On the 148-row alternating assessment, lookback change has 36 reversals and 74 turnover units, while the other rules have 37 reversals and 76 units. At three basis points one-way, the proxies are 222 and 228 bp. Changing only that setting to six doubles them to 444 and 456 bp without changing any signal.
Hold everything except the cost coefficient fixed
This case uses engine version 1.0.0 and its constructed alternating fixture, which combines deterministic oscillations around a reference level. The input is not an exchange price series or a sample of actual trading. Its Node reference output was reproduced at fast 10, slow 30 and lag two, first with the chosen one-way cost at three basis points, then at six.
Both settings use the same 180 input rows, 32-row common warmup and 148 assessment rows labelled February 15 through September 8, 2023. The labels are generated weekdays, not an exchange calendar. The two-observation lag governs information availability within that sequence; it does not represent an actual fill delay. Positions remain abstract fixed unit states of -1, zero or +1.
See why occupancy is insufficient
All three methods record 72 positive and 76 negative rows, with no neutral observations. That corresponds to approximately 48.6486% positive and 51.3514% negative occupancy. These shares describe time spent in a label, not money allocated or exposure to a specified instrument. The identical totals do not reveal the order in which the positive and negative states appear.
To see the distinction with a small original example, compare +1, +1, -1, -1 with +1, -1, +1, -1. Both contain two positive and two negative observations. The first has one sign reversal and the second has three. Including entry from zero and final flattening, their turnover totals are four and eight units respectively. Sequence matters even when occupancy matches exactly.
Reconstruct the alternating-path turnover
The verified lookback-change output contains 36 sign reversals. Starting from flat contributes one unit, each direct sign reversal contributes two and flattening the final nonzero state contributes one. Its turnover is therefore 1 + 2 times 36 + 1, or 74 units. The level and crossover rules each have 37 reversals, giving 76 units by the same calculation.
The engine reports 37 changes for lookback change and 38 for each other rule because the changes count includes the initial entry but excludes terminal flattening. Terminal turnover is recorded separately and equals one for all three. Keeping these definitions visible prevents the tempting but incorrect interpretation that every reversal is one unit of activity or that the ending position disappears without an accounting entry.
| Method | Positive / negative rows | Reversals | Turnover including boundaries | Cost proxy at 3 bp |
|---|---|---|---|---|
| Lookback change | 72 / 76 | 36 | 74 | 222 bp |
| Level vs mean | 72 / 76 | 37 | 76 | 228 bp |
| Fast / slow means | 72 / 76 | 37 | 76 | 228 bp |
Apply the declared linear cost formula
The cost calculation is turnover multiplied by the chosen one-way basis-point coefficient. Thus 74 times three equals 222 bp, while 76 times three equals 228 bp. The six-basis-point difference between methods comes from two additional turnover units, exactly the activity associated with one extra full sign reversal. No commission schedule or observed spread is inferred by that multiplication.
The constructed reversal fixture provides a useful fixed-convention comparison: every method there has four turnover units and a 12 bp proxy at the same coefficient. Relative to that activity, the alternating fixture has 18.5 times as much turnover for lookback change and 19 times as much for the other rules. These ratios compare constructed sequences, not their desirability or financial outcomes.
Double the coefficient without changing the signals
Changing only the one-way setting from three to six basis points gives 74 times six, or 444 bp, for lookback change and 76 times six, or 456 bp, for the other methods. The method-to-method gap becomes 12 bp. On the constructed reversal fixture, the same coefficient change moves every proxy from 12 to 24 bp because turnover remains four.
Direct comparison of the two engine outputs confirms identical timelines, including directional states, information dates and calculated means. Occupancy, reversals, turnover and agreement also remain unchanged. This is expected from the code: the cost coefficient enters the summary multiplication, not the directional formulas. The exercise is a sensitivity check of a stipulated linear coefficient, not an empirical estimate of transaction costs.
| Constructed path and method | Turnover | At 3 bp one-way | At 6 bp one-way |
|---|---|---|---|
| Reversal: each method | 4 | 12 bp | 24 bp |
| Alternating: lookback change | 74 | 222 bp | 444 bp |
| Alternating: level and crossover | 76 | 228 bp | 456 bp |
Separate the proxy from execution evidence
CME's discussion of liquidity identifies volume, open interest and bid-offer spread as relevant evidence. None is measured by this constructed sequence. A chosen constant cannot demonstrate that a particular order size would transact at a particular cost. The basis-point-labelled output is tied to abstract unit exposure, not account NAV, and should not be converted into an account charge without additional assumptions.
Real futures activity can also involve changing contract months while keeping the same directional state. CME's expiration and roll explanation describes closing one maturity and establishing another. This case has no contract identities or roll ledger, so its state-change turnover cannot count that activity. It likewise does not model changing position size, order execution or liquidity-dependent impact.
Read the sensitivity result at its proper scale
The 222 and 228 bp figures accumulate over this finite assessment sequence under its boundary conventions. They are not annualized figures, percentages of account NAV, P/L or returns. The assessed states carry fixed unit magnitude rather than volatility-targeted sizing. Initial entry and terminal flattening are included deliberately, making a short isolated sequence comparable only with other sequences using the same convention.
The strongest conclusion is mechanical: state order determines activity, and a linear coefficient scales the resulting cost proxy proportionally. Equal occupancy does not establish equal turnover, while doubling the chosen coefficient supplies no new information about direction. This case helps readers reconcile the reported numbers and recognize omitted implementation evidence without promoting a lower-switching rule into an investment recommendation.
Research checkpoints
- Identical 72-positive and 76-negative occupancy can coexist with different reversal counts.
- Including initial entry and terminal flattening gives 74 or 76 turnover units, not 36 or 37.
- Doubling the chosen one-way coefficient doubles only the cost proxy; it changes no signals and establishes no account-NAV cost.
Source record
Related methods
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Reversals and Whipsaw: What Changing Signals Actually Show
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Published 16 October 2026. Illustrations and reference diagnostics do not establish strategy profitability or execution quality.