L1 ⚛ L1-444 ⊙ Testnet

Markowitz Mean-Variance Portfolio Optimization

Computational Finance · Portfolio optimization

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⬇ L1-444.md

# ⚛ L1 Principle — Markowitz Mean-Variance Portfolio Optimization **ID:** `L1-444` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Portfolio optimization* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** portfolio weight vector > **📡 Carrier:** N/A · **🌫 Noise:** estimation gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555259 --- ## 🧠 1. Introduction **Markowitz Mean-Variance Portfolio Optimization** is a **parameter-estimation problem** whose unknown lives in **portfolio weight vector** space, within the **Portfolio optimization** sub-domain of **Computational Finance**. Measurements consist of N/A via a **expected return covariance estimation** sensing mechanism. The forward operator applies, in order: adds a prior term that biases the solution toward smoothness/sparsity; O · qp · quadratic programming operator; S · efficient frontier · trace operator. Observations are corrupted by estimation gaussian. Existence of the recovered portfolio_weight_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); estimation_error_expected_returns dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Estimation gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → O · qp · quadratic programming → S · efficient frontier · trace → **y** (detector). ``` y = `S.efficient_frontier.trace` `O.qp.quadratic_programming` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `O.qp.quadratic_programming` | O · qp · quadratic programming operator | | `S.efficient_frontier.trace` | S · efficient frontier · trace operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Portfolio optimization | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | portfolio_weight_vector | | Noise model | estimation_gaussian | | Integration axis | asset_universe | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered portfolio_weight_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 50); estimation_error_expected_returns dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Estimation gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | out_of_sample_Sharpe_ratio | | Secondary | portfolio_turnover | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `expected_return_covariance_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N assets | — | 50 | | T lookback days | — | 252 | | Risk aversion lambda | — | 1 | | Estimation error sigma mu | — | 0.01 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N assets | — | 5 – 500 | | T lookback days | — | 63 – 2520 | | Risk aversion lambda | — | 0.1 – 10.0 | | Estimation error sigma mu | — | 0.001 – 0.05 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.6 out_of_sample_Sharpe_ratio | Metric | Range | |---|---| | Out of sample sharpe ratio | 0.0 – 2.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **out_of_sample_Sharpe_ratio**, with κ = `1000.0` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x965145a7038c20862dd0396f13ebb116ae61e27b8c9dc11a2acdfd4387130cad` - **Chain tx hash:** `0xd3de09a18faf929abd82a23b0b558921f307841494e358e1a5eebac81db35c06` - **Chain block:** `41555259` --- ## File Mapping This bundle consists of: `L1-444.md`, `L1-444.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-444.md` | Source of truth — edit this | Human or LLM | | `L1-444.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-444`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "status": "testnet",
  "sub_domain": "Portfolio optimization",
  "title": "Markowitz Mean-Variance Portfolio Optimization"
}

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