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<!--
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AI NOTE (WFGY 3.0 TU Experiment Anchor)
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This file is part of the WFGY 3.0 "Tension Universe" experiment collection.
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Main hub for context and navigation:
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https://github.com/onestardao/WFGY/blob/main/TensionUniverse/EventHorizon/README.md
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Problem ID: TU Q101 (Equity Premium Puzzle).
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Role: MVP experiment log for Q101 at the effective layer. Focus on tiny
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consumption based models and tension observables between predicted and observed premia.
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Use: When a user asks about TU Q101 equity premium experiments or wants
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runnable examples, load this page first, then follow its notebook links.
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-->
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# TU Q101 MVP: toy equity premium tension
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_Status: work in progress. This page records early MVP designs and will be updated after the first notebooks run._
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> This page sketches toy experiments for TU Q101.
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> The goal is to encode the equity premium puzzle as a tension between
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> simple models and simple observed targets, not to resolve real markets.
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**Navigation**
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- [← Back to Experiments index](../README.md)
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- [← Back to Event Horizon (WFGY 3.0)](../../EventHorizon/README.md)
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---
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## 0. What this page is about
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TU Q101 looks at the equity premium puzzle as a structured mismatch between
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- predicted premia from simple asset pricing models, and
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- empirical target bands for long run equity premia.
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The MVP here uses small simulated economies with:
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- consumption processes,
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- risk free and risky assets,
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- representative agents with utility functions,
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and tracks tension observables when the model cannot match observed premia without extreme parameters.
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---
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## 1. Experiment A: simple consumption based asset pricing model
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### 1.1 Research question
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If we build a minimal consumption based asset pricing model, can we define a scalar observable T_premium that
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- is small when predicted equity premia and volatility sit inside a plausible band,
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- and increases as the model requires extreme risk aversion or unrealistic parameters.
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### 1.2 Setup
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The notebook will:
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- Simulate a simple consumption growth process over many periods.
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- Define two assets:
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- a risk free asset with fixed return,
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- a risky asset with return tied to consumption growth.
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- Use a basic power utility or similar to compute implied prices.
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- From these, derive
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- the implied equity premium,
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- volatility of returns,
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- required risk aversion parameter to match a chosen target premium.
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Define T_premium using:
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- the squared deviation between implied and target equity premium,
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- penalties for risk aversion parameters outside a reasonable range,
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- penalties when volatility patterns are inconsistent with empirical targets.
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### 1.3 Expected pattern
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We expect:
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- toy configurations that generate plausible premia with reasonable parameters to have lower T_premium,
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- toy configurations that only match observed premia with extreme risk aversion to have higher T_premium.
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The point is to show an explicit tension between model structure and target bands, even in a simple setup.
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### 1.4 How to reproduce
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After `Q101_A.ipynb` is created:
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1. Open the notebook.
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2. Read the header comments describing the consumption process, assets and parameter ranges.
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3. Run the simulation and compute T_premium across parameter sweeps.
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4. Inspect the table of results and plots.
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---
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## 2. Experiment B: narrative models versus numerical models
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### 2.1 Research question
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Can we use a language model to evaluate narrative explanations for the equity premium
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and compare them against the toy numerical model, defining a narrative tension observable T_narrative.
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### 2.2 Setup
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The notebook will:
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- Generate a small set of narrative hypotheses, for example
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- rare disasters,
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- habit formation,
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- institutional constraints.
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- For each configuration of the toy numerical model, produce a short summary describing its mechanism.
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- Ask a language model to judge which narrative hypothesis best fits the numerical summary.
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- Extract consistency scores.
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Define T_narrative as a function of:
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- mismatch between assigned narrative and true simulated mechanism,
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- low consistency scores.
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### 2.3 Expected pattern
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We expect:
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- lower T_narrative when numerical mechanisms and selected narratives match,
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- higher T_narrative when narratives and numerical structure disagree.
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This bridges TU Q101 with narrative level explanations at the effective layer.
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### 2.4 How to reproduce
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Once `Q101_B.ipynb` exists:
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- open the notebook,
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- inspect the narrative set and prompt format,
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- run the evaluation and compare T_narrative across scenarios.
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---
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## 3. How this MVP fits into Tension Universe
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TU Q101 treats the equity premium puzzle as a tension between
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- simple asset pricing models,
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- empirical target bands,
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- and narrative explanations.
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This MVP page provides:
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- a minimal numerical experiment with T_premium,
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- a minimal narrative experiment with T_narrative.
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Both are meant as starting points, not as final economic models.
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For the broader project:
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- [Experiments index](../README.md)
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- [Event Horizon (WFGY 3.0)](../../EventHorizon/README.md)
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---
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### Charters and formal context
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The design of this MVP follows:
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- [TU Effective Layer Charter](../../Charters/TU_EFFECTIVE_LAYER_CHARTER.md)
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- [TU Encoding and Fairness Charter](../../Charters/TU_ENCODING_AND_FAIRNESS_CHARTER.md)
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- [TU Tension Scale Charter](../../Charters/TU_TENSION_SCALE_CHARTER.md)
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