Glossary term
Signal vs gate
Definition
A constructive lean can still produce zero fills if a size rule refuses. The clash is the lesson. A failed cap is not a stock grade.
How it works
A signal, in this course, is a lean from a voting rule. A gate is a rule about process. They answer different questions: the lean asks which way the panel tilted on a name, and the gate asks whether the process is permitted to act at all. When they disagree, the process is arranged so that the refusing instrument wins.
Cross three lean states with two gate states and five of six combinations produce no fill. Only a constructive lean with every gate quiet permits anything, and even that is not an instruction. Many of the wrong sentences students write come from merging the two instruments into a third one that does not exist, such as hold or confirmation.
Worked example
A scan leans constructive on five names, and the sizing formula wants a larger line in each. Take a hypothetical win probability of 0.55 and net odds of 1.6: f* = 0.55 − 0.45 / 1.6 = 0.55 − 0.28125 = 26.9%, quarter Kelly is 6.7%.
A 2% position cap refuses all five. Even the quarter-Kelly figure is about 6.7% ÷ 2% = 3.4 times the cap. The day's record is one line: net process fills, zero. Weaken the assumed edge to a win rate of 52% at odds of 1.5 and f* is still 0.52 − 0.48 / 1.5 = 20.0%; quarter Kelly is 5.0%, which the cap still refuses by a factor of 2.5. The cap, not the formula, set the size.
Hypothetical, for education only. Not a recommendation and not a prediction.
Common mistake
The mistake is treating a refusal as a stock grade, or writing the day up as though it almost produced a fill. A failed cap says nothing about whether a name is good; the cap never looked. Another version of the mistake is trusting the formula because it sits on a dashboard. Watching a boring rule outrank it repeatedly is what teaches suspicion of a number computed from invented assumptions.