Suppose you have an edge. Maybe a fund really does win more often than it loses, or a strategy really is favourable. The next question is the one most people skip: how much of your money goes in? Stake too little and you leave growth on the table. Stake too much and one ordinary losing streak takes you out — even when the bet was in your favour. The formula that finds the size in between is the Kelly criterion.
This page is about position sizing — “how much?”, not “which fund?”. It walks through a single fund, then a two-fund mix, in plain English, and there is a Kelly calculator to try your own numbers.
When a bet repeats, there is a sweet spot for how much you stake. Below it you grow slowly. Above it you grow more slowly too — and with far bigger swings. Kelly is the size that grows your money fastest over the long run.
It gets there by maximising the average of the log of your wealth — a compact way of saying “the compounding rate”. Optimising the compound rate, rather than the average gain, is what keeps an unlucky run survivable.
For a bet that repeats with independent outcomes, there is one formula:
f* = (p · W − q · L) / (W · L)
You will also see a second version quoted everywhere: f* = p − q / b — “edge ÷ odds”. That is not a different rule. It is the same formula for the special case where a loss costs you the entire stake (L = 1) and a win pays b per unit staked (so W = b). If you can lose 100% of what you put in, the two are identical.
A fund rarely loses your whole stake — a 20% drop gives back a fifth, not everything. So for a fund, use the general form (L = 0.20, not 1); the p − q/b shorthand is for bets where the stake itself can go to zero. And if either form gives a negative number, Kelly is not saying “bet small” — it is saying do not take the bet at all. No edge, no position.
Say you put money into something that, each period, either rises 20% or falls 20%, and you believe it rises 55% of the time. Put in p = 0.55, W = 0.20, L = 0.20:
f* = (0.55 × 0.20 − 0.45 × 0.20) / (0.20 × 0.20) = 0.50
Here L = 0.20 — a loss gives back a fifth of what you staked, not everything — so we use the general form, not the “lose it all” shorthand. Kelly says: put half your money in and keep half in cash. It is worth seeing what “too much” does. Stake the whole 100% and the compounding works out slightly negative — a 20% loss bites harder than an equal 20% gain helps. Stake 50% and you grow about +0.5% per round; stake 100% and you shrink. That asymmetry is the entire reason Kelly exists.
The coin above could only land two ways: +20% or −20%. A real fund can end a year just about anywhere, so the “how much do I win / lose” inputs don’t fit. Two ordinary numbers describe it instead:
Swap those in and the Kelly rule becomes a rule of thumb:
f* ≈ average return ÷ (bounciness)² — or in symbols, f* ≈ μ / σ²
The logic is the one you would guess: the more a fund earns (higher μ), the bigger the position Kelly supports; the more it bounces (higher σ), the smaller — and because bounciness is squared, “twice as bumpy” roughly cuts the position to a quarter. (That squared bounciness is what maths calls variance — hence “return over variance”.)
Try it: an 8% average return above cash and 20% volatility gives 0.08 ÷ 0.04 = 2.0. That “200%” is the model telling you to borrow to double the position — which is exactly why almost nobody runs full Kelly in real markets (more below). Treat the number as a sanity check, not a target.
Now the mix case. Two funds A and B behave like a seesaw: when A wins, B loses, and the other way round. Put w of your money in A and the rest in B. If A wins (chance p) it gains x and B loses y; if B wins it is the reverse. The compounding-optimal split is:
w* = (y + (2p − 1)) / (x + y)
Try p = 60%, with both legs swinging ±100% (x = y = 1.00): w* = (1 + 0.2) / 2 = 0.60 → 60% in A, 40% in B.
Now the striking part. Keep p = 90%, but shrink the swings to ±20% (x = y = 0.20): w* = (0.20 + 0.80) / 0.40 = 2.5 — more than 100%. Kelly is saying the edge is so large relative to the swings that you should lever up; without leverage, the practical answer is all of it in A. The same confidence therefore leads to very different sizes depending on how big the moves are. That is the genuinely useful lesson.
“Fractional Kelly” means betting a fixed slice of the full-Kelly figure instead of all of it. In the example above the full figure was 50%, so:
Same rule, deliberately scaled down by a factor you choose. Why scale down at all? Three reasons, all pointing the same way:
The cost of scaling down is small; the benefit is large: half Kelly gives up only about a quarter of the long-run growth, for roughly half the swings. That is why many practitioners use a half or a quarter rather than the full figure.
“Fractional Kelly” is not a different formula — it is the same answer multiplied by a safety factor you pick (½ and ¼ are the common ones). Less money at risk, close to the same compounding.
It is not a forecast of returns and it is not a recommendation to trade. It is a sizing lens: given that you already believe an edge exists, it tells you roughly how big the position should be. Everything depends on inputs you have to supply honestly — and on the assumption that the same odds keep repeating, which markets only loosely obey.
A formula for how much of your money to put into a favourable repeating bet so it grows fastest. Too small wastes the edge; too large grows slower and swings harder. The Kelly size is the sweet spot in between.
For a bet that pays b per unit staked and loses the whole stake: f* = (b·p − q)/b (edge ÷ odds). When a loss only gives back a fraction L of what you staked, use f* = (p·W − q·L)/(W·L).
Almost never in markets. Full Kelly assumes you know the true odds and that the bet repeats cleanly; neither holds. A fraction of Kelly (half or a quarter) gives up little growth for much smaller swings and more protection against an over-optimistic estimate.
If the two legs move in opposite directions and A wins with probability p while the legs swing by x and y, the Kelly weight for A is w* = (y + (2p − 1)) / (x + y), capped at 100%. Try it in our Kelly calculator.
No. It maximises the long-run growth rate only if your inputs are right and the outcomes repeat. Get the probabilities wrong and it will size you into trouble just as confidently. Treat it as a discipline for sizing, not a promise.
Related: Sharpe ratio: return per unit of risk · Maximum drawdown · How to compare two funds · Rebalancing calculator