Kelly criterion
ケリー基準。勝率と損益比に基づき、長期の資金成長を最速にするために投じるべき資本の割合を求める公式。フル・ケリーは変動が激しいため、多くのトレーダーはその一部だけを賭ける。
The Kelly criterion is a position-sizing formula that tells you what fraction of your capital to risk on a bet to maximise long-run compound growth. It weighs two things: your edge — how often you win and how much you make versus lose — and the odds. In its simplest form the fraction is your edge divided by the odds, so a bigger edge or better payoff justifies a larger bet, while a thin edge calls for a small one. Bet more than Kelly and growth actually slows while ruin risk climbs; bet less and you grow steadily but slower.
In options this is a discipline, not a plug-in number. To use it you need honest inputs — a realistic win rate and an average win-to-loss ratio from your own history — and defined-risk trades where the maximum loss is knowable. A trade with a 70% probability of profit that risks 200 dollars to make 100 has a positive but modest Kelly fraction, telling you to commit only a slice of the account, not to load up because the win rate looks high.
The common mistake is using full Kelly with over-optimistic inputs. Full Kelly is brutally volatile and a slightly overstated edge tips you into over-betting and deep drawdowns, so almost everyone trades half-Kelly or quarter-Kelly, which keeps most of the growth for a fraction of the swings. And it only makes sense on edges you can actually estimate — feed it a fantasy win rate and it will happily size you into ruin.
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