Defining the Universe
The Question Before the Question
Chapter Four examined what happened when the AMAAS Evidence Loop challenged our original accountability assumptions. We learned that average return, median return, positive-outcome frequency, and population structure can tell very different stories about the same set of securities.
That investigation exposed a deeper issue: before asking whether a model can rank securities effectively, we first have to decide which securities belong in the population being ranked.
What the First Accountability Results Revealed
The first one-day accountability results included several extreme observations. Some very-low-priced securities produced percentage returns measured in the hundreds or thousands of percent.
Those observations were mathematically correct. But arithmetic mean gives every percentage return equal statistical weight. That means an extreme move in a security priced at a fraction of a cent can influence the reported mean of an entire population.
The result can be numerically correct while still being difficult to interpret as evidence about the investable universe AMAAS was designed to evaluate.
Why We Did Not Simply Remove Outliers
The simplest response would have been to delete observations above an arbitrary percentage threshold. We rejected that approach.
An observed return should remain an observed return. If a security appreciated 500%, AMAAS should preserve that fact. If a security collapsed 80%, that observation should remain visible as well.
The evidence should be preserved. The population should be defined.
Price Is Not Quality
A higher share price does not automatically indicate a better company. A $25 common stock can be an excellent business, while a $250 stock can be overvalued or fundamentally weak.
For that reason, the AMAAS minimum-price requirement should never be described as a quality score. It is a research-universe eligibility rule.
Why Very-Low-Priced Securities Matter Statistically
Percentage return is calculated relative to the starting price. A $0.10 move on a $0.50 security represents a 20% return. The same $0.10 move on a $50 security represents a 0.2% return.
Both calculations are correct. But the denominator creates very different percentage sensitivity. This effect does not disappear immediately once a security rises above the traditional definition of a penny stock.
Testing the Threshold
Rather than choosing a minimum price immediately, we tested multiple thresholds against the frozen accountability evidence.
| Minimum price | Purpose |
|---|---|
| No minimum | Observe the complete raw population. |
| $5 | Remove the most extreme sub-$5 effects while retaining a broad universe. |
| $10 | Test a conventional low-price boundary. |
| $20 | Evaluate a more restrictive investability population. |
| $35 | Reduce low-price percentage sensitivity further while retaining a broad common-equity universe. |
| $50 | Compare with the stricter threshold used in earlier Equity Selection Engine designs. |
The experiment produced an important lesson: raising the threshold did not guarantee that the lower-scoring population's mean return would decline.
At a $10 minimum, the Below-50 group contained 606 observations with an average one-day return of approximately +1.01%, a median of 0.00%, and 45.9% positive outcomes.
At a $35 minimum, that group shrank to 90 observations, but its average increased to approximately +2.07%, its median increased to +0.92%, and its positive-outcome rate increased to 70.0%.
Why $35
AMAAS therefore does not select a $35 minimum because it made the one-day results look better. It did not. The rationale is methodological.
1. Reduce disproportionate statistical influence
Very-low-priced securities can generate unusually large percentage movements from modest absolute price changes. A higher price floor reduces the frequency and statistical influence of those observations in arithmetic-mean analysis.
2. Establish a clear and understandable research boundary
A methodology should be explainable. A $35 minimum is a simple, observable eligibility rule that can be applied before outcomes are known. It is not an optimized cutoff selected from the current results.
3. Reduce return-distribution heterogeneity beyond traditional penny stocks
The percentage-sensitivity issue does not end at $5 or $10. Securities priced between roughly $11 and $34 can still contribute materially greater return variance than more conventionally priced equities.
The Primary AMAAS Research Universe
Primary AMAAS Research Universe: eligible common equities with a baseline market price of at least $35, subject to the platform's existing security-type and listing exclusions.
The eligibility policy should continue to exclude instruments that are not economically comparable with ordinary common equity where appropriate, including warrants, rights, units, funds, ETFs, and other non-common-equity structures.
The Extended Research Universe
Defining a primary universe does not require throwing away everything outside it. AMAAS can preserve an Extended Research Universe containing lower-priced securities and other instruments useful for historical research, anomaly detection, event intelligence, or specialized analysis.
| Population | Purpose |
|---|---|
| Primary Research Universe | Investment Score ranking, Top 30 / Middle 40 / Bottom 30 accountability, portfolio-oriented research, and prospective model validation. |
| Extended Research Universe | Historical preservation, anomaly analysis, special situations, low-price behavior, and broader market research. |
Preserve the Past, Improve the Future
The August accountability observations should not be rewritten to pretend that the $35 rule always existed. They are part of the historical record and are the evidence that taught us why universe definition matters.
Why Timing Matters
At the time this methodology was established, the one-week, one-month, three-month, six-month, and twelve-month accountability outcomes had not yet matured.
We are therefore defining the research universe before those future results are known. Future outcomes may validate the AMAAS ranking hypothesis or challenge it. Either result should remain visible.
Universe Definition Is Model Governance
The Evidence Loop demonstrated that universe selection is not merely a data-engineering task. It is part of model governance.
A research system should be able to answer which securities were eligible, why they were eligible, when the rule changed, which historical predictions were generated under each rule, and whether the rule was established before or after outcomes were known.
Universe Reconciliation Becomes Essential
A research universe is not static. Companies are listed and delisted, symbols change, corporate actions occur, and new instruments appear.
Reconcile → Validate eligibility → Collect evidence → Score → Preserve → Evaluate
This protects the knowledge base from silent population drift and ensures that each research run clearly records the universe to which its conclusions applied.
A Better Question
Chapter Four asked whether higher-ranked AMAAS populations produced stronger subsequent outcomes. Chapter Five adds the question that must come first:
The Research Universe Is Part of the Hypothesis
Every quantitative model contains assumptions about the population to which it applies, whether those assumptions are documented or not.
Changing the population can change the result. That does not mean researchers should search for the population that produces the best result. It means they should define the intended population explicitly, justify it economically, preserve the definition historically, and test the model prospectively within it.
The Next Experiment
The $35 minimum price does not guarantee that AMAAS's highest-ranked securities will outperform its lowest-ranked securities. It is not supposed to.
It gives the next experiment a more clearly defined population. The predictions generated from that universe will again be frozen. Independent market evidence will accumulate. Accountability will measure what happens.
For informational and educational purposes only. AMAAS research, scores, forecasts, accountability measurements, universe definitions, and portfolio observations are analytical tools and do not constitute personalized investment advice, a recommendation to buy or sell any security, or a guarantee of future performance.