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.
Backtest on historical data: shows what the rule would have done, not what it will do. Not investment advice.
The backtest puts the rule against holding, going back as far as the index data reach; for the time before a product was launched, a reconstructed product price stands behind it.
One curve is the rule, the other holding without the rule; both start at the same value.
The value axis is on a log scale so that equal percentage steps look equally large, and the markers sit on the signal days.
On the Nasdaq basis this showed a property of leverage: it enlarged daily gains and losses, and the deep, multi-year slump of 2000 to 2002 threw a held leveraged product back to a small fraction of its value, the more so the higher the leverage. Later rises lifted both curves by the same percentage as long as the rule was in the market; the gap the rule had gained in that slump therefore largely remained on the log axis, and later slumps could widen it again.
What the backtest includes are two assumptions:
- Interest on the time out of the market is included by default: the time without a position earns the money market rate of the product's currency. Without it the rule looks worse than it was.
- Tax under the simplified German model is not included by default, because tax depends on your situation and not on the rule.
With the tax included, the page computes a deliberate simplification: German flat-rate investment income tax plus solidarity surcharge, 26.375 percent in total, on the realised gains of every exit, the partial exemption of 30 percent for funds with a high equity ratio, offsetting of losses within the same series, advance lump sum (Vorabpauschale), interest on the fallback side taxed in full, no annual allowance, and the position still open at the end left untaxed.
What applies to you is in the chapter Implementation and Taxes further down.
Community backtests
Someone else's backtest is usable when it states where its data comes from, how it computes and which costs and taxes are included. The numbers of the following analyses are there to be read, not here.
Gayed and Bilello (2016) are the origin of the argument. The Dow Award submission tests the filter on a price history of the US market reaching back into the 1920s and leaves the costs out: no financing cost of leverage, no fees, no taxes, nominal terms. It does not meet the third criterion. In September 2026 Gayed revised the paper. The main run now starts in 1988 and includes financing costs, a product fee and trading costs; taxes and inflation are still missing. The rule's lead shrinks as a result, and the paper itself rates it as not statistically established. What remains of it is in the chapter Criticism.
ZahlGraf, part 8 (2022) tests the rule on a price history from 1943, and does so in two stages: the window length is chosen on the years up to 1985 and then tested on the years from 1986 that were not used for the choice. The financing cost of leverage is modelled, and part 10 handles tax separately. The limit lies with the constructed series: the products did not exist back then. Part 8, plus part 9 for the combination with HFEA and part 10 for tax.
ChemicalStats, Vectis Mundi (2025) tests window length across broad indices rather than the US market alone, and the result is a zone rather than a value. German tax and the advance lump sum are included, which keeps this analysis closer to reality for a German account than the English-language ones. The limit lies in the dependence on index choice, which the second part sets out. Part I, part II.
Notgroschen (2025 to 2026) tests the rule on the leveraged MSCI World against holding, and in a second video an aggressive version against a moderate one. The procedure is what stands out: the result comes not from the one path history happened to take, but from many reassembled from stretches of it. Which costs are included is not documented, and that is where the limit lies: what exactly was computed is in the video and not in an appendix. Window lengths on the World, aggressive against moderate.
A single period says little, which is what the distribution over many is for:
The distribution shows the annual return across rolling periods of ten, twenty or thirty years, once for the rule and once for holding the same product, in your version.
What the backtest can and cannot do. It describes what the rule would have done, not what it will do: the past took exactly one course, and we know it.
Overlapping windows are not independent observations. Two ten-year windows a month apart share roughly ninety-nine percent of their days; counting them as if they were samples makes the spread look smaller than it is. For that reason we name the share of periods in which the rule was ahead of holding only alongside the whole distribution; it describes what the rule would have done in the past, and it is not a probability for a future period.
What follows from that. The widely used parameters were selected against history, and part of their strong showing in backtests is the selection itself. On top of that, the long history sits largely in a period of falling interest rates; that a rule works the same way in a different rate environment is an assumption, not a result.
Looking back over several decades takes the reconstruction on the index:
Here the same rule runs on the long history of the index. The curve goes back to 1934 in US dollars and to 1971 in euros (Deutsche Mark before 1999). Before 1957 the index ran as the S&P 90, before 1988 the dividends are estimated. The curves are reconstructed with assumed costs; they are not real fund prices and they do not depend on the product you picked. One curve shows the rule, the other holding; both start at the same value on the first day with a signal. The axis is logarithmic, so equal percentage moves look equally tall, early or late. You can switch the leverage; the rule stays the same.
In the Working Paper Market History, Rebuilt: A Reproducible Synthetic U.S. Total-Return Dataset for Leverage and Duration Research, version 0.8 dated 24 September 2026, ChemicalStats examines US equities over 1926 to 2026 using daily reset reconstructions at 2x and 3x leverage. In this backtest, 2x stayed ahead of 1x even with substantially higher financing costs; at 3x, the edge disappeared with small cost markups, leaving the direction relative to 1x unresolved. The edge of 2x rests mainly on the years 1929 to 1932. The paper tests neither the SMA rule nor volatility targeting. This is a backtest of the past; it says nothing about future returns and does not recommend a leverage level.