Guide · 6 min read

Li Lu's own trading record implies a 62 percent bet size

The Kelly criterion, run on Li Lu's own 14 disclosed trades, comes out at 62 percent of the portfolio on a single position. The formula is not wrong. It is just answering a narrower question than the one a reader wants answered.

Run Li Lu's disclosed trading record through the Kelly criterion and the formula says the optimal bet size for his next position is 62 percent of the portfolio. That number, kelly_f on Tenachine's own page for Li Lu, is 0.6197. It is not a typo and not a bug. It is what the formula returns when you feed it a 64.3 percent win rate and a payoff ratio, kelly_b on the same page, of 15.42.

The Kelly formula itself is f equals p minus q over b: the win probability, minus the loss probability divided by the payoff ratio between a typical win and a typical loss. Plug in Li Lu's numbers, a win rate of 0.6429 and a payoff ratio of 15.42, and 0.6429 minus 0.3571 divided by 15.42 comes out to 0.6197, the 62 percent figure published on the page. Tenachine's page does not spell out exactly how the payoff ratio is derived from the 14 trades beyond that it is a reward to risk figure, and that is worth naming as a real gap rather than guessing at the mechanics.

A payoff ratio of 15.42 is enormous, and it is why the formula's answer is so aggressive. Li Lu's own record shows a median return on winning trades of 69.78 percent against a median return on losing trades of negative 11.90 percent, a ratio closer to 6 to 1 on the median alone, and the formula's own 15.42 figure is pulled higher still by the tail: his best trade, GOOG, returned 250.36 percent, against a worst trade, SOC, of negative 53.70 percent. A formula built on a win rate and a payoff ratio from 14 trades is a formula built on a small, noisy sample, and 9 winners against 5 losers is not a large enough base to treat any of these ratios as fixed facts about how Li Lu trades.

Why nobody actually bets full Kelly

Full Kelly sizing maximizes the long run geometric growth rate of a bankroll, but only if the win rate and payoff ratio are exactly correct and never change, an assumption that gets weaker the smaller the sample behind the numbers. In practice a full Kelly bet also produces drawdowns that are large even when the underlying edge is real, because the formula is indifferent to how rough the ride gets on the way to the theoretical long run outcome. Half Kelly, betting half of what the formula recommends, is the number that actually shows up in practice among people who use this framework at all, trading a meaningful share of the theoretical growth rate for a much shallower ride. Applied to Li Lu's own number, that would be roughly 31 percent of the portfolio in one position rather than 62 percent, and even that is a large single bet by most standards.

Tenachine's guide on sizing a position from a stop walks through a completely different sizing approach on a completely different kind of strategy: risk exactly 1 percent of an account on a single trade, sized off the distance to a stop loss, which produced a position worth roughly 19 percent of the account in that guide's worked example. Kelly sizing and stop-based sizing are answering different questions. Stop-based sizing asks how large a position can be while keeping a single loss small and survivable. Kelly sizing asks how large a position should be to maximize long run growth given a win rate and a payoff ratio that are assumed to hold. Li Lu's 9 winning and 5 losing trades are nowhere near enough to treat that second assumption as settled.

The 62 percent figure is a real output of a real formula applied to real, published numbers. It is not a recommendation, and reading it as one skips past the question that actually matters: whether 14 trades are enough to trust the win rate and payoff ratio that produced it. Past performance does not predict future results, and neither does a formula's output when the inputs behind it come from a sample this small.