⏱️ Reading time: approx. 15–25 minutes
Hello everyone,
Up until now, I’ve mostly been a quiet reader on getquin. Behind the scenes, however, I’ve been exploring the topic of momentum strategies for quite some time. Over the past few weeks and months, I’ve been conducting relatively intensive backtests on leveraged GTAA and SpyTips using AI (Claude Opus 4.8 and 5.5). My price data—and thus the backtest period—covers the years 1987 to 2026 (Bitcoin data starting in 2014). I’ve also been regularly @Epi .
Due to the length of this particular post, I’m splitting it into three parts:
- Part 1 (this post): my momentum strategy, levGTAA
- Part 2: a comparison of implementations—wikifolio vs. personal portfolio
- Part 3: levTipsRegime, my slightly modified SpyTips strategy
First off: Nearly all of the following tests were conducted using AI. This is not investment or financial advice, nor is it a recommendation to buy or sell securities or financial products. AI can make mistakes. Do your own research! :)
Likewise, much of the text below was pre-written by the AI chatbot I most recently used to run the backtests. However, I have thoroughly proofread, edited, and expanded upon the text. Let’s get started!
📐 MY APPROACH
Data source: Daily prices from 1987 to 2026. Calculations are based on investable returns (for ETFs starting from their inception; prior to that, older indices/funds, calibrated to the ETF). For leveraged products, financing costs, product costs, and spreads are included. Signals are always generated based on the closing price; trades are executed only afterward—so there’s no attempt to predict the future.
Initial finding: When you trade during the month makes a big difference. In the final model, the return ranges from 24.2% to 30.4% per annum, depending on the trading day; the last day of the month ranks among the best days at 30.0% (3rd out of 21), while the average across all days is 28.1%. Anyone who tests only the last day of the month therefore overestimates the expected return by about 2 percentage points. That’s why I evaluate each variant as an average across all 21 possible trading days of a month. Although trading in the wikifolio still takes place at the turn of the month, the parameters were designed for the average of all days, not for the “lucky day.”
The Robustness Score
I tested a large number of asset baskets, parameter variations, and additional methods (e.g., dynamic parameters). To compare the variations fairly, I developed a robustness score. Of course, this does not guarantee future performance. However, the score assesses how stable past performance was and how large a portion of it was due to chance. It consists of three components:
1. MC5 (Monte Carlo, parameter robustness): Daily returns are randomly reassembled into monthly blocks. This generates 800 alternative scenarios that could have occurred. The Sortino ratio is measured in the pessimistic case (5th percentile). In the basket search, this was calculated not only for the selected parameters but also in parallel for several parameter variants (for the momentum strategy, e.g., SMA 100, 120, … 200 instead of 150; for other strategy types, a different ranking metric was also used), and the results were then averaged. If performance remains stable when the parameters are adjusted, the score increases.
2. Minimax5 (worst phase): The time period is divided into 5 equally long segments. The Sortino ratio is measured in the worst segment, specifically for the worst parameter variant (Worst of Worst). A strategy that performs well in only one of the five phases fails this test.
3. Risk: the maximum drawdown (score version “z-dd”) or the total Sortino (score version “z-Sor”).
Each component is compared against a large benchmark pool of all tested basket/strategy combinations (robust z-value based on median and standard deviation), and then the variants are averaged. z = 0 means “as good as the typical combination”; the higher the value, the more robust the strategy.
In addition, I examined: Minimax3 (the same with 3 segments), Worst Year, the longest drawdown period, separate halves and market phases, turnover, and the probability of experiencing a drawdown of more than 50% or 75% within 10 years (P50/P75; simulated from 2,000 10-year sequences randomly assembled from real annual blocks).
Overfitting Tests (brief explanation)
- PBO / CSCV (Bailey & López de Prado): The historical data is divided into 10 blocks and split into all possible training and test halves. The metric measures how often the top-performing strategy from the training half falls below the median in the test half. For context, based on my control simulation: By pure chance, the average value is 42%, but it varies widely (10–90%); only a very significant advantage (approx. +20% p.a.) brings the average down to 16%. PBO therefore reliably detects only large differences and is thus just one of several tests.
- Walk-forward: Select parameters in one period; test them in the next.
- Halving test: Does the parameter landscape look similar in both halves of the history?
- Paired bootstrap: What is the probability that variant B is truly better than A and not just by chance?
- Rolling 10-year windows: In what percentage of all windows does a variant win?
- Minimax regret: Which choice does the model regret the least across all scenarios?
- Stress Scenarios: Bitcoin calculated with a CAGR of 0% per year based on available price data from 2014; bonds calculated without the overweight scenario of falling interest rates during the test period; higher costs
- Plateau instead of peak: Whenever possible, choose the midpoint of a stable parameter range; never the single peak (the best value due to the risk of overfitting).
1️⃣ levGTAA (leveraged GTAA)—essentially a variation of 3xGTAA (in consultation with @Epi )
The basket: Nasdaq 100 (3x), Bitcoin (1x), gold (3x), and bonds (5x TLT, long-term U.S. Treasuries, or alternatively, for liquidity reasons, 3x IEF with 7–10-year maturities).
Trading takes place once a month. This is nothing new compared to 3xGTAA. The signals are always calculated based on the unleveraged prices in USD; the leverage is applied only during execution.
What is new or different, however, is the following:
A brief note up front: The parameters discussed below are not set in stone for all time, and I would logically adjust them in the future based on new, important insights.
▸ A range of SMA values instead of a single value: There is no clear-cut optimum for the best SMA, but rather a broad plateau, and it is nearly impossible to predict which specific length is the best. A halving test using the final rule clearly demonstrates this: The best length for 1987–2006 (SMA180) ranked only 15th out of 21 for 2007–2026, where SMA210 came out on top. Across all individual lengths from 100 to 300 days (in increments of 10), the Sortino ratio ranges between 0.99 and 1.06. That’s why I don’t commit to a single value, but rather evaluate a range of SMA values, so to speak. The equally weighted range of SMA values (Sortino 1.05) is close to the optimal value without needing to know it in advance. One result of this is that the signal is less of an “all-or-nothing” principle. For example, if 70% of the SMA lengths indicate “trend intact,” 70% of the position is built up.
As the short-term SMA value (SMAx/SMA range), I use a slower value for x instead of the daily price—similar to Epi’s SMA10/150—though my specific model currently considers SMA30/SMA range to be the best solution. The daily price performs significantly worse, presumably due to more false signals: With the daily price, the return would be only 25.3% p.a. and the Sortino ratio 0.98 instead of 28.1% and 1.05, and the SMA30 outperformed the daily price as x in 99% of all 10-year windows (i.e., the SMA30 and @Epi its SMA10 outperformed, so to speak, SMA1).
▸ Two momentum rankings, each using half the capital: a fast ranking (1/3/6/9 months) and a slow one (3/6/12 months). The fast one detects reversals earlier; the slow one is more stable. It was nearly impossible to predict which ranking would be best (PBO across 11 tested rankings ranged from 42% to 71% depending on the scenario—essentially within the range of chance), so we use both instead of choosing one. The period during which momentum parameter ranges performed significantly better without the 1-month value was the dot-com crash. The 1-month strategy sometimes produced short-lived rebounds and thus false signals in aggressive assets like the Nasdaq 100 or emerging markets, which proved costly in the early 2000s. In a bull run like the one from 2010 to 2026, however, the 1/3/6/9 strategy—excluding BTC—was clearly superior. Among the predefined rankings, the mixed strategy had the best “worst trading day,” the second-lowest regret compared to the alternatives, and 11% fewer portfolio rebalancings than the fast ranking alone. With Bitcoin, the combination outperformed the fast ranking alone in 76% of the 10-year windows; without Bitcoin, the two are neck and neck (Sortino 0.826 vs. 0.827)—so the mix doesn’t hurt even without BTC. To be honest: In the backtest, the slow ranking alone actually came out ahead WITH Bitcoin (29.0% p.a., Sortino 1.07). However, this lead came almost entirely from the years 2022–2026 (especially BTC in 2024/25).
▸ Top 2 with 40/60 – The asset with the strongest momentum (1st place) receives 40%, and 2nd place receives 60%. It sounds counterintuitive, but the backtests support this (4-asset portfolio, 1987–2026):
- 40/60: 28.1% p.a. | maxDD −62% | Sortino 1.05 | P50 31%
- 50/50: 28.1% p.a. | maxDD −70% | Sortino 1.03 | P50 34%
- 66/33 (No. 1 overweighted): 26.9% p.a. | maxDD −83% | Sortino 0.96 | P50 48%
With the same return, overweighting the No. 2 position significantly reduces the risk of a sharp decline. One possible explanation: By that point, the momentum of the frontrunner has often already run out of steam. The 33/66 allocation is practically on par with 40/60 (Sortino 1.05), but involves more portfolio turnover (435% vs. 385% per year). Which allocation leads depends on the time period: From 1987 to 2006, 33/66 was ahead; from 2007 to 2026, 50/50 was even slightly ahead (Sortino 1.39 vs. 1.38). The 40/60 allocation falls in between and is chosen as a pragmatic solution: Across all stress scenarios, it never lagged behind the best allocation by more than 0.013 Sortino over the entire period. If only one asset in the basket has positive momentum and SMA, it receives 50%; the rest remains in cash.
▸ Vola-Cap 55% (a new methodology): Once a month, when selecting the Top 2, the volatility of the newly selected Top 2 portfolio (including leverage) is measured retrospectively over the last 2, 3, and 4 months. If the annualized volatility exceeds 55%, the position is proportionally reduced and the remainder is converted to cash. In other words: For each of the three time periods, the factor 55% / volatility (up to a maximum of 100%) is calculated, and the average of the three factors is invested. Example: The top 2 most recently had 80% volatility → only 55/80 ≈ 69% is invested instead of 100%. Without a volatility cap, the result was worse with an 89–94% probability according to paired bootstrap analysis (Sortino 1.02 instead of 1.05, P50 34% instead of 31%). There is hardly any difference between the volatility cap values of 50% and 60%: 50% was slightly ahead (Sortino 1.056 vs. 1.050), 60% lagged slightly behind (1.042), mainly because a 60% Volacap increases the maxDD compared to 55%, but does not provide a CAGR advantage. I therefore chose 55% as the midpoint of this stable range.
🧺 Selecting the Asset Basket
The final idea after all the backtests: When using only the Top 2, each asset should have its own role—ideally one asset per asset class, two offensive and two defensive.
A look at the correlations of monthly returns (unleveraged, 2015–2026) explains a lot: The stock markets tend to move in tandem (QQQ–EM 0.65, QQQ–EuroStoxx 50 0.66, EM–EuroStoxx 50 0.74; very similar since 1994). Bitcoin, on the other hand, is only weakly correlated with stocks (QQQ 0.31, EM 0.15), while gold and long-term bonds show little correlation with the other assets (Gold–QQQ 0.08, TLT–QQQ 0.23). A second equity asset therefore provides little real diversification, whereas Bitcoin, gold, and bonds do.
(Data format: CAGR | maxDD | Sortino | z-dd | z-Sor | P50 = probability of a >50% drawdown in 10 years)
First off—why not just include more assets? Comparison starting in 1987 (assets for which price data was not available prior to 1987 were simply added to the portfolio starting from the earliest available date):
- 4-asset portfolio (QQQ/BTC/Gold/TLT): 28.1% | −62% | 1.05 | 1.93 | 2.60 | 31%
- 7-asset portfolio (+ EM, EuroStoxx 50, WTI): 22.3% | −80% | 0.84 | 0.70 | 1.56 | 50%
- Group 9 (plus S&P 500, silver): 16.3% | −90% | 0.66 | −0.18 | 0.69 | 65%
→ More assets clearly perform worse here: The more similar assets compete for the top two spots, the less effectively assets can leverage their momentum, and the more often two related stock or commodity assets are likely to be in the lead at the same time, causing the decorrelation to be lost.
Step 1 – The Core: Stocks + Gold + Bonds
Do I even need bonds? Test: QQQ/BTC/Gold without bonds vs. with TLT, starting in 1987:
- without bonds: 22.3% | −61% | 0.87 | 1.22 | 1.61 | 17% | longest drawdown period 114
months (!)
- with 5x TLT: 28.1% | −62% | 1.05 | 1.93 | 2.60 | 31% | longest drawdown period 47 months
→ Add bonds to the portfolio: significantly higher returns, better Sortino and robustness scores, and drawdown periods are more than halved because bonds often rise during deflationary crashes like those in 2000–02, 2008, or 2020. The trade-off: The 5x leverage on bonds increases the risk of a deep drawdown (P50 31% instead of 17%). A possible solution: 3xTLT. However, it is not currently tradable in a practical way. More on this below.
Step 2 – The Fourth Asset Excluding Bitcoin: EM, EuroStoxx 50, or Oil? (from 1987 onward)
Regarding the data: EM is included in my analysis only starting in 1994, EuroStoxx 50 starting in 1990, and oil starting in 1987. Prior to that, the respective basket consists effectively only of the core trio.
- QQQ/Gold/TLT trio: 20.5% | −62% | 0.83 | 1.51 | 1.85 | 32%
- 3-component + EM: 24.7% | −62% | 0.91 | 1.68 | 2.14 | 36%
- 3-stock + EuroStoxx 50: 21.6% | −62% | 0.84 | 1.55 | 1.91 | 32%
- 3-Year+ EM and EuroStoxx 50: 25.0% | −62% | 0.91 | 1.67 | 2.14 | 36% (turnover 508% instead of 444% per year with EM alone)
- 3-year+ Oil (WTI 2x): 19.0% | −80% | 0.76 | 0.61 | 1.35 | 41% (longest drawdown period: 10 years)
Important note on maxDD: For all portfolios except WTI, the −62% stems from the crash of 1989–90, i.e., before EM or BTC data were available. Based on maxDD, these baskets cannot be distinguished from one another starting in 1987; however, they can be distinguished using P50, Sortino, and z-scores.
→ EM clearly outperforms the EuroStoxx 50. Together, they add practically nothing compared to EM alone—just more portfolio rebalancing—which makes sense given the 0.74 correlation between the two. EM delivers returns but also carries slightly more tail risk (P50 of 36% instead of 32%). The EuroStoxx 50 is eliminated. WTI significantly hurt the model on balance through 2015, costing total returns and pushing the maxDD to −80%, so it’s also out. Oil only looked good starting in 2015, mainly due to 2021 and 2026.
Step 3 – The actual portfolio decision: BTC, EM, or both? (Fair comparison starting in October 2015; short backtest period!)
My BTC data begins in 2014 (fully signal-capable starting in October 2015). That’s why the comparison starts in October 2015. To ensure BTC doesn’t win solely because of its exceptional rally, I technically stripped it of its entire return in one variant (0% CAGR over the period) while retaining its actual volatility. (-> Overfitting stress test).
(Data format: CAGR | maxDD | Sortino | P50; the z-scores are not comparable to the others in this short window)
- QQQ/Gold/TLT trio: 18.6% | −44% | 0.75 | 11%
- 3-stock portfolio + EM: 27.8% | −47% | 0.96 | 16%
- 3-stock portfolio + BTC with 0% CAGR: 30.1% | −50% | 1.07 | 24%
- 3-Year + BTC with 0% CAGR + EM (5 assets): 25.2% | −64% | 0.93 | 50%
- with actual BTC CAGR: 3-year + BTC 47.9% | −48% | 1.49 | 7% · 3-year + BTC + EM 43.5% | −58% | 1.37 | 16%
→ Particularly revealing: Even Bitcoin, which generated no returns, outperformed EM as the fourth asset in the past, delivering higher returns and a better Sortino ratio—albeit with a slightly higher drawdown risk (P50 24% vs. 16%). Apparently, momentum benefits from BTC’s strong trend phases, and BTC is less correlated with stocks (correlation with QQQ 0.31, vs. 0.65 for EM). Adding EM to BTC results in worse performance across all metrics, both with a real BTC CAGR and with a “BTC 0% CAGR”: Presumably, the strategy—with two equity assets in the portfolio and 3x leverage—is hit twice as hard during crises (5-asset portfolio with EM and BTC: maxDD with “BTC 0%” −64% from late 2017 to March 2020; with actual BTC, −58%).
To be honest: 11 years is not a long time. Logically, the differences in this short timeframe are therefore not statistically significant.
Interim conclusion—QQQ/BTC/Gold/TLT. EM as an addition is the only component I’m still considering, but the data tends to argue against it given the short backtest period.
Also eliminated (as already noted in the latest GTAA Workshop reports @Epi ): Currency pairs such as USD/EUR and EUR/USD have been eliminated due to a lack of stable momentum trends. Likewise, −TLT (short bonds): If interest rates do not continue to rise but instead stagnate, −TLT will likely lose value. -TLT tends to have asymmetrically negative volatility and is therefore unfavorable for momentum trends (which is typical for short indices).
Step 4 – The Bond in Practice: 5x TLT or 3x IEF or 1x TLT?
The product $TLT5 (+0,71 %) has exorbitant costs (TCO over 7% per year). That’s why I compared the options directly (starting in 1992, since my data on medium-term bonds doesn’t begin until late 1991; all paired with BTC): (Data format: CAGR | maxDD | Sortino | P50)
- 5x TLT with low product costs: 33.0% | −48% | 1.20 | P50 15%
- 5x TLT with the actual 7% TCO: 31.1% | −48% | 1.15 | P50 17%
- 3x TLT: 31.2% | −44% | 1.20 | P50 7%
- 3x IEF (7–10-year term, only 0.3% TCO according to gq): 30.6% | −44% | 1.18 | P50 5%
- 1x TLT: 28.4% | −43% | 1.12 | P50 5%
→ When factoring in actual costs, 5x TLT offers virtually no advantage over 3x IEF but carries higher tail risk (P50). 3x TLT is slightly better than IEF but, unfortunately, is not currently tradable. That’s why I’m implementing 3x IEF (7–10y) for now. Important: All other backtests in this post use 5x TLT and low 5x TLT product costs.
Step 5 – Top 2 or Top 3? (from 1987 onward, same rule; Top 2 weighted 40/60, Top 3 equally weighted at 33/33/33)
(Data format: CAGR | maxDD | Sortino | P50)
- QQQ/BTC/Gold/TLT: Top 2 28.1% | −62% | 1.05 | 31% · Top 3 22.6% | −54% | 0.99 | 13%
- QQQ/EM/Gold/TLT: Top 2 24.7% | −62% | 0.91 | 36% · Top 3 19.5% | −54% | 0.81 | 21%
- QQQ/Gold/TLT/WTI: Top 2 19.0% | −80% | 0.76 | 41% · Top 3 15.1% | −66% | 0.68 | 23%
- QQQ/EM/Gold/TLT/WTI: Top 2 19.0% | −80% | 0.75 | 46% · Top 3 17.2% | −66% | 0.72 | 28%
- QQQ/EM/BTC/Gold/TLT/WTI: Top 2 22.6% | −80% | 0.86 | 48% · Top 3 21.9% | −66% | 0.87 | 27%
- QQQ/EU50/EM/Gold/TLT/WTI: Top 2 17.8% | −80% | 0.72 | 49% · Top 3 18.4% | −67% | 0.75 | 29%
→ The Top 3 strategy reduces the drawdown risk (maxDD and P50) in all portfolios. However, in 4-asset portfolios, it significantly reduces returns and Sortino, presumably because 3 out of 4 assets are held and the selection process barely filters anything. For 5- and 6-asset portfolios, the “Top 3” strategy is roughly on par in terms of Sortino (−0.03 to +0.03), but clearly ahead in terms of drawdown risk (maxDD −66/−67% instead of −80%, P50 27–29% instead of 46–49%). Rule of thumb: The larger the basket, the more likely “Top 3” is the better choice. For my 4-asset basket, I’m therefore sticking with “Top 2.”
Additional stress tests for the 4-asset basket starting in 1987: BTC 0% CAGR 23.6% p.a. | maxDD −62% | Sortino 0.92; bonds calculated without the overweight scenario of falling interest rates during the test period: 23.7% | −71% | 0.92; entirely without BTC (core 3-asset basket consisting of QQQ, gold, TLT) 20.5% | −62% | 0.83. While the strategy does lose significantly in this case, it is not dependent on a single stroke of luck.
📊 OVERALL
Backtest 1987–2026 for 3xQQQ, 1xBTC (starting in 2015), 3xGold, and 5xTLT:
- Average across all 21 possible trading days: 28.1% p.a. | maxDD −62% | Sortino 1.05 | z31 1.93 | z4 2.60 | P50 31% | P75 1.3%
- Only on the actual signal day (last day of the month): 30.0% | −70% | 1.08 | 1.88 | 2.82 | P50 34% | P75 3.0%
- Since 1992 (following the crash of 1989–90): 33.0% | −48% | 1.20 | P50 15%; with the implemented 3x IEF instead of 5x TLT: 30.6% | −44% | 1.18 | P50 5%
The probability of being down more than 50% at least once within 10 years (P50) was thus around 30–35% starting in 1987, and the probability of a maxDD exceeding 75% within 10 years was around 1–3%. Leverage also means deep troughs. My method aims to mitigate this primarily through the 55% volatility cap, the 40/60 weighting, and—above all—the portfolio selection, which includes only one asset per asset class; however, it cannot be prevented with 100% certainty.
⚖️ levGTAA vs. 3xGTAA – (even though I personally don’t view the two variants as competitors, but rather as two valid, equally valid options/variants)
In a direct comparison to 3xGTAA, levGTAA is, on the one hand, more complex to implement (SMA range instead of a single SMA value, 55% volatility cap, two momentum rankings), but on the other hand, it is leaner (4 assets in the basket instead of 6, as in @Epi currently, with the addition of WTI and EU50; top 2 instead of top 3). Overall, of course, both of our models can easily change at any time in light of new, promising insights and may even converge.
My assessment: @Epi The basket with the additional EU50 and WTI offers more variability and a wider selection of assets in case the trend consistency or momentum of QQQ and BTC becomes more unstable or if those two assets fall by the wayside over the decades. That is the disadvantage of my 4-asset basket and, at the same time, the strength of its asset basket. On the other hand, @Epi 's basket has other weaknesses: back-and-forth movement or inefficiency between the two equity assets, QQQ and EU50 (correlation 0.66), the drawdown risk of WTI, and the risk that WTI will no longer perform in the future the way it has since 2015. Both systems therefore have their respective advantages and disadvantages—and one must @Epi give 3xGTAA credit for the fact that its live track record on wikifolio to date provides thoroughly valid arguments for the validity of its model.
The most important insight for me: All of the optimizations mentioned above are fine-tuning. Much more important is the following consideration:
1. The greatest "optimization" of performance and robustness metrics is most likely to result from diversification across strategies—that is, combining, for example, B&H investments with systematic trend-following strategies and other methods that theoretically exist. In my opinion, this offers the best chance of improving the metrics and opportunities of one’s overall portfolio. Incidentally, levGTAA and levTipsRegime (Part 3) have a monthly correlation of approximately 0.5.
2. Second in importance, but far less relevant, is, in my opinion, the selection of the asset basket: Using exactly the same parameter rules, the tested baskets yield a CAGR ranging from about 16% to 29% per year (Sortino ratio 0.66 to 1.05). The goal should be to position oneself in the middle range or the top third. However, the optimal asset basket in the future is, of course, by no means predictable.
3. Parameter adjustments and other nuances are significantly less important: SMA length (Sortino 0.99–1.06), volatility cap (1.02–1.06), weighting 33/66 to 50/50 (1.03–1.05), top 2 vs. top 3 in a 4-asset portfolio (0.99–1.05; which is more a question of return versus drawdown depth than of quality).
So I’ve decided to implement both strategies as wikifolios.
Here are the two links:
levGTAA: https://www.wikifolio.com/de/de/w/wfxlevgtaa
levTipsRegime: https://www.wikifolio.com/de/de/w/wfxtipsreg
The next (much shorter) post (Part 2) will focus on a comparison of implementation: wikifolio vs. private portfolio. I’ll then introduce levTipsRegime in Part 3.
If I’ve forgotten anything or there’s a mistake somewhere, feel free to leave a short comment, and I’ll update the post.
Do you have any questions, criticism, comments, or requests?
Best regards, your flyingSquirrel
(or Sineqz, squirrel, flying squirrel, or whatever you want to call me)
⚠️ Important:
This is not investment or financial advice, nor is it tax advice. This is my personal approach and always my personal opinion. I created and evaluated the backtests with the help of AI, and AI can make mistakes. Backtests reflect past performance and are no guarantee of future results. Leveraged products can incur very high losses in a short period of time; the drawdowns mentioned above—and even higher ones, up to total loss—are a real possibility. Everyone should assess for themselves whether this approach is suitable for their own situation.
#gtaa
#momentum
#momentumstrategie
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