Trading Defined
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Kelly Criterion

The Kelly criterion is a formula for the fraction of capital to risk that maximises long-run growth, given a known win probability and payoff. For a bet with win probability p and payoff b to 1, the fraction is p − (1 − p) ÷ b. Because real edges are uncertain, many traders use a fraction of it (“fractional Kelly”).

The Kelly criterion is a formula that suggests what fraction of capital to put on a bet or trade so that capital grows fastest over many repeats. It needs a win probability and a payoff ratio, and both are hard to know in markets. Because a wrong estimate can lead to oversized bets, many traders use only part of the Kelly result.

Category
Risk Management
Reading time
4 min
Also called
Kelly formula, Kelly ratio, Kelly bet sizing
Updated

Kelly in plain words

The Kelly criterion is a formula that tells you how much to stake on a bet or investment with a positive expected return.1

It aims to grow capital as fast as possible over time without taking on needless risk.2

The core idea: put more money behind the ideas with the best expected value.3

How to use the Kelly formula

  1. Estimate the win rate

    Estimate W, your win probability, and R, the ratio of average win to average loss; then Kelly % = W − (1 − W) ÷ R.1

  2. Estimate the payoff

    Work out R, the average win divided by the average loss, from your own records.

  3. Compute the fraction

    Plug both into the formula; a zero or negative answer means the edge is not there.

  4. Treat it as a ceiling

    Pyxis notes it provides an upper limit for allocation.2

  5. Scale it down

    Bet only a fraction of the Kelly result to keep swings manageable.2

  6. Recheck often

    Keep updating W and R — over-optimistic inputs produce a bet far larger than justified, with the risk of heavy losses.3

Worked examples

Example 1 — Full Kelly

10%

A hypothetical strategy wins 55% of the time and wins as much as it loses (R = 1).

Example 1 — Full Kelly — calculation
W0.55
Kelly0.55 − 0.45 ÷ 1 = 10%

Using Kelly % = W – [(1 – W) / R], the made-up inputs give 10% of capital per trade.1

Example 2 — Half Kelly

Smoother path

The same hypothetical trader halves the 10% and risks 5% instead.

Example 2 — Half Kelly — calculation
Full10%
Half5%

Many traders use half-Kelly, giving up a little growth for a much smoother ride.2

Example 3 — Overestimated edge

Oversized bet

A hypothetical trader believes W = 0.70 with R = 1 and bets 40%, but the true W is 0.45, so the real Kelly is negative.

Example 3 — Overestimated edge — calculation
Believed0.70 − 0.30 = 40%
True0.45 − 0.55 = −10%

With inflated inputs, Kelly recommended a far bigger bet than the real edge justified, leaving the trader open to large losses.3

Full Kelly vs fractional Kelly

AspectFull KellyFractional Kelly
Bet sizeLargestSmaller
SwingsLargeSmaller
Input errorsCostlyCushioned
Typical useTheoryPractice

Where traders use it

Advantages and disadvantages

Advantages

  • Links bet size to the size of the edge.
  • Says not to trade when the edge is negative.
  • Gives an upper bound for allocation.
  • Simple formula for two-outcome bets.

Disadvantages

  • Inputs are estimates and often wrong.
  • Full Kelly produces big swings.
  • Ignores the size of moves, only their ratio.
  • Real trades have more than two outcomes.

Going deeper

Read as far as you need. Each level builds on the one before it.

The idea

Beginner

Kelly only makes sense when you expect a positive return.1

Volatility blind spot

Intermediate

The formula looks only at the ratio of wins to losses, not at how big the swings are.1 Most people can't stomach the resulting volatility and drawdowns, so they bet less.1

A baseline, not an answer

Advanced

Kelly is a sensible starting point for sizing, not a final answer, which is why many use half or less of what it suggests.3

Common mistakes

  1. Trusting a short sample

    Use many trades to estimate W.

  2. Using full Kelly

    Start with a fraction.

  3. Ignoring costs

    Fees cut the payoff ratio.

  4. Forgetting correlation

    Several related bets act like one big bet.

Check your understanding

Test yourself before moving on. Each answer comes with an explanation.

Q1W = 0.60 and R = 1. What does Kelly suggest?
Q2Why do traders use half Kelly?

Key points to remember

  1. Kelly sizes bets to maximise long-run growth.
  2. The formula is W − (1 − W) ÷ R.
  3. A negative result means no bet.
  4. Treat it as an upper limit.
  5. Most traders use half Kelly or less.

Frequently asked questions

Is Kelly used by professionals?

Some use it as a guide, usually scaled down.

What if the result is negative?

Do not take the bet.

Is half Kelly safer?

It cuts swings, though it grows more slowly.

Further learning

Sources

This article is written in our own words. The sources below support the specific facts, rules and figures marked with a number in the text. Links open the original publisher’s page.

  1. CFA Institute. The Kelly Criterion: You Don’t Know the Half of It (opens in a new tab) Checked .
  2. Pyxis Investment Management. Capital allocation to single investment opportunities (opens in a new tab) Checked .
  3. CFA Institute. Book Review: Concentrated Investing (opens in a new tab) Checked .

Educational content, not financial advice. Examples use hypothetical prices and simplified costs; actual fees, margin rules and regulations vary by broker, market and country. We are not affiliated with any publisher linked above. Last reviewed . Report an error or request a source credit.