How Unusual was Matterhorn's Top-10 Portfolio Result?
Measured September 8, 2026. Research comparison of the earlier hardened 30% ML / 70% component model. No ranking, feature, model, production record or code was changed.
Start with the Intent
The critical question is whether using Matterhorn's ranked selections helps a user allocate the annual investment contributions better than buying SPY or choosing a basket of un-ranked companies at random. As part of this effort, we note discovering attractive sectors and related companies is part of Matterhorn's potential capabilities which can bring success on its own.
The reference benchmark is SPY using same investment amounts and timing. The original returns modeled with $58,342 for Matterhorn Top 10 versus $38,953 vs. SPY, approximately 49.8% more wealth and 17.83% versus 6.71% annualized investor return.
The critical, albeit justified comparison asks a second question: How unusual was that result among alternative selections from the measurable eligible options? The answer, only 0.475% of other stock investments reached the same return as Matterhorn.
The Details
In this window, 16.85% of uniformly random portfolios beat SPY, while only 0.4745% matched or exceeded Matterhorn's ending value. Random portfolios with Matterhorn's annual sector and company-size composition beat SPY 50.70% of the time and matched Matterhorn 1.0765% of the time.
| Random selection rule | Beat same-date SPY | Match or exceed Matterhorn | Median ending value | Median annualized investor return |
|---|---|---|---|---|
| Uniformly choose ten measurable names each year | 16.85% | 0.4745% (about 1 in 211) | $33,068 | 2.46% |
| Match annual sector and company-size composition | 50.70% | 1.0765% (about 1 in 93) | $39,046 | 6.77% |
| Original Matterhorn selections | — | — | $58,342 actual simulated endpoint | 17.83% |
| SPY, identical contributions | — | — | $38,953 actual simulated endpoint | 6.71% |
In this analysis there were 200,000 independently sampled portfolios per random comparison.
Complete sensitivity, including sector only
Following the trader's questions about the relevance of matching, an additional fixed protocol completed every combination of sector and size conditioning. No new weight, threshold, stock, date, holding rule or model was selected based on this follow-up.
| What the random controls hold fixed | Beat SPY | Match Matterhorn |
|---|---|---|
| Neither — primary random benchmark | 16.85% | 0.4745% |
| Sector only — secondary diagnostic | 35.39% | 1.9155% |
| Company size only — secondary diagnostic | 32.58% | 0.2160% |
| Both — secondary diagnostic | 50.70% | 1.0765% |
All four results are reported. Sector-only controls match the annual sector mix already selected by Matterhorn, while choosing stocks uniformly within each sector. This is a transparent sector-awareness sensitivity, not a fitted simulation of an investor deciding to "add some tech." The size-only control likewise conditions on the original size mix. Their differing results show that the quoted random-tail frequency depends on the comparison; selecting whichever number looks most favorable would be inappropriate.
Reproduce the added diagnostics with python ml-research/portfolio-random-controls/run_sensitivity.py. The pre-run sensitivity settings and complete strata are in sensitivity-protocol.json and sensitivity-results.json; both additional sets contain 200,000 trials. These add simulation precision within this one historical example, not independent validation histories.
Exact experiment
- Observe frozen rankings on March 31, 2015, 2016 and 2017. The same historical score pools used by the original case contain 1,969, 1,980 and 1,970 companies.
- Buy at the first following trading-session close: April 1, 2015; April 1, 2016; and April 3, 2017. These dates were carried over unchanged from the original calendar rule.
- Add $10,000 each year, divided into ten $1,000 allocations. Sample without replacement within a year. Repeated issuers across years are allowed, and every earlier purchase remains held.
- Value all holdings on March 31, 2020, following the original split, dividend and corporate-action conventions. Ordinary gross dividends are reinvested; documented merger cash stays cash at zero interest. No fees or taxes.
- Compare ending wealth with $38,952.54527050957 for SPY and the original Matterhorn interval of $58,341.77128328316–$58,341.84763065910. Identical contribution dates mean terminal-wealth and XIRR orderings are equivalent.
- The historical ranking had one already-acquired 2017 selection. Its allocation remains cash under the original rule, including if sampled in the controls; it is not replaced by a more successful stock. Thus the original case contains 29 stock purchase lots and one cash allocation, across 26 named companies.
What these results demonstrate
The original ending value exceeded approximately 99.53% of uniform random portfolios and 98.92% of sector/size-matched random portfolios in the measurable sample. Sector and size selection explain part of why beating SPY is easier for the matched controls. Even after that matching, reaching Matterhorn's much higher ending value was uncommon.
The results highlight Matterhorn's prioritization of exceptional growth and compounding candidates. It does not show if this can be done at any time or as a guarantee. This test was requested after seeing its attractive result. Neither tail frequency adjusts for that development history, repeated experiments, incomplete historical security identities, missing outcomes, or the selection of this example. It is an exploratory conditional benchmark, not a confirmatory p-value or model graduation gate. See Bailey, Borwein, López de Prado and Zhu, The Probability of Backtest Overfitting.
Numerical precision and reproducibility
The 95% Wilson Monte Carlo intervals are:
| Conditional comparison | Beat SPY | Match Matterhorn |
|---|---|---|
| Uniform | 16.69%–17.02% | 0.445%–0.506% |
| Sector/size matched | 50.48%–50.92% | 1.032%–1.123% |
These details describe simulation precision conditional on fixed inputs.
The protocols, random seeds, original selections, input fingerprints, all 600,000 original trial outcomes and 400,000 added sensitivity outcomes, source coverage and results are retained alongside this report. All original top-ten selections match the archived score order. Original Matterhorn and SPY endpoint values tie out. Repeating both simulations produces byte-identical results and trial files, recorded in verification.json and sensitivity-verification.json. 17 automated tests pass, covering cash-flow, without-replacement sampling, matched annual composition, reproducibility, probability bounds, exact execution dates, price gaps and discontinuity rejection.
Reproduce from the Matterhorn scripts and models within the repository root:
.venv-ml/bin/python ml-research/portfolio-random-controls/run_study.py build
.venv-ml/bin/python ml-research/portfolio-random-controls/run_study.py simulate
.venv-ml/bin/python ml-research/portfolio-random-controls/run_sensitivity.py
.venv-ml/bin/python -m pytest ml-research/portfolio-random-controls/test_study.py ml-research/portfolio-random-controls/test_sensitivity.py ml-research/portfolio-top10/test_portfolio_math.py -q
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