The Kelly Criterion Tells You the Mathematically Optimal Bet Size for Any Edge You Think You Have
6 min read
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6 min read
Say you are sure a stock is going to outperform. Not a hunch, an actual edge: you think you will be right more often than the market's own pricing implies, and by a decent margin when you are right. The question that actually decides your return is not whether you are right. It is how much money you put behind it. Bet too little and you leave most of your edge on the table. Bet too much and one bad stretch wipes you out before the edge ever gets the chance to work. There is a formula that answers this exactly: the Kelly Criterion.
The Kelly Criterion is a formula for the fraction of your capital to risk on a single bet, given two numbers: how often you expect to win, and how much you expect to win relative to how much you expect to lose.
Kelly % = W − (1 − W) ÷ R
Two terms worth pinning down before anything else:
Win probability (W) is how often you expect this specific bet to pay off, expressed as a decimal. If you think a trade works out 55% of the time, W is 0.55.
Payoff ratio (R) is your average win size divided by your average loss size. If your typical winning trade gains 1.5 times what your typical losing trade costs you, R is 1.5.
A physicist named John L. Kelly Jr. worked this out in 1956 at Bell Labs, in a paper called "A New Interpretation of Information Rate," published in the Bell System Technical Journal. Kelly was not thinking about stocks. He was solving a problem in information theory, about how a gambler with an informational edge on a noisy signal should size bets to grow their money fastest over time. The math turned out to apply just as well to any bet with a known edge, which is why it later found its way into blackjack card counting and, eventually, position sizing in markets.
Plug different win probabilities and payoff ratios into the formula and the recommended bet size moves a lot, including down to nothing at all.
| Win probability (W) | Payoff ratio (R) | Kelly % |
|---|---|---|
| 50% | 1:1 | 0% |
| 55% | 1.5:1 | 25% |
| 60% | 2:1 | 40% |
At a 50% win rate with an even payoff, Kelly says to bet nothing, because there is no real edge to size in the first place: you are as likely to win as lose, and you win and lose the same amount either way. Nudge the win rate to 55% and improve the payoff to 1.5 times, and Kelly says 25% of your capital. Improve both further, to 60% and a 2-to-1 payoff, and it jumps to 40%. Small changes in your assumed edge move the recommended bet size a lot, which is exactly the problem with taking Kelly at face value.
Full Kelly assumes you know W and R exactly. In real markets, you do not know them. You estimate them, from a limited and noisy history, and every estimate carries error.
Even when the edge is real and correctly estimated, a full-Kelly bettor still rides a rough path to get there. Swings of 50% or more in account value are common along the way, because the formula is built to maximize long-run growth, not to minimize how bumpy the ride feels while that growth compounds.
Because of both problems, estimation error and the size of the ride, almost nobody who uses Kelly in practice bets the full amount. Most bet a fraction of it, commonly half or a quarter.
Leonard MacLean, William Ziemba and George Blazenko modeled this tradeoff directly in "Growth Versus Security in Dynamic Investment Analysis," published in Management Science in 1992: betting half of what full Kelly recommends keeps roughly 75% of full Kelly's long-run growth rate, while cutting volatility by roughly half. You give up a modest amount of theoretical growth in exchange for a materially calmer ride and much more room for your original edge estimate to be wrong.
Ed Thorp, the mathematician who first applied Kelly-style sizing to blackjack and later to markets, has long recommended half-Kelly or smaller for exactly this reason. It is the version of the formula that shows up in actual portfolios, not the textbook one.
This series has already covered a few different ways to decide how much of something to hold, and Kelly answers a genuinely different question from all of them. Risk parity weighs positions by how much risk they contribute to a portfolio, not by dollar size. The posts on gold allocation and crypto allocation size a whole asset class as a percentage of a portfolio.
Kelly Criterion is narrower than any of those. It does not tell you how to split a portfolio across asset classes at all. It tells you, for one specific bet where you believe you have a stated edge, what fraction of capital the math says to risk on that single position. It is a sizing rule for one active view, layered on top of whatever broader allocation framework you are already using, not a replacement for one.
Before sizing anything, you need real return data behind the bet, not a guess. NetWort's asset pages carry that price history for individual names, for example BBCA, Bank Central Asia, letting you check how a stock has actually behaved rather than assuming. If you are still narrowing down which position to size in the first place, the market movers page is a faster starting point than scanning the whole index by hand.
NetWort does not calculate a Kelly percentage directly. But your win-rate and payoff-ratio inputs both come from the same underlying return dispersion that already feeds your Sharpe ratio, volatility and IRR on the Portfolio Health section of your dashboard. Pull those numbers before you estimate an edge on any single position, and treat the Kelly output, whatever it comes out to, as a ceiling to size down from, not a target to size up to.