What Is the Kelly Criterion — the Maths Behind Position Sizing

How Much Should You Bet?

Most investors obsess over what to buy. Far fewer think carefully about how much to buy. The Kelly Criterion — developed by John Kelly at Bell Labs in 1956 — provides a mathematical answer to the position sizing question: given your edge, how large should each position be?

Kelly % = (Win Probability × Average Win / Average Loss) − (1 − Win Probability) / (Average Win / Average Loss)

Or in simplified form for even payoffs: Kelly % = 2p − 1, where p is your probability of winning.

The Logic Behind It

Kelly maximises the long-run growth rate of your capital. Bet too small and you leave money on the table. Bet too large and a string of losses can devastate your account — even if you have a genuine edge. Kelly finds the sweet spot that grows wealth fastest without risking ruin.

If you have a 60% win rate on trades with equal risk and reward, Kelly says to risk 20% of your capital per trade. That sounds aggressive — and it is. In practice, most professionals use “half Kelly” or “quarter Kelly” to smooth out the ride.

How to Read It

• Kelly suggests 0% or negative: You don’t have an edge. Don’t take the trade. This is actually one of the most valuable outputs — it tells you when to stay out.
• 1–10%: Modest edge. Size accordingly. This is where most real-world trading edges fall.
• 10–25%: Strong edge. Full Kelly at this level is aggressive; half Kelly (5–12.5%) is more practical.
• Above 25%: Either an extraordinary opportunity or your estimates are too optimistic. Double-check your win rate and payoff assumptions before sizing this large.

Why Full Kelly Is Dangerous

Kelly assumes you know your exact win probability and payoff ratio. In reality, you’re estimating both — and overconfidence is the norm, not the exception. Full Kelly also produces stomach-churning drawdowns. A portfolio running at full Kelly can easily drop 40–50% before recovering. Most investors — even professionals — can’t stomach that.

That’s why the standard practice is to use a fraction of Kelly. Half Kelly gives you 75% of the growth rate with dramatically less volatility and drawdown risk. Quarter Kelly gives roughly 50% of the growth rate with a much smoother equity curve.

Practical Example

You’ve backtested a strategy that wins 55% of the time with an average win of $1,200 and average loss of $1,000. The win/loss ratio is 1.2. Kelly % = (0.55 × 1.2 − 0.45) / 1.2 = (0.66 − 0.45) / 1.2 = 17.5%. Full Kelly says risk 17.5% per trade. Half Kelly — a more sensible approach — says 8.75%. On a $100,000 account, that’s $8,750 at risk per position.

Kelly in Portfolio Context

When running multiple positions, the total Kelly allocation across all trades matters more than any individual bet. If you have five positions each sized at 10% Kelly, you’re running 50% Kelly across the portfolio — which may be far more aggressive than intended.

Combine Kelly with Sharpe Ratio analysis to understand whether your edge actually justifies the position size. A strategy with a low Sharpe ratio and high Kelly allocation is a recipe for trouble. The best outcomes come from strategies where both metrics align: a genuine, consistent edge sized appropriately.

Key takeaway: Kelly tells you the mathematically optimal bet size — but optimal for growth is not optimal for comfort. Use half Kelly or less in practice, and always question whether your edge estimates are realistic.