Break-Even Probability

Break-even probability is the accuracy the payoff economics require, not a property of your model. The higher the purchase price, the more often the contract must pay 1 just to return the money spent.

Before and after costs #

Without costs,

$$EV=q-p=0 \quad\Longrightarrow\quad q_{break-even}=p.$$

If $c$ is a correctly measured additional per-share cost not already included in $p$,

$$EV_{net}=q-p-c, \qquad q_{break-even}=p+c.$$

Slippage already reflected in the execution price must not be counted again in $c$.

Required accuracy table #

At $p=0.60$ with $c=0.02$, break-even rises from 60% to 62%. A model at $q=0.65$ now has only three cents of net edge rather than five.

Life example #

If a game ticket costs 7 and pays 10 on success, you must succeed 70% of the time to break even over repetitions. The 3-unit winning profit alone hides the 7-unit losing loss.

Application to no-hedge #

The required no-hedge threshold is the maker execution price plus fees, capital cost, expected adverse-selection loss, and other non-overlapping expenses. The reference-derived fair value must exceed that all-in threshold with a safety buffer.