Sources

The tiles above show, per source, which chapter it supports; the work by Gayed and Bilello is where the argument comes from.

What the sources support. The 2026 revision by Gayed and Bilello only tests window lengths up to 200 days; on longer ones it says nothing. It therefore does not support this page's zone, which comes from the series below. Philosophical Economics supports the main weakness of the pure price filter, the false signals, not the claim that its economic secondary filter is suitable for leveraged holdings. The posts by ZahlGraf, Finanztyp and ChemicalStats are forum posts, not peer-reviewed literature, and their assumptions are stated in each post.

One check stands out among them: in part 8 of ZahlGraf's series the window length is chosen on an early stretch of the price history and then checked on a stretch that was not used for the choice. The check runs by eye on the pictures: the cloud of points shifts, the annual return declines. Gayed's revision has a follow-up for the years since 2021, but only for the one window and in hindsight, without a separate test stretch. Other evaluations from the scene work with rolling windows and with paths reassembled from stretches of the history. The counter-voice belongs next to it; it stands with its evidence in the chapter Criticism.

That part of the benefit is available without any timing at all, by leveraging only part of the holding, has been recomputed publicly, among others on the Notgroschen channel. The numbers from it are not on this page; the direction is documented.

What no source supports. None of the works named shows that a particular window length or buffer will work in the future. They all compute on the same market history, which lies for large parts in an environment of falling interest rates; the ones read off the one path history happened to take, the others work with rolling windows and with paths reassembled from stretches of it. One exception on the interest rates is ZahlGraf's series: it starts in 1943 and therefore also contains a long phase of rising rates.

Open questions. How the filter behaves through a longer environment of rising rates is unclear. So is how much asymmetric buffers help once they are not chosen against the past. And the version on the MSCI ACWI has no public derivation of its own window length: it is an analogy to the versions on the S&P 500 and the MSCI USA.

What LETF.io shows and what it does not. Our numbers come from two sources, and both are labelled at the chart. The backtest computes on the long index history and reproduces the time before a product's launch with a leverage model, including financing costs and fees; it shows derived quantities only, condensed to weekly. The chart in the chapter Rule shows the recent years on the price series itself, with no model in between.

What we do not show are the index providers' raw levels, for which we have no licence, and no probabilities: the share of periods in which the rule was ahead of holding we name only alongside the whole distribution, because overlapping periods are no independent samples. Nor do we offer a parameter search: presets with a reason instead of an optimisation hunt.