The Hump
Kelly tells you how much to bet when you know your edge. I published my edge for every brief on this site: a bull, a base and a bear case, each with a target and a probability. Feed those odds to the formula and it puts the whole book in one stock. My book holds a fraction of that. The curve below shows which bear probability explains the difference.
What Kelly
says
The Kelly criterion picks the fraction of your capital that maximizes long-run growth. Bet a fraction f of the book on an outcome with return r and your wealth multiplies by 1 + f · r. Average the logarithm of that over every outcome and you get the growth rate: g(f) = Σ p · ln(1 + f · r). The best bet is the top of that curve.
Below the top, you leave growth on the table. Past it, you take all of the pain and none of the growth; at twice the right size the expected growth is zero. That shape is the hump. It only exists when the odds include a loss big enough to hurt. If the bear case is mild, the curve never bends and the formula says: all in.
The hump
Pick a brief. The three cases load with their published targets and odds; the price is live. Then drag the bear probability and watch the curve get a top, and where that top lands against the mandate cap and the real Desk weight.
Reverse Kelly
Run the formula backwards. Type a position size and read the bear probability it implies, holding the published targets and the bull-to-base ratio fixed. This is not advice; it is a mirror. The size you hold is a probability you never wrote down.
Four traps
The odds are an opinion
Kelly assumes you know the probabilities. A published bull, base and bear case is a considered opinion, not a measurement, and the formula amplifies every error in it. A wider band of uncertainty is a reason to size down, which is why fractional Kelly exists.
One period, one bet
This page sizes a single position over one horizon. It ignores the rest of the book and the correlation between names. Nvidia sits in an AI demand chain the mandate caps at 50 percent of the portfolio; no single-name Kelly can see that. Three scenarios cannot hold a tail; that is what the fourth row above is for.
Log utility tolerates pain
Full Kelly maximizes growth and accepts drawdowns most people cannot sit through. Half Kelly gives up a quarter of the growth for half the variance. The knife edge on this page, a few points of bear probability between all in and nothing, is the same warning.
The unconstrained number is a warning
When the curve never bends, the formula asks for leverage. Treat that number as a diagnosis of the inputs, never as a target. This page caps every answer at 100 percent of the book.
Under the hood
Sources: the published brief · The Desk · The Slope (same nine names).
ODDS AND TARGETS FROM THE PUBLISHED BRIEFS. PRICE LIVE FROM YAHOO VIA /API/QUOTES. ONE-PERIOD DISCRETE KELLY, LONG-ONLY, WITH THE UNCONSTRAINED VALUE SHOWN AS A DIAGNOSTIC. MANDATE AND DESK WEIGHTS FROM THE PUBLISHED PORTFOLIO. TAIL SCENARIO: A FOURTH OUTCOME, ODDS SCALED PRO RATA FROM THE PUBLISHED THREE. RESEARCH NOTES, NOT INVESTMENT ADVICE.