive. Then sum the probability assigned to those regions by the selected price distribution.

A long call profits above its upper breakeven. A long put profits below its lower breakeven. A long straddle profits outside its two breakevens, while a short iron condor profits between its outer breakevens. Read the actual payoff to locate the winning region of a multi-leg structure.

How does POP differ from finishing in the money?

An existing 105 call bought for $2.50 per share needs stock above $107.50 to earn an expiration profit before costs. The call is in the money above $105.

With current spot at $100, 30 calendar days left, 30% volatility, and zero rates and dividends, the risk-neutral lognormal model assigns 27.08% probability above the strike and 18.84% above breakeven. The call’s current delta is 0.30.

Read the 27.08% for the chance of finishing in the money, the 18.84% for the chance of a profit, and the 0.30 delta for how much the call moves per $1. Both probabilities are risk-neutral model odds, so check them against your own view of the move before you size the trade.

How does volatility change POP?

The result follows the position’s profitable regions. Holding the $107.50 breakeven and 30-day horizon fixed, the example’s probability above that level is 9.85% at 20% volatility, 18.84% at 30%, and 24.57% at 40%. Recalculate the distribution when the volatility scenario changes.

For a position that profits inside a band, evaluate the mass inside that band. For one that profits in either tail, add both tails. This keeps the probability tied to the actual payoff.

Probability of touch vs probability of profit

Touch probability measures whether price reaches a selected level during the holding period. Expiration probability measures the ending price. A stock reaches levels along its path and then finishes elsewhere, so those questions require separate calculations.

Use touch probability to evaluate price-triggered management. Use expiration POP to evaluate the terminal payoff.

How do you use POP to choose a trade?

Compare probability, payoff size, and entry cost together. Expected value weights each possible gain or loss by its probability. The payoff chart shows the amounts; POP summarizes the profitable regions.

The options profit calculator compares strikes, premiums, and structures around the same thesis, with the probability and payoff of each candidate at the target price and holding period.

Limitations of probability of profit

• Name the volatility input with every POP. The example’s figure moves from 9.85% to 24.57% as volatility rises from 20% to 40%.
• Weigh POP against payoff size. A trade that wins most of the time still loses money overall when its losses are larger than its gains.
• Calculate POP from the breakeven. The call’s 0.30 delta sits close to its 27.08% in-the-money probability and well above its 18.84% probability of profit.
• Use touch probability for a stop or target along the way. Expiration POP measures where price finishes, and a path-triggered exit needs its own calculation.
• Add transaction costs to the breakeven: they raise a long call’s breakeven above $107.50 and lower its 18.84% POP.

Bottom line

Probability of profit measures how likely a complete position is to show a positive result at a selected date under a chosen price distribution. Calculate it from the trade’s breakevens, state the volatility input behind it, and always read it next to the size of the potential gain and loss.