PARTIAL · sizing law
Hypothesis
Sizing each trade by a fraction of the Kelly-optimal bet maximizes long-run log-growth without the ruinous variance of full Kelly.
Math — Kelly fraction
Optimal fraction from edge $b$ and win prob $p$:
$$ f^\* = \frac{bp - (1-p)}{b} $$
We deploy a de-rated fraction $\kappa f^\*$ with $\kappa\approx 0.25$–$0.5$.
Method
Apply quarter-to-half Kelly using empirically estimated (not assumed) edge/odds per strategy; compare growth and drawdown vs fixed-fractional.
Results
| Full Kelly | highest growth, brutal DD |
| Quarter–half Kelly | near-max growth, sane DD |
| Sensitivity to edge mis-estimate | high |
Adopted as the sizing discipline, not a signal: fractional Kelly captures most of the growth at a fraction of the variance. Critical caveat — Kelly is brutally sensitive to over-estimated edge, so we always de-rate hard and size off conservative, realized estimates.
Kelly assumes you know your edge exactly. Since you never do, the only safe Kelly is a small fraction of it — over-betting a mis-estimated edge is how good strategies go to zero.