Fractional Kelly

Full Kelly is the theoretically growth-maximizing fraction if you know the true probabilities and outcomes exactly and face this one bet in isolation. You never do. So no serious investor bets full Kelly; they bet a fraction of it (half-Kelly, quarter-Kelly, or less) and they are right to, for four compounding reasons:

1. Estimation error, punished asymmetrically. Your p is a judgment, not a measured frequency, and the overbetting cliff means the cost of overestimating your edge dwarfs the cost of underestimating it. Betting fractional Kelly is buying insurance against your own overconfidence, and the shape of the growth curve makes that insurance nearly free: half-Kelly sacrifices only a quarter of the growth. When in doubt, you are overestimating your edge; fractionalize.
2. The drawdowns are unbearable, and unbearable is dangerous. A full-Kelly bettor routinely watches capital halve in an interim drawdown. Almost no human holds through that calmly. The real danger is that the drawdown may force a sale (a margin call, a redemption, a loss of nerve at the bottom), which converts the mathematical optimum into a realized catastrophe. Half-Kelly's drawdowns are roughly half as deep and vastly more survivable, emotionally and structurally.
3. Real positions are correlated (hidden correlation). Kelly for a single bet ignores that your positions share factors. Summing full-Kelly sizes across correlated ideas massively over-stakes the portfolio's true independent risk: you think you placed ten bets and really placed one large one. Fractionalizing at the single-position level is a crude but effective first correction for the correlation you will formalize in hidden correlation.
4. The inputs may be Knightian, not merely noisy (sizing under uncertainty). Sometimes you cannot even estimate p reliably because the situation is genuinely uncertain (a first-of-its-kind business, a new regulatory regime). Then the "fraction" must shrink further still, to quarter-Kelly or a token size, because Kelly assumes you know the distribution, and here you don't.

How do you choose the fraction?

How to choose the fraction, practically. Treat the Kelly fraction c as a dial set by your confidence in the inputs, not by how exciting the idea is:

• Half-Kelly (c ≈ 0.5) for your best, most analyzable ideas: a predictable business, a well-understood downside, inputs you would defend under cross-examination.
• Quarter-Kelly (c ≈ 0.25) or less for ideas where the edge is real but the inputs are shakier, like a cyclical whose mid-cycle earnings you're estimating, or a business at the edge of your circle of competence.
• A token size or pass where the outcome distribution itself is a guess (genuine uncertainty), or where the downside floor d cannot be trusted.

And then, always, the fractional-Kelly number is still only a ceiling proposal, to be run through the hard caps of the anti-ruin overlay. Raw Kelly on a favorable, capped-downside investment routinely spits out 150%, 250%, even more (you will compute exactly these); it is a ranking and ceiling signal, telling you which ideas the math wants bigger, never a literal instruction to bet the farm. The workflow is: raw Kelly → fractional Kelly (dial for confidence) → hard cap (for survival) → correlation/factor check. In practice the cap almost always binds before the Kelly number does, which is exactly as it should be: the math tells you the direction and relative size; the caps keep you alive.