Kelly Criterion

The Kelly criterion is a mathematical formula that determines the optimal fraction of your capital to risk on a trade based on your edge and the odds. Developed by John Kelly at Bell Labs in 1956, it maximizes the long-term growth rate of your portfolio while avoiding ruin. The formula balances the desire to bet big when you have an edge with the need to survive losing streaks.

Why It Matters

Position sizing is the most underappreciated factor in trading success. Two traders with identical strategies and identical entries can have dramatically different results based solely on how much they risk per trade. The Kelly criterion provides a mathematically optimal answer to the question every trader faces: how much should I put on this trade?

Overbetting leads to ruin — even with a positive edge, risking too much per trade creates drawdowns you cannot recover from. Underbetting leaves money on the table — risking too little means your edge compounds slowly. Kelly finds the sweet spot that maximizes long-term wealth accumulation.

How It Works

The basic Kelly formula:

f* = (bp - q) / b

Where:

• f* = fraction of capital to risk
• b = odds received (profit / loss ratio)
• p = probability of winning
• q = probability of losing (1 - p)

For options trading, a more practical version:

f* = (Win Rate x Average Win - Loss Rate x Average Loss) / Average Win

Or equivalently:

f* = Expected Value / Average Win

Applying Kelly to options: Suppose you sell put spreads with a 70% win rate. When you win, you make $150 (average). When you lose, you lose $300 (average).

f* = (0.70 x $150 - 0.30 x $300) / $150 f* = ($105 - $90) / $150 f* = $15 / $150 f* = 0.10 or 10%

Kelly says to risk 10% of your portfolio on each trade.

Why most traders use fractional Kelly: Full Kelly is aggressive. It produces the highest long-term growth rate but comes with severe drawdowns — 50%+ peak-to-trough declines are common. Most practitioners use "half Kelly" (risk half the Kelly amount) or "quarter Kelly":

• Full Kelly: Maximum growth, maximum drawdowns
• Half Kelly: 75% of maximum growth, significantly smaller drawdowns
• Quarter Kelly: 50% of maximum growth, much smoother equity curve

Key requirements for Kelly to work:

• Accurate estimates of win rate and average win/loss (garbage in, garbage out)
• Many trades (Kelly is a long-run formula)
• Independent outcomes (trades should not all be correlated)
• Ability to fraction your capital precisely

Limitations:

• Overestimates optimal size if you overestimate your edge
• Assumes you know your true probabilities (you often do not)
• Does not account for correlated positions
• Can suggest very large bets when the edge appears large

Quick Example

Your iron condor strategy has a 75% win rate, average win of $200, and average loss of $350 based on your last 100 trades.

Kelly fraction: (0.75 x $200 - 0.25 x $350) / $200 = ($150 - $87.50) / $200 = 0.3125

Full Kelly says risk 31.25% per trade. That is dangerously aggressive. At half Kelly (15.6%), a string of four losses would draw down your account by roughly 50%. At quarter Kelly (7.8%), four losses would cost about 28% — painful but recoverable.

With a $100,000 account at quarter Kelly, you would risk $7,800 per iron condor. If the max loss is $300 per contract, that means roughly 26 contracts maximum.