The Kelly Criterion for Position Sizing

The Kelly criterion is a formula for sizing a bet to maximise long-term growth of capital, based on your edge and the odds. In investing it suggests larger positions where your edge is high and the downside limited, and smaller ones where it is not. Full Kelly is too aggressive and too precise for the uncertain world of stocks; most practitioners use a fraction of it as a sizing discipline, not a precise rule.

Where this fits: Kelly is one lens on position sizing — the decision of how much to bet on each idea. It serves the same master as diversification and survival-first investing: growing capital over time without ever risking ruin.

Most investors agonise over what to buy and give almost no thought to how much. Yet how much you bet on each idea often matters more to your long-term result than which ideas you pick. The Kelly criterion is the most famous attempt to answer the “how much” question with mathematics — and it is both more useful and more dangerous than most people realise.

This guide explains what Kelly is, where it comes from, why its pure form will hurt you, and how thoughtful investors actually use it.

Where Kelly comes from

The Kelly criterion was devised by John Kelly, a researcher at Bell Labs, in the 1950s, originally in the context of information theory and signal transmission. It was later taken up by gamblers — famously by those seeking an edge at blackjack — and then by a number of successful investors who recognised that sizing bets to compound capital is the same mathematical problem whether the “bet” is a card game or a share purchase.

The question Kelly answers is precise: given an edge and a set of odds, what fraction of my capital should I stake on each opportunity to grow my wealth as fast as possible over the long run — without going broke?

That last clause is the key. Kelly is not about maximising your expected return on any single bet (that would tell you to bet everything whenever you have an edge, which guarantees eventual ruin). It is about maximising the compound growth rate across many bets, which is a very different, and much wiser, objective.

The formula

In its classic form for a simple bet, Kelly says:

f* = (bp − q) / b

where:

• f* is the fraction of your capital to stake,
• p is the probability of winning,
• q is the probability of losing (which is 1 − p),
• b is the net odds — how much you win per unit staked if you win.

A worked example

This is a hypothetical for illustration only. Imagine a repeatable bet where you win £2 for every £1 staked if you win (so b = 2), you have a 60% chance of winning (p = 0.6), and therefore a 40% chance of losing (q = 0.4).

Kelly says: f* = (2 × 0.6 − 0.4) / 2 = (1.2 − 0.4) / 2 = 0.8 / 2 = 0.40.

The formula recommends staking 40% of your capital on this bet. That already feels enormous — and it is. That discomfort is your first clue that full Kelly is not something to apply literally to a stock portfolio.

The formula captures two sensible intuitions precisely:

• More edge, bigger bet. The higher your probability of winning relative to the odds, the more you should stake.
• No edge, no bet. If bp = q, the formula gives zero — if you have no edge, you should not bet at all. And if your edge is negative, Kelly tells you to bet nothing (you cannot sensibly bet a negative amount).

Why full Kelly will hurt you in investing

The formula is mathematically correct for its assumptions. The problem is that its assumptions do not hold in investing. Applying full Kelly to stocks is a recipe for grief, for several reasons.

1. You do not know the true inputs

Kelly assumes you know p, q, and b exactly. At a blackjack table with a counted deck, you roughly do. With a stock, you are estimating the probability of success and the range of payoffs — and those estimates are uncertain, often badly so. If you overestimate your edge (and optimistic humans routinely do), Kelly will tell you to bet far too much. The formula is exquisitely sensitive to errors in inputs you cannot actually measure.

2. The volatility is savage

Even when the inputs are correct, full Kelly produces wild swings in capital. It is optimised for growth, not comfort, and the drawdowns along the way are enormous — far beyond what almost any real investor could hold through without panicking. A strategy that is theoretically optimal but gets you to sell at the bottom is not optimal for you.

3. Stocks are not clean, repeatable bets

Kelly’s logic relies on many independent, repeatable bets with stable odds. A stock purchase is a one-off, with a payoff that unfolds over years, correlated with your other holdings and with the market. The neat mathematics simply does not map cleanly onto this messy reality.

4. It ignores correlation and ruin at the portfolio level

Applied bet by bet, naive Kelly takes no account of the fact that your “bets” (stocks) move together — especially in a crisis, when correlations spike towards one. Several large Kelly-sized positions that all share a driver can combine into a ruinous concentration.

Fractional Kelly: how it is actually used

The practical fix is elegant: bet a fraction of what full Kelly recommends. This is called fractional Kelly, and half-Kelly (50%) or quarter-Kelly (25%) are common choices.

The beauty of fractional Kelly is the trade-off it offers. Because the growth curve is relatively flat near its peak but the volatility rises steeply, betting half the Kelly amount:

• cuts your volatility and drawdowns roughly in half, but
• sacrifices only a small portion of the long-term growth rate.

In other words, you give up a little theoretical growth for a large reduction in risk and a big cushion against your own estimation errors. For uncertain, real-world investing, that is an excellent bargain.

Approach	Growth	Volatility / drawdowns	Suitable for investing?
Full Kelly	Maximum (in theory)	Extreme	No — too aggressive, too precise
Half-Kelly	Nearly as high	Roughly halved	Much more realistic
Quarter-Kelly	Somewhat lower	Low	Conservative, forgiving of errors
Ignore Kelly entirely	Suboptimal, undisciplined	Unmanaged	No — you need some sizing logic

How to actually use Kelly as an investor

Here is the honest, practical takeaway. Do not plug stock estimates into the formula and bet the result — your inputs are not reliable enough, and the output will be dangerous. Instead, use Kelly as a conceptual discipline that sharpens how you think about position sizing:

1. Size up where your edge is genuine and the downside is limited. A business you understand deeply, with a durable moat and bought with a real margin of safety, is a high-edge, limited-downside bet — it warrants a larger position.
2. Size down where edge is thin or downside is large. A speculative idea, a business outside your circle of competence, or one bought near full value deserves a small position, if any.
3. Always stay fractional. Whatever your instinct says, bet less than the aggressive maximum. The investor who survives is the one who leaves a margin for being wrong.
4. Cap any single position. Regardless of how high your perceived edge, impose a hard ceiling on position size so that no single error can threaten your survival. This directly addresses Kelly’s blindness to ruin and correlation.
5. Account for correlation. Treat several positions sharing one driver as one larger bet when deciding sizes, so your effective Kelly exposure is not secretly enormous.

Used this way, Kelly stops being a false-precision calculator and becomes what it should be: a rigorous argument for the thing great investors do by instinct — betting bigger on their best, safest ideas and smaller on the rest, while never betting so big that a single mistake ends the game.

Kelly and the great investors

The investors most associated with concentrated, conviction-weighted portfolios — Buffett and Munger among them — have spoken approvingly of Kelly’s underlying logic: that bet size should scale with edge, and that you should bet heavily when the odds are genuinely in your favour and rarely. But they apply it with judgement, enormous margins of safety, and a horror of permanent loss — never as a mechanical formula. That is exactly the spirit in which an individual investor should take it. The maths is a servant of judgement, not a replacement for it.

Frequently Asked Questions

What is the Kelly criterion formula? In its classic form, f* = (bp − q) / b, where f* is the fraction of capital to wager, b is the net odds received on the bet, p is the probability of winning, and q is the probability of losing (1 − p). The result is the bet size that maximises long-term growth of capital.

Why is full Kelly too aggressive for investing? Full Kelly assumes you know the true probabilities and payoffs exactly. In investing you only estimate them, and overestimating your edge leads to oversized, dangerous positions. Full Kelly also produces large drawdowns that most investors cannot stomach. Fractional Kelly is far more practical.

What is fractional Kelly? Betting a set fraction of the full Kelly amount — commonly half (half-Kelly) or a quarter. This dramatically reduces volatility and drawdowns while sacrificing only a little long-term growth, and it provides a cushion against the inevitable errors in your probability estimates.

Can the Kelly criterion really be used for stocks? Only loosely. Stocks do not offer the clean, repeatable odds of a coin toss or a hand of blackjack, and the inputs are uncertain. Kelly is best used as a conceptual guide — size up with edge and limited downside, size down without them — rather than as a precise position-sizing calculator.

Does Kelly tell me when to sell? Not directly — it is a sizing tool, not a selling tool. That said, its logic implies trimming a position if your estimated edge falls or the downside grows. For a full treatment of exits, see our guide on when to sell a stock.

Your Next Step

Kelly is one input into the bigger discipline of sizing bets wisely:

• Make it practical in position sizing as the ultimate edge.
• Protect against ruin with survival first: the math of staying in the game.
• Build the limited-downside edge Kelly rewards with a margin of safety.
• Only bet big within your circle of competence.

---

About the author: Cameron Hayes is a senior investor relations and finance professional who has worked in IR at Nasdaq Copenhagen-listed companies including Nilfisk and Maersk Drilling. He holds an MSc from Copenhagen Business School and a BCom from the University of Ottawa, and founded Gingernomics to teach individual investors the Five Criteria framework. More about Gingernomics.

The content on Gingernomics is for educational and informational purposes only and does not constitute financial advice. Always do your own research and consult a licensed financial advisor before making any investment decisions. Past performance is not indicative of future results.