Think of it as the speed limit on a mountain road. Drive well under the limit and you arrive later than you could have. Drive over it and your odds of a crash climb fast, even though the trip feels quicker. Kelly tells you where that limit sits, and experienced practitioners deliberately stay below it.
In this guide you will learn the Kelly formula, the growth math showing why half Kelly keeps about three quarters of the growth with far less pain, a five-step way to estimate your inputs from a trade journal, and the mistakes that turn a real edge into a blown account. Every number uses USD or neutral percentages, so it applies wherever you trade.
The Kelly formula for investments as shown on Wikipedia, captured 29 September 2026.
What Is the Kelly Criterion?
The Kelly criterion is a formula for risk allocation. It sizes a sequence of bets to maximise the long-term expected growth rate of your wealth, which is the same as maximising the expected logarithm of wealth. John Larry Kelly Jr. described it in 1956 in A New Interpretation of Information Rate, published in the Bell System Technical Journal (volume 35, issue 4, pages 917 to 926). Its roots go back further: Wikipedia's overview notes that Daniel Bernoulli suggested a similar geometric-mean idea in 1738.
For a simple bet, let p be your probability of winning, q = 1 - p your probability of losing, and b the net odds, meaning how many dollars you win per dollar risked. The Kelly fraction is f = p - q / b. It tells you what share of your capital to put at risk on each bet.
Markets rarely force you to lose everything, so the investing version adds two inputs. If l is the fraction you lose in a bad outcome and g the fraction you gain in a good one, the formula becomes f = p / l - q / g. A stop-loss that caps your loss at 5% of the position makes l equal 0.05, which allows a larger position than an unprotected trade would.
Edward O. Thorp carried the idea from blackjack into markets. His 1992 paper with Rotando estimated a full Kelly fraction of about 117% for the S&P 500, which means a modest amount of leverage. Treat that as an illustration of the method, because it rested on historical return estimates that may not repeat.
Why the Kelly Criterion Matters
Position sizing controls the shape of your equity curve. Two traders with an identical edge can end up in very different places: one compounds steadily, the other takes a deep drawdown and never climbs out. Losses compound against you, since a 50% loss needs a 100% gain to recover, which is why maximum drawdown matters so much. Oversizing costs far more than undersizing.
Half Kelly keeps about 75% of the maximum growth rate in the coin-flip model worked through later in this guide.
Kelly also answers a question most rules of thumb dodge. A flat 1% risk rule ignores how strong your edge is. Kelly scales with it: no edge means a bet of zero, and a bigger edge means a bigger bet. To judge whether your edge is real in the first place, pair it with the Sharpe ratio and the Sortino ratio.
The formula also carries a built-in warning. It is perfectly valid only when outcome probabilities are fully known, which is almost never true for investments. Paul Samuelson also argued that maximising log growth accepts more risk of large losses than most people will tolerate. Your own risk tolerance should decide how much of the Kelly number you actually use.
How to Apply the Kelly Criterion: A Five-Step Framework
You can run this framework on your own trade journal in about an hour. Use one strategy at a time, because mixing strategies blends different edges into a number that describes none of them.
Step 1: Estimate Your Win Rate Honestly
Pull at least 100 closed trades from a single strategy. Your win rate p is the number of winners divided by total trades. Small samples mislead badly: after 30 trades, an observed 60% win rate is statistically consistent with a true rate anywhere from roughly 42% to 78% at 95% confidence.
Step 2: Measure the Payoff Ratio
The payoff ratio b is your average winning trade divided by your average losing trade. If winners average $300 and losers average $200, then b is 1.5. Use realised results after fees and slippage, not the numbers your backtest shows before costs.
Step 3: Compute the Kelly Fraction
Put the inputs into f = p - q / b. With p = 0.55, q = 0.45, and b = 1.5, you get 0.55 - 0.45 / 1.5 = 0.25. Full Kelly says to risk 25% of capital on every trade. That number should make you uneasy, and the unease is correct: almost nobody who understands the math trades full Kelly.
Step 4: Shrink It
Apply a fraction of the result, commonly half or quarter Kelly, and cap any single position at a hard limit such as 2% to 5% of capital. In the example above, half Kelly is 12.5% and quarter Kelly is 6.25% of capital at risk. Also haircut your inputs, because your measured edge is an estimate with error around it.
Step 5: Recalculate on a Schedule
Re-estimate p and b every 50 trades, or whenever market conditions change. If the result falls to zero or turns negative, the formula is telling you to stop betting on that strategy until the edge returns. A sizing rule that cannot say no is not doing its job.
A simulation-based case for fractional Kelly under uncertainty, captured 29 September 2026.
Kelly Criterion Examples With Real Numbers
Start with a coin that lands heads 60% of the time and pays even money, so b is 1. Kelly gives f = 0.60 - 0.40 = 0.20, a bet of 20% of your bankroll. The table shows expected growth per bet at different fractions of that Kelly bet.
Growth per bet is the expected natural-log return: p x ln(1 + b x f) + q x ln(1 - f). Notice the asymmetry. Dropping from full to half Kelly costs about a quarter of the growth while halving the size of every bet, and therefore much of the swing. Going to double Kelly turns growth negative, so you lose money on average despite a genuine edge.
28% of participants went bust in an experiment where people started with $25 and could place up to 300 bets on a 60% coin, as summarised on Wikipedia.
Now a market version. Suppose a hypothetical asset offers a 5% expected excess return over cash with 20% annual volatility. A common continuous-time approximation gives a Kelly leverage of 0.05 / 0.20 squared, which is 125% of capital. Half Kelly is about 62.5%. The point is the sensitivity: change the return estimate from 5% to 3% and the full Kelly figure falls to 75%.
Common Kelly Criterion Mistakes
Mistake 1: Trusting a Small Sample
A hot streak of 20 trades produces a flattering p and an oversized bet. The bigger the bet, the more one bad estimate costs you. Use at least 100 trades before you trust any Kelly output.
Mistake 2: Overestimating Your Edge
This is the most expensive error. The table below uses a coin with a true 55% win rate at even odds, where true Kelly is 10% of capital.
A five-point overestimate pushes you to double the true Kelly bet and wipes out all growth. Half Kelly on the inflated estimate lands exactly on the correct bet. That is the strongest practical argument for fractional Kelly: it works as insurance against your own optimism.
Mistake 3: Ignoring Correlation
Kelly assumes independent bets. Five long positions in highly correlated growth stocks behave like one large position. Size the combined exposure, and use asset allocation rules to keep the total in check.
Mistake 4: Running Full Kelly Because the Math Says So
Full Kelly maximises long-run growth, but the ride includes large drawdowns. Wikipedia notes that gamblers use fractional Kelly to reduce the chance of ruin, reduce volatility, and allow for model error. If a 40% drawdown would make you abandon the strategy, you never collect the long-run growth, so the theoretical maximum is worthless to you.
Mistake 5: Forgetting Costs
Commissions, spreads, and slippage shrink your payoff ratio b. Since Kelly is sensitive to b, ignoring costs makes the formula recommend a bigger size than your real edge supports. If you trade forex, see how sizing works in practice in this guide to Claude AI for forex position sizing.
A trading guide covering personal Kelly fractions, captured 29 September 2026.
Frequently Asked Questions
What is the Kelly criterion in trading?
It is a formula that converts your win rate and payoff ratio into the fraction of capital to risk per trade so that long-run growth is maximised. It returns zero when you have no edge.
Is half Kelly better than full Kelly?
For most people, yes. In the coin-flip model half Kelly delivers about 75% of the maximum growth with half the bet size, and it protects you from errors in your inputs. Full Kelly is only optimal when your probabilities are known exactly.
What is the Kelly criterion formula for stocks?
The investing form is f = p / l - q / g, where l is the fraction lost and g the fraction gained. For a portfolio with continuous returns, a common approximation is expected excess return divided by variance. Both need honest, conservative inputs.
Can the Kelly fraction be negative?
Yes. A negative result means the bet has negative expected value, so the correct size is zero. Some strategies use it as a signal to reduce or flip exposure, but most retail traders should read it simply as a reason to skip the trade.
Does Kelly work for long-term index investing?
Only loosely. Long-run return and volatility estimates for an index are uncertain, so Kelly works better as an upper bound on leverage than as a precise target. Most long-term investors are better served by a fixed allocation and regular rebalancing.
Key Takeaways
- The Kelly fraction is f = p - q / b: your win rate minus your loss rate divided by the payoff ratio.
- Half Kelly captured about 75% of maximum growth in the coin-flip model, with half the bet size.
- Betting double the Kelly fraction turned expected growth negative even with a real edge.
- Overestimating your edge is the costliest error, so shrink both your inputs and your fraction.
- Use at least 100 trades per strategy and recalculate every 50 trades.
- Like a mountain road speed limit, Kelly marks the fastest safe pace, and smart drivers stay under it.
What to Watch Next
- v Does your measured win rate hold above your break-even level over your next 50 trades?
- v Does your average payoff ratio stay stable once fees and slippage are included?
- v Do your open positions become more correlated during market stress?
- v Does your worst drawdown stay inside the limit you set before you started?
References
- Kelly criterion, Wikipedia: origin, formula, fractional Kelly, and criticisms.
- J. L. Kelly Jr., A New Interpretation of Information Rate, Bell System Technical Journal, 35(4), 917 to 926, 1956.
- Kelly Criterion, Investopedia: definition and formula.
- Why fractional Kelly? Simulations of bet size with uncertainty: simulation evidence, published April 2023.