SMA stands for simple moving average.
Read from the start: chapter 1 The RuleLeveraged ETFs can lose a large part of their value in a short time.
The rule is older than its current popularity. What made it popular is a chain of public posts. It shows which number is in circulation for which reason.
Michael A. Gayed and Charles Bilello publish Leverage for the Long Run. The work joins two things that were discussed separately before: leverage, and where the market stands relative to its long average. Their argument is not that an average knows the future, but that calm and turbulent phases look different and that leverage is especially expensive in turbulent ones. The full text stands as the Dow Award submission at the CMT Association.
In the same year the author behind Philosophical Economics describes in Growth and Trend the main weakness of the pure price filter: the false signals in sideways markets. His proposal is a second filter built from economic data, which takes the signal seriously only when the economy turns as well. The piece remains standard reading on false signals today.
In the English-speaking forums the paper's backtest is taken apart. Two objections come up again and again: the backtest is missing the internal cost of leverage and alongside it fees and taxes; and it computes on gross rather than net total return, which lifts the curve further. None of these refutes the idea, but all three move the numbers down. The 2026 revision takes up the first two, see the station below.
The German-language series ZahlGrafs Exzellente Abenteuer recomputes the rule with European products and German tax rules. ZahlGraf is the pseudonym of a member of the German-language Reddit forum r/mauerstrassenwetten, and the series is a set of public posts there, not the work of a research institute. What it added to the debate about the rule are the window lengths that later discussions start from. Part 8 is where the widely used window lengths come from: 200 trading days on the S&P 500, 220 on the Nasdaq-100. ZahlGraf computed in calendar days and converted to trading days; the 200 come from the run with threefold leverage, for twofold leverage on the S&P 500 the value was slightly higher. More important than the numbers is the procedure: the length is chosen on an early stretch of the price history and then tested 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. Alongside it, evaluations from the scene work with rolling windows and with paths reassembled from stretches of the history.
ChemicalStats picks the question up again in Eine kleine Reise in gehebelte Welten, Vectis Mundi (Teil I), with the focus on broad indices rather than the US market alone. The result is not a single number but a zone of roughly 200 to 300 trading days within which results resemble each other. For the MSCI World it comes out at 255 trading days, the value the preset on this page carries. Part II clarifies how the window is counted and which series the signal is computed on. ChemicalStats, too, is the pseudonym of a member of the same forum writing in German, and both parts are public posts that anyone can read, not a study from a research institute. What they add to the discussion is that the window question is no longer answered on the US market alone but checked across broad indices.
The YouTube channel Notgroschen recomputes the rule for a German-speaking audience, with European products and in euro. Two of its posts belong to this page. One sets trend following on the leveraged MSCI World against holding and finds no single right value there either, but a zone of usable window lengths. The other compares an aggressive version with a moderate one and reads the result not off the one path history happened to take, but off many paths reassembled from stretches of it.
The direction matches this page: part of the benefit is available without any timing at all, by leveraging only part of the holding. No numbers from the videos appear here; the window lengths on this page come from the series above.
Ten years after the submission Gayed publishes a revised version, this time alone. It runs the main test from 1988 instead of 1928, with financing costs, a product fee and trading costs, and adds a follow-up for the years since publication. Three things change compared to 2016. The rule's lead gets smaller, and the paper itself rates it as not statistically established. The argument about winning streaks above the average is withdrawn; the rule now rests solely on the lower volatility above the average. And the window lengths it runs as a complete grid with costs and leverage; the 2016 version already compared several usual lengths between 10 and 200 days. Among the lengths tested up to 200 days the shorter ones fall off markedly; on lengths beyond 200 days the paper says nothing. The numbers are in the paper, not here.