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Fractional Kellythe optimal size, and why nobody trades it

Evidence: ModerateProfessionalRisk · Optimal sizing

Kelly's 1956 result gives the position size that maximises the long-run growth rate of an account, given the odds. It is a real theorem and the answer is exact.

It is also, applied literally, close to unusable — because the formula assumes you know your edge, and you do not. Overestimate the edge and Kelly does not merely underperform; it destroys the account, which is the opposite of how most sizing errors behave.

So the practical version is a fraction of it: a quarter or a half. That keeps most of the growth and removes most of the catastrophe, and it is the only form of this rule worth putting near real money.

This is a sizing rule, not a trade. It sits on top of whatever entries you run, and its effect is on the shape of the equity curve rather than on whether any individual trade wins.

Applies to
Strategies with a long, stable record — not new ones
Timeframe
Any, but the estimate needs hundreds of trades
The formula
f = W − (1 − W) ÷ R, where W is the win rate and R the average win divided by the average loss
Typical setting
A quarter to a half of the computed f, capped by your fixed-fractional limit
Tools
Your own realised win rate and win/loss ratio, from a sample large enough to mean something

Valid setup

RK-03 · FRACTIONAL KELLY — ACCOUNT EQUITY quarter-Kelly against full Kelly on the same trades — the growth rate is similar and the drawdown is not EQUITY 84.7 90.4 96.1 101.8 107.4 113.1 118.8 BOTH VERSIONS LOOK FINE HERE THE SAME LOSING RUN AT FOUR TIMES THE SIZE IS WHERE FULL KELLY ENDS ACCOUNTS ONLY THE SURVIVOR GETS THIS PART 10-period mean of the quarter-Kelly curve starting balance quarter-Kelly trough where the same run takes full Kelly 1 2 3 100.0 97.0 88.0 ① f computed from REALISED results, not a backtest ② A quarter of it — the rest is insurance against being wrong ③ Capped by the fixed-fractional limit regardless ④ Growth rate barely differs at a quarter ⑤ Drawdown differs enormously ⑥ Recompute quarterly — decaying edges show up here first

Exact rules

When it applies

  • Compute f from realised results, never from a backtest's. The gap between the two is exactly the thing that makes full Kelly dangerous.
  • Use a quarter of f to start. Half is defensible for a strategy with years of live record behind it.
  • Cap the result at your fixed-fractional limit regardless of what the formula says. If Kelly suggests 8% per trade, the answer is not 8%, it is that your estimate is wrong.
  • Recompute quarterly, on a rolling window. An edge that has decayed will show up here before it shows up in the equity curve.

The risk cap

  • The stop is unchanged — Kelly sizes the position, it does not place the level.
  • A negative f means the strategy has no edge at the sizes you are trading. The correct response is to stop, not to reduce.
  • Never apply Kelly per trade to a portfolio of correlated positions. The formula assumes independent bets and correlated ones compound in the way it warns about.

Sizing and review

  • Track the gap between computed f and what you are actually risking. That gap is your margin for being wrong about yourself.
  • Full Kelly produces drawdowns that almost nobody can sit through — the theory is about growth rate, not comfort, and the two are not the same objective.
  • If the computed f rises sharply after a good month, that is estimation noise, not a discovery. This is where the quarterly rolling window earns its place.

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Trading carries risk and most retail accounts lose money. Nothing on this page is financial advice or a recommendation to trade. The chart is an illustration of the rules on constructed candles — it is not a record of a trade and not a backtest.