Temperature ladders and similar boards cut a continuous quantity into a dozen bands. Exactly one must be true, so the bands' prices sum to $1 — seemingly the cleanest possible form of set arbitrage. I checked it through two unrelated data paths. Both netted to zero.
Take weather: a city's daily high is cut into a dozen bands (under 20°, 20–22°, 22–24°, and so on). Those bands are mutually exclusive and exhaustive — no two can both be true, and one must be.
So in theory: if they sum to 0.95, buy the whole set, merge, take five cents. No weather forecasting required, no judgement of any kind.
| Reason | Detail |
|---|---|
| Many bands | a dozen quotes, so one of them mispricing is likelier |
| Cold bands are neglected | the extreme temperatures often go unquoted for long stretches |
| Less professional participation | weather has a high retail share |
| Frequent new boards | a fresh set per city per day |
All four are true, which is why the path deserved a serious look. It got two.
| Method | Result | |
|---|---|---|
| Path one | one data source and basis | nets to zero |
| Path two | a completely unrelated data source | nets to zero |
Because a single-source conclusion can die of the source's own problems — missed data, a wrong basis, misaligned timestamps. Check once and conclude "no opportunity" and you cannot distinguish genuinely none from you failed to see it.
Two unrelated paths reaching the same answer rules out the "tooling problem" explanation. It is the same technique I used on the instrument failure: when you suspect the measurement, measure again with something entirely separate.
The same family as complementary-set arbitrage, but worse on ladders:
| Problem | Why worse here |
|---|---|
| Cold bands unbuyable | more bands means more very cold ones — and you must have them all |
| Fees on every leg | a dozen bands means a dozen taker fees |
| Minimum 5 shares × N | the minimum viable trade scales with band count |
| Unpaired is naked | a dozen legs — any one missing and the set does not exist |
Multi-outcome boards allow swapping "NO on one band" for "YES on all the others", which are logically identical. A common hope is that this routes around some of the cost.
It does not. Conversion is a chain action and cannot remove a fee already paid when the legs were built. It changes when the cash arrives — time value, not a discount.
And practically: many toolchains have no conversion entry point. I measured this; the SDK in use offered split, merge and redeem only.
| Rule | Note |
|---|---|
| Doubt a conclusion? Redo it on an independent path | rules out "tooling problem"; two zeros are what counts |
| Judgement-free opportunities: assume already taken | count what remains before building anything |
The ladder rule is real: a dozen bands necessarily sum to $1. But those few cents on paper usually sit precisely in the band you cannot buy — checked twice through unrelated paths, and both netted to zero.