Persistence and strength as one close-to-close switch

Editorial framing: this note teaches a daily trend-following streak rule and a two-name momentum-rank as one close-to-close procedure. Persistence, the strength handoff, and abstention are kept in the same switch rather than stacked as separate overlays.

A close-to-close persistence-switch

The persistence-switch is a close-to-close trend-following rule. It enters on the first up session just before the 3:59 close and exits at the same clock on the first down session.

Because the buy is at the close, the signal up session is not captured. The first exit is also booked as a loss. Each cycle therefore donates two days. Net up days equal bias times session count minus twice the switching-rate.

The rule is written so a losing run cannot extend past one consecutive down session. That streak-break is the stated drawdown-control feature: a mechanical refusal of a second consecutive down session.

Donated days and the six-day sketch

A 252-session year can be taught as 42 repeats of a six-day block with bias 0.5, obtained by dividing session count by switching-rate. Other period, bias, and rate triples can recover the same annualized day count.

In that six-day sketch three sessions are flat, so half the year, 126 sessions, is out of the market. Abstention is the idle half of the same switch, not a later cash overlay.

When the switch can match a fully invested path

The persistence-switch matches a fully invested path when switching-rate equals session count times one minus bias, divided by one plus the win-ratio. With bias 0.525 and win-ratio 1 that rate is 59.85. A round ceiling near 63 is treated as the random-persistence boundary.

The persistence-gate admits a series only when its switching-rate sits below that random band near 63 switches per 252 sessions.

Plotted against bias, with a 1 percent session return and a unit win-ratio, the fully invested line steepens about twice as fast as the persistence-switch line. The rate must fall below that boundary before the switch can keep pace.

How win-ratio tilt moves the breakeven

Win-ratio is average up-move size divided by average down-move size. A downward tilt of the win-ratio below 1, already identified as the suppressor of fully invested equity-stock results, also shrinks persistence-switch outcomes computed at a zero tilt.

A 5 percent drop in the win-ratio raises the breakeven rate to 61.4. A 5 percent rise lowers it to 58.4.

Rank-rotation after the gate

Once a series is eligible, rank-rotation is a conjunction that assigns the next session’s return only to the name that is both the stronger print and above a near-zero floor, then adds the two assigned streams. On an eligible switch, the position is routed to the currently stronger name instead of remaining in a single series.

Momentum-rank is that same-session comparison. It treats the stronger print as the momentum leader for the next holding interval.

Daily clocks, ignored costs, and extensions

The two-name illustration was chosen for low switching rates over a 28.7-year window from 1 July 1985 to 6 March 2014. The composite rate path is described as generally below the 63 random threshold.

Trading costs were ignored at a pace of about 120 switches per year. Finer than daily clocks are flagged as cost-vulnerable. The same procedure is described as extensible to more persistent, less correlated names and to funds or currency vehicles.