Here is an interactive Claude artifact that begins to give us reliable statistics on P123 Designer Models using the Benjamini–Hochberg (BH) procedure. It is not perfect, and the truth is it will never be perfect without better data. Anyone who has a specific concern can modify it with Claude’s help.
The BH equations are straightforward and can easily be run in a spreadsheet without any programming. Anyone who has read past the abstract of the academic papers regularly cited on P123 has seen this test before. If we cite those papers in the forum and suggest they are a good source of information, we should actually use their statistical tools, though not everyone here agrees, for reasons I still don’t quite understand.
The BH procedure identifies the subset of models that pass a pre-selected False Discovery Rate (FDR). The test here uses each model’s 2-year excess return over the designer’s own benchmark. Setting the FDR at 0.20 (meaning that within the group of passing models, the expected proportion of false positives, the “just lucky” models, is capped at 20%), 3 models pass:
The winners are Marchus Wagenberg, Kumar Kumar, and Andreas Himmelreich. At the stricter FDR of 0.10, only Marchus’s model passes.
However, that baseline assumes zero survivorship bias, since it only counts currently live models. When we account for retired models, the multiple-testing hurdle gets steeper:
- Assuming 50 or 100 retired models, only Marchus’s model survives the BH threshold.
- Assuming 200 retired models, none of the models pass at the 0.20 FDR level.
Note: This survivorship adjustment is an estimate, as we cannot know the exact number of retired models without seeing the graveyard data or their p-values.
The takeaway is encouraging: P123 is close to having real statistical evidence of the out-of-sample value of its top models. The main obstacle is the survivorship blind spot in the data. The retired models and each model’s weekly returns would settle much of this.
Take a look at the calculator here: Claude Artifact
Note: It would help a lot if we had each model’s excess return relative to the designer’s chosen benchmark since launch. With that data, and with the retired models included, I suspect P123 could show the usefulness of its platform statistically, free of both incubation bias and survivorship bias.
While some might disagree, I think that kind of evidence would not be an entirely bad thing for a platform that offers machine learning as an option.