Kelly Criterion

Context & Mechanics

Definition and formula

The Kelly criterion – developed in 1956 by John L. Kelly at Bell Labs – answers the question of optimal stake: which fraction of capital per trade maximises long-term growth? Formula: f* = p − q ÷ b, where p is the win probability, q the loss probability (1 − p) and b the win/loss ratio. Example with a strategy's journal values: p = 0.55, b = 1.5 → f* = 0.55 − 0.45 ÷ 1.5 = 0.55 − 0.30 = 0.25 – arithmetically 25 % of capital per trade.

Why nobody trades full Kelly

The Kelly value maximises growth, not comfort: full Kelly produces drawdowns of 50 % and more with high probability – barely bearable psychologically and incompatible with any prop-firm rulebook whose overall loss limit sits at 10 %. Add the estimation problem: p and b are not natural constants but noisy journal estimates; overestimating them means systematically betting too much (over-betting), which not only slows growth but can ruin it long-term. The practical standard is therefore fractional Kelly: quarter Kelly yields 6.25 % in the example – still far above what tight rulebooks allow.

Kelly as a thinking tool

For prop-firm traders Kelly is less a staking formula than a compass: if one's position sizing (typically 0.5–1 % risk per trade) sits far below the Kelly value, position size is not the bottleneck. A negative Kelly value, by contrast, is an alarm signal: the strategy has negative expectancy and does not belong in the account – at any size.

Why it matters for traders

Kelly connects hit rate, win ratio and stake size into one consistent logic. The GlanWick simulator lets traders play through, by way of example, how different stake sizes change the same strategy – GlanWick is a training and simulation tool and not a prop firm itself.

Execution Example

A trader has determined in a journal of 100 trades: 55 % hit rate, $1,500 average win, $1,000 average loss (b = 1.5) on a $100,000 account. The question: is a risk of 1 % per trade arithmetically too conservative?

Kelly value: f* = 0.55 − 0.45 ÷ 1.5 = 0.25 → 25 % capital fraction (full Kelly).
Quarter Kelly as the conservative practical variant: 25 % ÷ 4 = 6.25 %.
Comparison with reality: the traded 1 % risk sits far below both values – position size is not the strategy's bottleneck.
Rulebook context: even quarter Kelly would breach a 10 % overall loss limit in a normal losing streak (5–6 losers) – the prop-firm limits, not Kelly, define the maximum sensible risk here.

Execution Risk & Errors

Trading full Kelly and underestimating the extreme drawdown depth

Plugging hit rate and win ratio from samples that are too small into the formula

Over-betting: estimating p and b optimistically and systematically trading too large

Applying Kelly values without regard to prop-firm loss limits

Ignoring negative Kelly values instead of reworking the strategy

Frequently Asked

What does a negative Kelly value indicate?

That the strategy has negative expectancy: on statistical average every trade loses money. No position-sizing trick changes that – the strategy itself must be reworked.

Why do traders use fractional Kelly instead of full Kelly?

Full Kelly only maximises theoretical growth while producing drawdowns of 50 % and more. Half or quarter Kelly sacrifices little growth but reduces fluctuations drastically.

Is the Kelly criterion compatible with prop-firm rules?

Usually only as an upper-bound check: even quarter Kelly typically sits above what a 10 % loss limit allows. The rulebook limits are the binding factor in practice.

Where do I get p and b for the formula?

From your own trading journal: hit rate and the ratio of average win to average loss across a sufficiently large sample – historically at least 100 trades count as a rough lower bound.