Expected Value

What Is Expected Value?

Expected value (EV) is the probability-weighted average outcome of a trade. If you repeated this trade many times under identical conditions, what would the average result be?

The calculation: multiply each possible outcome by its probability, then sum the results. A trade with 70% chance of making $100 and 30% chance of losing $200 has EV of (0.70 × $100) + (0.30 × -$200) = $70 - $60 = $10. Over many repetitions, this trade produces $10 on average per occurrence.

Positive EV means profit over many repetitions. Negative EV erodes capital over time. Zero EV is a fair game — no edge.

Why It Matters for Options Traders

Expected value is the true measure of trade quality. Probability of profit tells you how often you win. Expected value tells you whether wins and losses actually add up to profits. A high-probability trade that loses more than it wins has negative EV and will destroy a portfolio.

Options markets create the illusion of edge through high POP. A short strangle with 85% POP sounds compelling until the rare losing trade — a large gap move — results in a loss 10× the size of any individual credit. Whether that strategy has positive EV depends entirely on whether premium collected compensates for expected frequency and magnitude of large losses.

Selling options in high IV environments improves EV by collecting more premium relative to realized volatility. When IV systematically overstates realized volatility — a documented historical tendency in equity index options — selling premium has positive expected value.

Key Characteristics

• Calculation: EV = sum of (outcome × probability) for all scenarios
• Sign determines edge: Positive EV = statistical advantage; negative EV = statistical disadvantage
• Must account for all scenarios: Ignoring low-probability large losses is the most common EV miscalculation
• Implied vs. realized volatility: When IV consistently exceeds realized volatility, premium selling has structural positive EV
• Position sizing matters: Even positive EV strategies can cause ruin if position sizes allow catastrophic loss on a single outcome
• Kelly Criterion connection: Kelly uses EV to determine optimal position sizing for long-run growth