How Much to Bet When You Are Probably Wrong
A view has two parts. The first is the claim: this asset is mispriced, this outcome is more likely than the price implies. The second is the size: how much of the account stands behind the claim. People spend almost all of their attention on the first part and almost none on the second, which is backwards. The claim is where you are most likely to be wrong. The size is the only part of the position you fully control.
This is the gap again, in a narrower form. You can hold a belief for free. The belief becomes a position only when you put weight behind it, and the weight is where being wrong actually costs you. A forecast that is right about direction and wrong about size loses money. A forecast that is wrong about direction and small enough barely registers. Sizing is the part of the work that survives contact with the outcome.
There is a clean answer to how much to bet, and it has been around since 1956. The Kelly criterion asks for two numbers: your probability of being right, and what you win per unit risked when you are. It returns the fraction of the account that maximizes the long-run growth rate. Bet more than that and you grow more slowly, not faster, because losses compound against you. Bet a lot more and you go broke with probability one, even with a real edge. The math does not care how good the trade was; it cares how big it was relative to what you can lose.
Move the inputs and watch the stake. The thing worth noticing is how sensitive the full-Kelly number is to the win probability. You do not know your true edge. You have an estimate of it, and the estimate is itself uncertain. If you think you win 55 percent of the time and you actually win 52, full Kelly has you betting far too much, and the penalty for betting too much is much worse than the penalty for betting too little. The growth curve is roughly flat just below the optimum and falls off a cliff just above it. Asymmetry like that should decide the bet.
Which is why almost nobody who uses this seriously bets full Kelly. They bet a fraction of it. Half Kelly gives up only about a quarter of the growth rate while cutting the chance of a deep drawdown by a lot, and the drawdown is the thing that ends careers, not the slightly slower compounding. The fraction is not timidity. It is the correct response to the fact that the inputs are estimates and the cost of overbetting is convex. You are sizing to your uncertainty about your edge, not to the edge itself.
[McKinley: insert the specific trade or stretch here where you sized to full conviction, took the drawdown, and rebuilt the position at a fraction of the size. Name the instrument and the rough magnitude.]
There is a second discount most people skip. Kelly assumes you know your probability. You do not, so the honest move is to size as if your edge were smaller than your best guess, and then take a fraction of that. Two haircuts: one for estimation error, one for the convex cost of being wrong on size. After both, the number that comes out is small. It is supposed to be small. A position you can hold through a drawdown without flinching is a position you can hold long enough for the edge to show up. A position that forces you out at the bottom was too big regardless of whether the original view was right.
[McKinley: insert the running analogy here if it holds up. Something like training volume: the weeks that wreck you are the ones where you sized the session to how you felt that morning instead of to what you could absorb and repeat. Keep it concrete.]
None of this tells you what to trade. That is the part you cannot control and should hold loosely. Sizing is the part you can control completely, and it is where the discipline actually lives. Decide how wrong you might be, assume you are more wrong than that, and let the size carry the humility the forecast cannot.