How much to put on one market

Suppose you are genuinely good at this and your estimates beat the market by a few points on average. You can still end up with nothing, because a run of losses is not merely possible but statistically expected, and a position large enough to be wiped out by that run ends the exercise regardless of how good the estimates were.

That is the whole subject in one sentence: the size that maximises your expected return over one trade is not the size that maximises what you actually end up with over many. Compounding punishes large drawdowns asymmetrically - losing half requires doubling to recover.

The Kelly criterion answers the question mathematically: given your estimated probability and the price on offer, what fraction of your bankroll maximises the long-run growth rate? For a binary contract, the answer has a compact form - the size scales with your edge and shrinks as the price gets more expensive.

A worked example makes it concrete. If a contract trades at 50 cents and you believe the true probability is 60 per cent, full Kelly suggests staking 20 per cent of your bankroll. That number surprises most people, and it should: it is enormous, and it is the mathematically optimal answer to a question nobody is actually asking.

The reason it is enormous is that the formula assumes your probability estimate is exactly right. It has no term for the possibility that you are wrong about being right, which in practice is the dominant risk.

Because the estimate is uncertain, and Kelly is brutally sensitive to that. Overestimating your edge causes you to overbet by more than proportionally, and betting above full Kelly reduces long-run growth while increasing volatility - the worst combination available.

The standard response is to use a fixed fraction: a quarter or a half of what the formula says. Half Kelly gives up roughly a quarter of the theoretical growth rate while cutting volatility substantially, which is a trade almost everyone should take. A quarter Kelly is more conservative still and is a reasonable default for anyone who has not measured their own calibration.

This is not timidity. It is an adjustment for the one input the formula cannot supply: how confident you should be in your own confidence.

Sizing formulas treat positions as independent. Real books are not. Five contracts that all depend on the same election, the same central bank decision or the same conflict are one position wearing five labels, and sizing each at a quarter Kelly produces a total exposure far above what any of them individually justified.

This is the most common real-world sizing failure and it is invisible if you look at positions one at a time. The library entries repeatedly flag it for exactly this reason - the four Iran contract families, the two obesity-drug questions, the leadership ladder on one person.

The practical fix is to size the theme rather than the contract. Decide what fraction of the bankroll a single underlying event may account for, then divide that across however many contracts express it.

Every sizing calculation should use the price you can actually get, including the spread, and the edge should be net of fees. A five-point edge against a six-point spread is not a small position - it is no position, and running it through a formula will produce a confident answer to the wrong question.

Similarly, capital committed for a long time has an opportunity cost. A contract resolving in two years at a modest edge may be worse than sitting in cash, and sizing formulas say nothing about this because they have no clock in them.