Half-Kelly: Why Optimal Position Sizing Is Too Aggressive

The Kelly Criterion answers a question exactly. Given an edge, what fraction of your capital maximises long-run growth?

For a system winning forty percent of the time with 2R winners, the answer is ten percent of the account per trade.

Nobody should trade it. Including, and this is the interesting part, the people who derived it.

What full Kelly actually feels like

Run the optimal fraction for five hundred trades, thirty thousand times.

The optimal fraction produces a median maximum drawdown of eighty-nine percent. Not a tail event. The median. Half of all Kelly bettors experience something worse.

The mathematics is not wrong. It is answering the question it was asked, which was about growth, and it was never asked about whether a human being can sit through an eighty-nine percent drawdown without closing the account, changing the system, or being closed by somebody else.

The asymmetry that decides everything

Look at the table again, but read it as a curve. Growth rises to a peak at Kelly and falls away on either side. Symmetrically.

Half Kelly keeps 75.7% of the growth. One-and-a-half times Kelly keeps 76.5%. Practically identical. The growth curve does not care which side of the peak you stand on.

The drawdown curve cares enormously.

Identical reward. One of them costs you sixty-one percent of your account at the worst moment. The other costs you ninety-eight.

Underbetting is nearly free. Overbetting is nearly fatal. And there is no symmetry anywhere in the consequences, only in the arithmetic that produced them.

Why you will overbet, specifically

Kelly requires your win rate. You do not have your win rate. You have an estimate of it, computed from a sample of trades that is smaller than you think, taken in conditions that have since changed.

Suppose you believe you win forty-five percent of the time. You actually win forty.

Read that once more. A five-point overestimate of your win rate destroys half your growth at full Kelly. The same five-point error costs you one and a half percent at half Kelly.

Half Kelly is not a timid version of Kelly. It is Kelly, made robust to the fact that you do not know your own edge. And you do not. Nobody does. The edge is estimated from a finite sample, in a market that is not stationary, by a person with an interest in the answer.

Three more reasons the number is even lower than half

Your edge decays. Kelly assumes the probabilities are fixed. Yours are not. Every estimate you feed it is a description of a market that no longer exists, and the direction of the error is not random: strategies are adopted, edges crowd, and win rates fall.

Your trades are not independent. Kelly assumes sequential, uncorrelated bets. Three correlated positions sized at half Kelly each are one position at 1.5× Kelly, and the drawdown column applies.

Ruin is absorbing. Kelly maximises the growth of a bettor who is permitted to reach any equity, however low, and continue. Prop firms are not. Margin clerks are not. Spouses are not. If a barrier exists anywhere above zero, the optimal fraction is lower than Kelly, and the barrier is always closer than you think.

So where does one percent come from?

Here is the reconciliation between this article and every risk lesson you have ever read.

The Kelly fraction for a 40% / 2R system is ten percent. Half Kelly is five. And the universally recommended figure is one, which is a tenth of Kelly.

That is not conservatism for its own sake. It is what falls out once you account for correlation, non-stationarity, estimation error, and the absorbing barriers that populate a real trading life. The one percent rule is not an arbitrary tradition. It is roughly quarter-Kelly on a realistic edge, discounted again for the fact that you are usually holding more than one position.

Which means the one-percent trader is not being timid. He has, without doing the arithmetic, arrived at approximately the right answer.

What to do

Compute your Kelly fraction. (p·b − q) ÷ b, from your own journal, in R. If you cannot fill in p and b, that is the finding, and it is upstream of this article.

Halve it. Then halve it again if you hold correlated positions.

Recompute quarterly, and treat every increase in your estimated win rate with suspicion. A rising win rate is exactly what a favourable run of variance looks like from the inside, and it is precisely when Kelly will tell you to bet more.

Never size up because a number told you to. The number is a ceiling. It was derived under assumptions you violate every day, and its errors run entirely in one direction.