From ff8ba8906673cd7e55b0d6ea5095989d83dc7f43 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:31:04 +0400 Subject: [PATCH 01/12] README corrected --- README.md | 24 ------------------------ 1 file changed, 24 deletions(-) diff --git a/README.md b/README.md index 58ead100..c363a602 100644 --- a/README.md +++ b/README.md @@ -67,30 +67,6 @@ We alter some of their Python code. Our experiments to combine it with Niedermay ideas to accelerate the computation of the matrix inverses did not yet justify the additional complexity. -## ๐Ÿ› ๏ธ uv - -You need to install [task](https://taskfile.dev). -Starting with - -```bash -task cvxcla:install -``` - -will install [uv](https://github.com/astral-sh/uv) and create -the virtual environment defined in -pyproject.toml and locked in uv.lock. - -## ๐Ÿ”ฌ marimo - -We install [marimo](https://marimo.io) on the fly within the aforementioned -virtual environment. Executing - -```bash -task cvxcla:marimo -``` - -will install and start marimo. - ## ๐Ÿ” previous work In the [repo](https://github.com/phschiele/PyCLA) by Philipp Schiele. From 5e79ccad8949239bbaf08061706af70ebafdbadb Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:31:21 +0400 Subject: [PATCH 02/12] workflows commented --- .github/workflows/book.yml | 9 +++++++++ .github/workflows/ci.yml | 8 ++++++++ .github/workflows/pre-commit.yml | 9 +++++++++ 3 files changed, 26 insertions(+) diff --git a/.github/workflows/book.yml b/.github/workflows/book.yml index 2052a21a..4bb2f311 100644 --- a/.github/workflows/book.yml +++ b/.github/workflows/book.yml @@ -1,9 +1,13 @@ +# Workflow for building and deploying the book +# This workflow is triggered on push events to the repository + name: "book" on: - push jobs: + # Job to process marimo notebooks marimo: runs-on: "ubuntu-latest" permissions: @@ -15,6 +19,7 @@ jobs: - uses: cvxgrp/.github/actions/marimo@v2.2.8 + # Job to run tests and generate coverage reports test: runs-on: "ubuntu-latest" permissions: @@ -26,6 +31,7 @@ jobs: - uses: cvxgrp/.github/actions/coverage@v2.2.8 + # Job to process Jupyter notebooks jupyter: runs-on: "ubuntu-latest" permissions: @@ -36,6 +42,7 @@ jobs: - uses: cvxgrp/.github/actions/jupyter@v2.2.8 + # Job to generate API documentation using pdoc pdoc: runs-on: ubuntu-latest permissions: @@ -47,6 +54,8 @@ jobs: - uses: cvxgrp/.github/actions/pdoc@v2.2.8 + # Final job to build and deploy the book + # This job runs only after all other jobs have completed successfully book: runs-on: "ubuntu-latest" needs: [test, jupyter, marimo, pdoc] diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 040dd729..16aeb896 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -1,3 +1,7 @@ +# Continuous Integration workflow +# This workflow runs tests across multiple operating systems and Python versions +# It is triggered on push events to the repository + name: "CI" on: @@ -11,6 +15,8 @@ jobs: # The type of runner that the job will run on runs-on: ${{ matrix.os }} + # Matrix strategy to test across multiple environments + # Tests will run on all combinations of the specified operating systems and Python versions strategy: matrix: os: [ ubuntu-latest, windows-latest, macos-latest ] @@ -18,9 +24,11 @@ jobs: # Steps represent a sequence of tasks that will be executed as part of the job steps: + # Step 1: Set up the Python environment with the specified version - name: "Build the virtual environment for ${{ github.repository }}" uses: cvxgrp/.github/actions/environment@v2.2.8 with: python-version: ${{ matrix.python-version }} + # Step 2: Run the tests using the cvxgrp test action - uses: cvxgrp/.github/actions/test@v2.2.8 diff --git a/.github/workflows/pre-commit.yml b/.github/workflows/pre-commit.yml index 53fc8107..931512ff 100644 --- a/.github/workflows/pre-commit.yml +++ b/.github/workflows/pre-commit.yml @@ -1,3 +1,7 @@ +# Pre-commit workflow +# This workflow runs code quality checks and dependency analysis +# It is triggered on push events to the repository + name: pre-commit on: @@ -7,15 +11,20 @@ permissions: contents: read jobs: + # Job to run pre-commit hooks for code quality checks pre-commit: runs-on: ubuntu-latest steps: + # Run pre-commit hooks (linting, formatting, etc.) - uses: cvxgrp/.github/actions/pre-commit@v2.2.8 + # Job to analyze dependencies using deptry deptry: runs-on: ubuntu-latest steps: + # Set up the Python environment - name: "Build the virtual environment for ${{ github.repository }}" uses: cvxgrp/.github/actions/environment@v2.2.8 + # Run deptry to check for dependency issues - uses: cvxgrp/.github/actions/deptry@v2.2.8 From a31e4595706207c2a7f51398aa24d778037407d7 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:32:38 +0400 Subject: [PATCH 03/12] index pointing to README --- book/docs/index.md | 91 +--------------------------------------------- 1 file changed, 1 insertion(+), 90 deletions(-) mode change 100644 => 120000 book/docs/index.md diff --git a/book/docs/index.md b/book/docs/index.md deleted file mode 100644 index 2e9fd861..00000000 --- a/book/docs/index.md +++ /dev/null @@ -1,90 +0,0 @@ -# cvxcla - -[![PyPI version](https://badge.fury.io/py/cvxcla.svg)](https://badge.fury.io/py/cvxcla) -[![Apache 2.0 License](https://img.shields.io/badge/License-APACHEv2-brightgreen.svg)](https://github.com/cvxgrp/cvxcla/blob/master/LICENSE) -[![Downloads](https://static.pepy.tech/personalized-badge/cvxcla?period=month&units=international_system&left_color=black&right_color=orange&left_text=PyPI%20downloads%20per%20month)](https://pepy.tech/project/cvxcla) -[![Coverage Status](https://coveralls.io/repos/github/cvxgrp/cvxcla/badge.png?branch=main)](https://coveralls.io/github/cvxgrp/cvxcla?branch=main) - -## Critical line algorithm - -The critical line algorithm is a method to compute the efficient frontier of a -portfolio optimization problem. - -The algorithm has been introduced by Markowitz in -[The Optimization of Quadratic Functions Subject to Linear Constraints](https://www.rand.org/pubs/research_memoranda/RM1438.html) -and subsequently described in his book [Portfolio Selection](https://www.wiley.com/en-us/Portfolio+Selection%3A+Efficient+Diversification+of+Investments%2C+2nd+Edition-p-9781557861085). - -The algorithm is based on the observation that the efficient frontier is a piecewise -linear function if expected return is plotted over expected variance. -The critical line algorithm computes the turning points, e.g. the corners -of the efficient frontier. - -## Literature - -We are using the following sources - -### Niedermayer and Niedermayer - -They suggested a method to avoid the expensive inversion of the covariance matrix. -[Applying Markowitz's critical line algorithm](https://www.researchgate.net/publication/226987510_Applying_Markowitz%27s_Critical_Line_Algorithm) -It turns that implementing their method in Python is not significantly faster -than the inversion of the covariance matrix relying on LAPACK via `numpy.linalg.inv`. - -### Bailey and Lopez de Prado - -We have initially started with their code published in -[An Open-Source Implementation of the Critical-Line Algorithm for Portfolio Optimization](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2197616). -We have updated their original code and covered it in tests. We have made a few -noteworthy changes: - -* Use a boolean numpy array to indicate whether a weight is free or blocked. -* Rewrote the computation of the first turning point. -* Isolated the computation of $\lambda$ and the update of weights to make them testable. -* Use modern and immutable dataclasses throughout. -* Use GitHub Actions to run tests, create documentation and deploy to PyPI. - -The code is not part of the published package though. -It is only used for testing purposes. We recommend it for educational purposes only. - -### Markowitz et al - -In [Avoiding the Downside: A Practical Review of the Critical -Line Algorithm for Mean-Semivariance Portfolio Optimizatio](https://www.hudsonbaycapital.com/documents/FG/hudsonbay/research/599440_paper.pdf) -Markowitz and a team of researchers from Hudson Bay Capital Management and Constantia -Capital provide a step-by-step tutorial on how to implement the critical line -algorithm. - -We address a problem they oversaw: After finding the first starting point -all variables might be blocked. We need to enforce that one variable is labeled -as free even it sits on a boundary. - -Rather than using their involved construction of the sparse matrix to estimate -the weights we bisect the weights into a free and a blocked part. -We then use a linear solver to compute the weights only for the free part. - -We alter some of their Python code. Our experiments to combine it with Niedermayer's -ideas to accelerate the computation of the matrix inverses did not justify -the additional complexity. - -## Poetry - -We assume you share already the love for [Poetry](https://python-poetry.org). -Once you have installed poetry you can perform - -```bash -make install -``` - -to replicate the virtual environment we have defined in [pyproject.toml](pyproject.toml) -and locked in [poetry.lock](poetry.lock). - -## Jupyter - -We install [JupyterLab](https://jupyter.org) on fly within the aforementioned -virtual environment. Executing - -```bash -make jupyter -``` - -will install and start the jupyter lab. diff --git a/book/docs/index.md b/book/docs/index.md new file mode 120000 index 00000000..fe840054 --- /dev/null +++ b/book/docs/index.md @@ -0,0 +1 @@ +../../README.md \ No newline at end of file From 1e1b438dbe9f5302cf7bf3c93c0af2f7d21dc85c Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:37:46 +0400 Subject: [PATCH 04/12] hooks --- .pre-commit-config.yaml | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index 29e439e4..9d840408 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -8,7 +8,7 @@ repos: - id: check-yaml - repo: https://github.com/astral-sh/ruff-pre-commit - rev: 'v0.11.5' + rev: 'v0.11.11' hooks: - id: ruff args: [ --fix, --exit-non-zero-on-fix ] @@ -16,12 +16,12 @@ repos: - id: ruff-format - repo: https://github.com/igorshubovych/markdownlint-cli - rev: v0.44.0 + rev: v0.45.0 hooks: - id: markdownlint - repo: https://github.com/asottile/pyupgrade - rev: v3.19.1 + rev: v3.20.0 hooks: - id: pyupgrade @@ -46,6 +46,6 @@ repos: - id: validate-pyproject - repo: https://github.com/crate-ci/typos - rev: v1.31.1 + rev: v1.32.0 hooks: - id: typos From 24b9bba7e39dd828f2645c6c9339f67c51733e87 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:38:03 +0400 Subject: [PATCH 05/12] dependencies --- pyproject.toml | 9 +- uv.lock | 780 ++++++++++++++++++++++++------------------------- 2 files changed, 395 insertions(+), 394 deletions(-) diff --git a/pyproject.toml b/pyproject.toml index 9ba94d95..b325548d 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -14,7 +14,8 @@ dependencies = [ ] # add Philipp -authors = [{name = "Thomas Schmelzer", email = "thomas.schmelzer@gmail.com"}] +authors = [{name = "Thomas Schmelzer", email = "thomas.schmelzer@gmail.com"}, + {name = "Philipp Schiele", email = "pschiele@stanford.edu"}] [project.urls] 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cleaner Makefile --- Makefile | 1 - 1 file changed, 1 deletion(-) diff --git a/Makefile b/Makefile index 21337ebf..6787c277 100644 --- a/Makefile +++ b/Makefile @@ -39,4 +39,3 @@ help: ## Show this help message # Marimo & Jupyter marimo: install ## Install a run a Jupyter Lab server uv pip install marimo # Install Marimo - #uv run jupyter lab # Start JupyterLab server (currently commented out) From 96315ceb12025d1788ec90ddf149e6aab09caa69 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:40:55 +0400 Subject: [PATCH 07/12] cleaner Makefile --- Makefile | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/Makefile b/Makefile index 6787c277..c72ea3e2 100644 --- a/Makefile +++ b/Makefile @@ -11,7 +11,7 @@ venv: ## Create a Python virtual environment using uv install: venv ## Install dependencies and setup environment uv pip install --upgrade pip # Ensure pip is up to date - uv sync --dev --frozen # Install dependencies from pyproject.toml + uv sync --dev --frozen --all-extras # Install dependencies from pyproject.toml # Code Quality fmt: venv ## Format and lint code @@ -27,7 +27,7 @@ clean: ## Clean build artifacts and stale branches # Testing test: install ## Run tests uv pip install pytest # Install pytest - uv run pytest src/tests # Run tests in src/tests directory + uv run pytest tests # Run tests in src/tests directory # Help help: ## Show this help message From 7e3f31d8280fe96b8691485e49572e9d1fc9acbc Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:43:31 +0400 Subject: [PATCH 08/12] documented tests --- tests/conftest.py | 60 ++++++++++++++++++++++++++++---- tests/test_aux.py | 43 ++++++++++++++++++++--- tests/test_bailey/test_cla.py | 16 ++++++++- tests/test_bailey/test_schur.py | 27 ++++++++++++-- tests/test_first.py | 36 ++++++++++++++----- tests/test_frontier.py | 25 ++++++++++--- tests/test_markowitz/test_cla.py | 30 ++++++++++++++-- tests/test_numpy.py | 21 ++++++++--- tests/test_solver.py | 28 +++++++++++++-- tests/test_types.py | 58 ++++++++++++++++++++++++------ 10 files changed, 297 insertions(+), 47 deletions(-) diff --git a/tests/conftest.py b/tests/conftest.py index 29dcc2b5..3d82e560 100644 --- a/tests/conftest.py +++ b/tests/conftest.py @@ -1,4 +1,8 @@ -"""global fixtures""" +""" +Global fixtures for testing the cvxcla package. + +This module contains fixtures that are used across multiple test files. +""" from __future__ import annotations @@ -7,33 +11,75 @@ import pandas as pd import pytest +from pandas import DataFrame from cvx.bson import read_bson @pytest.fixture(scope="session", name="resource_dir") -def resource_fixture(): - """resource fixture""" +def resource_fixture() -> Path: + """ + Fixture that provides the path to the test resources directory. + + Returns: + Path to the resources directory + """ return Path(__file__).parent / "resources" @pytest.fixture() -def input_data(resource_dir): +def input_data(resource_dir: Path) -> SimpleNamespace: + """ + Fixture that loads input data from a BSON file. + + Args: + resource_dir: Path to the resources directory + + Returns: + SimpleNamespace containing the input data (covariance, mean, bounds) + """ data = read_bson(file=resource_dir / "input_data.bson") return SimpleNamespace(**data) @pytest.fixture() -def results(resource_dir): +def results(resource_dir: Path) -> SimpleNamespace: + """ + Fixture that loads test results from a BSON file. + + Args: + resource_dir: Path to the resources directory + + Returns: + SimpleNamespace containing the expected test results + """ data = read_bson(file=resource_dir / "results.bson") return SimpleNamespace(**data) @pytest.fixture() -def example(resource_dir): +def example(resource_dir: Path) -> DataFrame: + """ + Fixture that loads example data from a CSV file. + + Args: + resource_dir: Path to the resources directory + + Returns: + DataFrame containing the example data + """ return pd.read_csv(resource_dir / "example.csv", header=0, index_col=0) @pytest.fixture() -def example_solution(resource_dir): +def example_solution(resource_dir: Path) -> DataFrame: + """ + Fixture that loads example solution data from a CSV file. + + Args: + resource_dir: Path to the resources directory + + Returns: + DataFrame containing the example solution data + """ return pd.read_csv(resource_dir / "example_solution.csv", header=0, index_col=None) diff --git a/tests/test_aux.py b/tests/test_aux.py index e0c0b5cf..ce8a3af1 100644 --- a/tests/test_aux.py +++ b/tests/test_aux.py @@ -1,4 +1,7 @@ +from __future__ import annotations + from dataclasses import dataclass +from typing import Any import numpy as np import pytest @@ -10,11 +13,22 @@ @dataclass(frozen=True) class Cla(CLAUX): + """Test subclass of CLAUX for testing purposes.""" + pass @pytest.fixture() -def cla(input_data): +def cla(input_data: Any) -> Cla: + """ + Fixture that creates a Cla instance for testing. + + Args: + input_data: Test data containing covariance, mean, and bounds + + Returns: + A configured Cla instance + """ return Cla( covariance=input_data.covariance, mean=input_data.mean, @@ -27,9 +41,13 @@ def cla(input_data): ) -def test_claux(cla, input_data): +def test_claux(cla: Cla, input_data: Any) -> None: """ - Test that the CLAUX class is initialized correctly + Test that the CLAUX class is initialized correctly. + + Args: + cla: The Cla instance to test + input_data: The input data used to create the Cla instance """ np.testing.assert_equal(cla.covariance, input_data.covariance) np.testing.assert_equal(cla.mean, input_data.mean) @@ -38,7 +56,16 @@ def test_claux(cla, input_data): assert cla.tol == 1e-5 -def test_append(cla): +def test_append(cla: Cla) -> None: + """ + Test the _append method of CLAUX class. + + This test creates a random weight vector, creates a TurningPoint with it, + and tests that appending it to the Cla instance works correctly. + + Args: + cla: The Cla instance to test + """ weights = np.random.rand(10) weights = weights / np.sum(weights) @@ -66,7 +93,13 @@ def test_append(cla): assert fig is not None -def test_raise(): +def test_raise() -> None: + """ + Test that the _append method raises AssertionError for invalid weights. + + This test creates a Cla instance and tests that appending TurningPoints + with invalid weights (sum != 1, outside bounds) raises AssertionError. + """ cla = Cla( covariance=np.eye(2), upper_bounds=np.ones(2), diff --git a/tests/test_bailey/test_cla.py b/tests/test_bailey/test_cla.py index ae978629..fbcf45a3 100644 --- a/tests/test_bailey/test_cla.py +++ b/tests/test_bailey/test_cla.py @@ -1,9 +1,23 @@ +from __future__ import annotations + +from typing import Any + import numpy as np from tests.bailey.cla import CLA -def test_big(input_data, results): +def test_big(input_data: Any, results: Any) -> None: + """ + Test the Bailey CLA implementation against expected results. + + This test verifies that the Bailey CLA implementation produces the expected + lambda values, mean returns, variances, and weights for the turning points. + + Args: + input_data: Test data containing covariance, mean, and bounds + results: Expected results for comparison + """ cla = CLA( mean=input_data.mean, lower_bounds=input_data.lower_bounds, diff --git a/tests/test_bailey/test_schur.py b/tests/test_bailey/test_schur.py index fb80d503..c349d304 100644 --- a/tests/test_bailey/test_schur.py +++ b/tests/test_bailey/test_schur.py @@ -1,10 +1,18 @@ +from __future__ import annotations + import numpy as np import pytest from tests.bailey.cla import _Schur -def test_compute_lambda(): +def test_compute_lambda() -> None: + """ + Test the compute_lambda method of the _Schur class. + + This test verifies that the compute_lambda method correctly calculates + the lambda value and gamma value for different inputs. + """ # Create a _Schur instance with some sample data covariance = np.array([[1, 0.5, 0.2], [0.5, 2, 0.3], [0.2, 0.3, 3]]) mean = np.array([1, 2, 3]) @@ -31,7 +39,13 @@ def test_compute_lambda(): assert np.isclose(actual_gamma, expected_gamma) -def test_compute_weight(): +def test_compute_weight() -> None: + """ + Test the update_weights method of the _Schur class. + + This test verifies that the update_weights method correctly calculates + the new weights for a given lambda value. + """ # Define some test data covariance = np.array([[1, 0.5, 0.2], [0.5, 2, 0.3], [0.2, 0.3, 3]]) mean = np.array([1.0, 1.0, 3.0]) @@ -48,7 +62,14 @@ def test_compute_weight(): np.testing.assert_allclose(actual_weights, np.array([0.75, 0.25, 0.0]), rtol=1e-3) -def test_special_minvar(): +def test_special_minvar() -> None: + """ + Test special cases of the _Schur class for minimum variance portfolios. + + This test verifies that the _Schur class correctly handles special cases + such as freeing an asset that is already at its bound or blocking an asset + that is already at its bound. + """ mean = np.array([0.1, 0.2]) lower_bounds = np.array([0.0, 0.0]) diff --git a/tests/test_first.py b/tests/test_first.py index 20071fdc..671aaa8c 100644 --- a/tests/test_first.py +++ b/tests/test_first.py @@ -1,3 +1,5 @@ +from __future__ import annotations + import numpy as np import pytest @@ -6,8 +8,16 @@ @pytest.mark.parametrize("n", [5, 20, 100, 1000, 10000]) -def test_init_algo(n): - """Compute a first turning point""" +def test_init_algo(n: int) -> None: + """ + Test computing a first turning point with different problem sizes. + + This test verifies that both init_algo and init_algo_lp can compute a valid + first turning point for problems of different sizes. + + Args: + n: The number of assets in the portfolio + """ mean = np.random.randn(n) lower_bounds = np.zeros(n) upper_bounds = np.random.rand(n) @@ -25,9 +35,12 @@ def test_init_algo(n): assert isinstance(first, TurningPoint) -def test_small(): +def test_small() -> None: """ - Test a first turning point + Test computing a first turning point with a small problem. + + This test verifies that both init_algo and init_algo_lp compute the correct + first turning point for a small problem with known solution. """ mean = np.array([1.0, 2.0, 3.0]) lower_bound = np.array([0.0, 0.0, 0.0]) @@ -45,10 +58,12 @@ def test_small(): assert np.allclose(tp.free, [True, False, False]) -def test_no_fully_invested_portfolio(): +def test_no_fully_invested_portfolio() -> None: """ - Test that the algorithm fails if no fully invested portfolio - can be constructed + Test that the algorithm fails when no fully invested portfolio can be constructed. + + This test verifies that both init_algo and init_algo_lp raise a ValueError + when the upper bounds are too restrictive to allow a fully invested portfolio. """ mean = np.array([1.0, 2.0, 3.0]) lower_bounds = np.array([0.0, 0.0, 0.0]) @@ -61,9 +76,12 @@ def test_no_fully_invested_portfolio(): init_algo(mean=mean, lower_bounds=lower_bounds, upper_bounds=upper_bounds) -def test_lb_ub_mixed(): +def test_lb_ub_mixed() -> None: """ - Test that the algorithm fails if lower bounds are greater than upper bounds + Test that the algorithm fails when lower bounds exceed upper bounds. + + This test verifies that both init_algo and init_algo_lp raise a ValueError + when the lower bounds are greater than the upper bounds. """ upper_bounds = np.zeros(3) lower_bounds = np.ones(3) diff --git a/tests/test_frontier.py b/tests/test_frontier.py index 5e615324..d2243324 100644 --- a/tests/test_frontier.py +++ b/tests/test_frontier.py @@ -1,5 +1,8 @@ from __future__ import annotations +from pathlib import Path +from typing import Any + import numpy as np import pytest @@ -10,9 +13,16 @@ @pytest.mark.parametrize("solver", [BAILEY, MARKOWITZ]) -def test_frontier(input_data, solver): +def test_frontier(input_data: Any, solver: type) -> None: """ - Test the frontier both for Bailey and Markowitz + Test the frontier computation for both Bailey and Markowitz implementations. + + This test verifies that both implementations correctly compute the efficient frontier + and that the interpolation of the frontier preserves its properties. + + Args: + input_data: Test data containing covariance, mean, and bounds + solver: The CLA implementation to test (either BAILEY or MARKOWITZ) """ f = solver( covariance=input_data.covariance, @@ -34,9 +44,16 @@ def test_frontier(input_data, solver): @pytest.mark.parametrize("n", [3, 5, 10, 20]) -def test_frontiers(n, resource_dir): +def test_frontiers(n: int, resource_dir: Path) -> None: """ - Compare the frontiers of BAILEY and MARKOWITZ for a variety of dimensions. + Compare the frontiers computed by Bailey and Markowitz implementations. + + This test creates random portfolio optimization problems of different sizes + and verifies that both implementations produce consistent results. + + Args: + n: The number of assets in the portfolio + resource_dir: Path to the test resources directory """ mean = np.random.randn(n) lower_bounds = np.zeros(n) diff --git a/tests/test_markowitz/test_cla.py b/tests/test_markowitz/test_cla.py index d97f96b2..3f23401d 100644 --- a/tests/test_markowitz/test_cla.py +++ b/tests/test_markowitz/test_cla.py @@ -1,11 +1,26 @@ +from __future__ import annotations + +from typing import Any + import numpy as np import pytest +from pandas import DataFrame from cvx.cla.first import init_algo_lp from cvx.cla.markowitz.cla import CLA -def test_solver(input_data, results): +def test_solver(input_data: Any, results: Any) -> None: + """ + Test the Markowitz CLA solver against expected results. + + This test verifies that the Markowitz CLA implementation produces the expected + lambda values, mean returns, and variances for the turning points. + + Args: + input_data: Test data containing covariance, mean, and bounds + results: Expected results for comparison + """ cla = CLA( mean=input_data.mean, lower_bounds=input_data.lower_bounds, @@ -26,7 +41,18 @@ def test_solver(input_data, results): assert np.allclose(results.variance, observed, atol=0.5) -def test_example(example, example_solution): +def test_example(example: DataFrame, example_solution: DataFrame) -> None: + """ + Test the Markowitz CLA solver against a known example from literature. + + This test uses the example from section 3.1 in the Markowitz 2019 paper + to verify that the Markowitz CLA implementation produces the expected results. + It also tests the init_algo_lp function for computing the first turning point. + + Args: + example: DataFrame containing the example data + example_solution: DataFrame containing the expected solution + """ # example from section 3.1 in the Markowitz 2019 paper means = example.mean(axis=0) std = example.std(axis=0, ddof=1) diff --git a/tests/test_numpy.py b/tests/test_numpy.py index efd34042..7ebc2444 100644 --- a/tests/test_numpy.py +++ b/tests/test_numpy.py @@ -1,10 +1,17 @@ +from __future__ import annotations + import numpy as np np.random.seed(42) -def test_last_diagonal(): - """test last diagonal element""" +def test_last_diagonal() -> None: + """ + Test accessing and modifying the last diagonal element of a numpy array. + + This test verifies that the last diagonal element can be accessed and modified + using both explicit indices and negative indices. + """ a = np.zeros((3, 3)) a[2, 2] = 1.0 @@ -14,8 +21,14 @@ def test_last_diagonal(): assert a[-1, -1] == 2.0 -def test_last_column(): - """test last column of a numpy array""" +def test_last_column() -> None: + """ + Test accessing and modifying the last column of a numpy array. + + This test verifies that the last column can be accessed and modified + using both explicit indices and negative indices, and that slicing + operations work correctly. + """ a = np.zeros((3, 3)) a[:, 2] = 1.0 diff --git a/tests/test_solver.py b/tests/test_solver.py index 739e2993..afc90bf2 100644 --- a/tests/test_solver.py +++ b/tests/test_solver.py @@ -1,12 +1,26 @@ +from __future__ import annotations + import numpy as np import pytest +from pandas import DataFrame from cvx.cla.markowitz.cla import CLA as MARKOWITZ from tests.bailey.cla import CLA as BAILEY @pytest.mark.parametrize("solver", [BAILEY, MARKOWITZ]) -def test_example(example, example_solution, solver): +def test_example(example: DataFrame, example_solution: DataFrame, solver: type) -> None: + """ + Test solver implementations against a known example from literature. + + This test uses the example from section 3.1 in the Markowitz 2019 paper + to verify that both solver implementations produce the expected results. + + Args: + example: DataFrame containing the example data + example_solution: DataFrame containing the expected solution + solver: The CLA implementation to test (either BAILEY or MARKOWITZ) + """ # example from section 3.1 in the Markowitz 2019 paper means = example.mean(axis=0) std = example.std(axis=0, ddof=1) @@ -36,7 +50,17 @@ def test_example(example, example_solution, solver): @pytest.mark.parametrize("solver", [MARKOWITZ, BAILEY]) @pytest.mark.parametrize("n", [2, 4, 8, 16, 32, 64, 128]) # , 256, 512]) -def test_init_solver(solver, n): +def test_init_solver(solver: type, n: int) -> None: + """ + Test solver initialization with random problems of different sizes. + + This test creates random portfolio optimization problems of different sizes + and verifies that both solver implementations can be initialized successfully. + + Args: + solver: The CLA implementation to test (either BAILEY or MARKOWITZ) + n: The number of assets in the portfolio + """ mean = np.random.randn(n) A = np.random.randn(n, n) sigma = 0.1 diff --git a/tests/test_types.py b/tests/test_types.py index a80ca1c0..90101780 100644 --- a/tests/test_types.py +++ b/tests/test_types.py @@ -1,3 +1,5 @@ +from __future__ import annotations + import numpy as np import pytest @@ -5,31 +7,67 @@ @pytest.fixture() -def tp(): - """Fixture for turning point""" +def tp() -> TurningPoint: + """ + Fixture that creates a TurningPoint instance for testing. + + Returns: + A TurningPoint instance with predefined weights and free variables + """ return TurningPoint(weights=np.array([0.5, 0.5]), free=np.array([True, False])) -def test_turningpoint(tp): - """Test turning point""" +def test_turningpoint(tp: TurningPoint) -> None: + """ + Test the basic properties of a TurningPoint. + + Verifies that the lambda value is infinity by default and that + the weights and free variables are correctly set. + + Args: + tp: The TurningPoint instance to test + """ assert np.isinf(tp.lamb) assert np.allclose(tp.weights, [0.5, 0.5]) assert np.allclose(tp.free, [True, False]) -def test_indices(tp): - """Test indices. Both free and blocked""" +def test_indices(tp: TurningPoint) -> None: + """ + Test the free_indices and blocked_indices properties of a TurningPoint. + + Verifies that the indices of free and blocked variables are correctly identified. + + Args: + tp: The TurningPoint instance to test + """ assert np.allclose(tp.free_indices, [0]) assert np.allclose(tp.blocked_indices, [1]) -def test_mean(tp): - """Test mean""" +def test_mean(tp: TurningPoint) -> None: + """ + Test the mean method of a TurningPoint. + + Verifies that the expected return is correctly calculated as the dot product + of the weights and the mean vector. + + Args: + tp: The TurningPoint instance to test + """ x = tp.mean(mean=np.array([1.0, 2.0])) assert x == pytest.approx(1.5) -def test_variance(tp): - """Test variance""" +def test_variance(tp: TurningPoint) -> None: + """ + Test the variance method of a TurningPoint. + + Verifies that the expected variance is correctly calculated using + the quadratic form with the covariance matrix. + + Args: + tp: The TurningPoint instance to test + """ x = tp.variance(covariance=np.array([[2.0, 0.2], [0.2, 2.0]])) assert x == pytest.approx(1.1) From 58dda45c8f57dac2d3c189987d75f47d612db8f3 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:46:07 +0400 Subject: [PATCH 09/12] mosek as dev dependency --- pyproject.toml | 3 ++- uv.lock | 16 ++++++++++++++++ 2 files changed, 18 insertions(+), 1 deletion(-) diff --git a/pyproject.toml b/pyproject.toml index b325548d..0f117e75 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -28,7 +28,8 @@ dev = [ "pre-commit==4.2.0", "loguru", "pandas", - "cvxbson" + "cvxbson", + "mosek" ] [tool.ruff] diff --git a/uv.lock b/uv.lock index 27485344..4a0f9c94 100644 --- a/uv.lock +++ b/uv.lock @@ -151,6 +151,7 @@ dependencies = [ dev = [ { name = "cvxbson" }, { name = "loguru" }, + { name = "mosek" }, { name = "pandas" }, { name = "pre-commit" }, { name = "pytest" }, @@ -163,6 +164,7 @@ requires-dist = [ { name = "cvxbson", marker = "extra == 'dev'" }, { name = "cvxpy-base", specifier = ">=1.6.0" }, { name = "loguru", marker = "extra == 'dev'" }, + { name = "mosek", marker = "extra == 'dev'" }, { name = "numpy", specifier = ">=2.1.3" }, { name = "pandas", marker = "extra == 'dev'" }, { name = "plotly" }, @@ -264,6 +266,20 @@ wheels = [ { url = "https://files.pythonhosted.org/packages/0c/29/0348de65b8cc732daa3e33e67806420b2ae89bdce2b04af740289c5c6c8c/loguru-0.7.3-py3-none-any.whl", hash = "sha256:31a33c10c8e1e10422bfd431aeb5d351c7cf7fa671e3c4df004162264b28220c", size = 61595, upload-time = "2024-12-06T11:20:54.538Z" }, ] +[[package]] +name = "mosek" +version = "11.0.20" +source = { registry = "https://pypi.org/simple" } +dependencies = [ + { name = "numpy" }, +] +wheels = [ + { url = "https://files.pythonhosted.org/packages/ed/f5/d54f015f44bc8a2fbdef8d1c15453916cec97e59eb261029821fb6715ef6/mosek-11.0.20-cp39-abi3-macosx_11_0_arm64.whl", hash = "sha256:8fa64362fee4ba0f5d6c861374081394da007f47bfda6a8cfd7d3f030fbbb9c9", size = 8338476, upload-time = "2025-05-07T16:55:59.933Z" }, + { url = "https://files.pythonhosted.org/packages/5c/38/3280321439a5e0b83c228a4e7c8e99bdcee82230b87950565da107f1ef20/mosek-11.0.20-cp39-abi3-manylinux2014_x86_64.whl", hash = "sha256:7906e44d366394681f218c70e4974897dbf99b7ae317d1107ec8446258e36105", size = 14725578, upload-time = "2025-05-07T16:56:04.004Z" }, + { url = "https://files.pythonhosted.org/packages/b9/d3/ed4cb75a7909df7e3a85c7368a31eaafd16d41cfe60673faf83775797723/mosek-11.0.20-cp39-abi3-manylinux_2_29_aarch64.whl", hash = "sha256:e84f80dcdd1eaa7eb64fedd91877d17fbb40e90034f4d2656b493eaefb9264a7", size = 10618981, upload-time = "2025-05-07T16:56:06.93Z" }, + { url = "https://files.pythonhosted.org/packages/36/9a/4f99f1c6ff395a9517f38efcbf72702019bf11ec0c951974cf3ffe266a43/mosek-11.0.20-cp39-abi3-win_amd64.whl", hash = "sha256:971b668dade7653b2abb45e0b42ef3a8ab18d693c9db7d73d8b5f2086a12ac9e", size = 10649438, upload-time = "2025-05-07T16:56:09.18Z" }, +] + [[package]] name = "narwhals" version = "1.34.1" From 5c49097de8f887d7cd302d812cf71c43694af833 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:49:45 +0400 Subject: [PATCH 10/12] experiments --- experiments/fusion1.py | 29 ++++++-- experiments/fusion2.py | 30 +++++++-- experiments/fusion3.py | 121 +++++++++++++++++++++------------ experiments/init_algo.py | 26 +++++++- experiments/minvar.py | 125 +++++++++++++++++++++++++---------- experiments/unconstrained.py | 65 ++++++++++++++++-- 6 files changed, 304 insertions(+), 92 deletions(-) diff --git a/experiments/fusion1.py b/experiments/fusion1.py index 63c87eaa..165749f1 100644 --- a/experiments/fusion1.py +++ b/experiments/fusion1.py @@ -1,7 +1,23 @@ +""" +Basic Linear Optimization Example using MOSEK Fusion API + +This script demonstrates how to solve a simple linear programming problem using MOSEK's Fusion API. +The problem is formulated as: + maximize c^T * x + subject to: + x[1] <= 10.0 + A[0] * x == 30.0 + A[1] * x >= 15.0 + A[2] * x <= 25.0 + x >= 0 +""" + from mosek.fusion import Domain, Expr, Model, ObjectiveSense if __name__ == "__main__": + # Define the coefficient matrix for constraints A = [[3.0, 1.0, 2.0, 0.0], [2.0, 1.0, 3.0, 1.0], [0.0, 2.0, 0.0, 3.0]] + # Define the objective function coefficients c = [3.0, 1.0, 5.0, 1.0] # Create a model with the name 'lo1' @@ -10,17 +26,22 @@ x = M.variable("x", 4, Domain.greaterThan(0.0)) # Create constraints + # Constraint: x[1] <= 10.0 (upper bound on the second variable) M.constraint(x.index(1), Domain.lessThan(10.0)) + # Constraint: A[0] * x == 30.0 (equality constraint) M.constraint("c1", Expr.dot(A[0], x), Domain.equalsTo(30.0)) + # Constraint: A[1] * x >= 15.0 (lower bound constraint) M.constraint("c2", Expr.dot(A[1], x), Domain.greaterThan(15.0)) + # Constraint: A[2] * x <= 25.0 (upper bound constraint) M.constraint("c3", Expr.dot(A[2], x), Domain.lessThan(25.0)) - # Set the objective function to (c^t * x) + # Set the objective function to maximize (c^T * x) M.objective("obj", ObjectiveSense.Maximize, Expr.dot(c, x)) - # Solve the problem - M._solve() + # Solve the optimization problem + M.solve() - # Get the solution values + # Get the optimal solution values sol = x.level() + # Print the solution values for each variable print("\n".join(["x[%d] = %f" % (i, sol[i]) for i in range(4)])) diff --git a/experiments/fusion2.py b/experiments/fusion2.py index b2545870..630a9603 100644 --- a/experiments/fusion2.py +++ b/experiments/fusion2.py @@ -1,27 +1,47 @@ +""" +Portfolio Optimization Example - Maximum Expected Return + +This script demonstrates how to solve a simple portfolio optimization problem using MOSEK's Fusion API. +The problem maximizes the expected return of a portfolio subject to: + - Lower and upper bounds on individual asset weights + - Fully-invested constraint (sum of weights equals 1) + +The input data is loaded from a BSON file containing: + - mean: Expected returns for each asset + - lower_bounds: Minimum allowed weight for each asset + - upper_bounds: Maximum allowed weight for each asset +""" + from mosek.fusion import Domain, Expr, Model, ObjectiveSense from cvx.bson import read_bson if __name__ == "__main__": + # Load portfolio data from BSON file data = read_bson(file="data/input_data.bson") - # Create a model with the name 'lo1' + # Create a model for the maximum expected return portfolio optimization problem with Model("max_expected_return") as M: - # Create variable 'x' of length 4 + # Create variable 'x' representing portfolio weights + # The weights are constrained by the lower and upper bounds from the data x = M.variable( "x", len(data["mean"]), Domain.inRange(data["lower_bounds"], data["upper_bounds"]), ) + # Add the fully-invested constraint: sum of all weights must equal 1 M.constraint("fully-invested", Expr.sum(x), Domain.equalsTo(1.0)) + # Set the objective function to maximize the expected return (mean^T * x) M.objective("expected_return", ObjectiveSense.Maximize, Expr.dot(data["mean"], x)) - # Solve the problem - M._solve() + # Solve the optimization problem + M.solve() - # Get the solution values + # Get the optimal portfolio weights sol = x.level() + # Print the optimal portfolio weights + print("Optimal portfolio weights:") print(sol) diff --git a/experiments/fusion3.py b/experiments/fusion3.py index bf1346bc..71a6d21a 100644 --- a/experiments/fusion3.py +++ b/experiments/fusion3.py @@ -1,53 +1,67 @@ -## -# Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved. -# -# File: portfolio_2_frontier.py -# -# Purpose : Implements a basic portfolio optimization model. -# Computes points on the efficient frontier. -# -## - - -import numpy as np -from mosek.fusion import Domain, Expr, Model, ObjectiveSense - """ -Purpose: - Computes several portfolios on the optimal portfolios by +Portfolio Optimization - Efficient Frontier Computation - for alpha in alphas: - maximize expected return - alpha * variance - subject to the constraints +This script implements a basic portfolio optimization model using MOSEK's Fusion API. +It computes points on the efficient frontier by solving a series of optimization problems +with different risk aversion parameters (alphas). -Input: - n: Number of assets - mu: An n dimensional vector of expected returns - GT: A matrix with n columns so (GT')*GT = covariance matrix - x0: Initial holdings +The optimization problem for each alpha is: + maximize expected return - alpha * variance + subject to: + sum(x) = w + sum(x0) (budget constraint) + x >= 0 (no short-selling) + +Where: + x: Portfolio weights w: Initial cash holding - alphas: List of the alphas + x0: Initial holdings + alpha: Risk aversion parameter -Output: - The efficient frontier as list of tuples (alpha, expected return, variance) +Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved. +Original file: portfolio_2_frontier.py """ +import numpy as np +from mosek.fusion import Domain, Expr, Model, ObjectiveSense + def EfficientFrontier(n, mu, GT, x0, w, alphas): + """ + Compute points on the efficient frontier for a portfolio optimization problem. + + This function solves a series of portfolio optimization problems with different + risk aversion parameters (alphas) to trace out the efficient frontier. + + Args: + n: Number of assets in the portfolio + mu: An n-dimensional vector of expected returns for each asset + GT: A factor matrix such that (GT')*GT = covariance matrix + x0: Initial holdings for each asset + w: Initial cash holding + alphas: List of risk aversion parameters to use + + Returns: + A list of tuples (alpha, expected return, variance) representing points + on the efficient frontier + """ + # Create a MOSEK Fusion model for the efficient frontier computation with Model("Efficient frontier") as M: frontier = [] - # Defines the variables (holdings). Shortselling is not allowed. - x = M.variable("x", n, Domain.greaterThan(0.0)) # Portfolio variables - s = M.variable("s", 1, Domain.unbounded()) # Variance variable + # Define the portfolio weight variables + # Shortselling is not allowed, so weights must be non-negative + x = M.variable("x", n, Domain.greaterThan(0.0)) # Portfolio weights + s = M.variable("s", 1, Domain.unbounded()) # Variable representing portfolio variance - # Total budget constraint + # Add the budget constraint: sum of weights equals initial wealth M.constraint("budget", Expr.sum(x), Domain.equalsTo(w + sum(x0))) - # Computes the risk + # Add the variance computation constraint using a rotated quadratic cone + # This efficiently represents: s >= x^T * Sigma * x, where Sigma = GT^T * GT M.constraint("variance", Expr.vstack(s, 0.5, Expr.mul(GT, x)), Domain.inRotatedQCone()) - # Define objective as a weighted combination of return and variance + # Define the objective function: maximize return - alpha * variance + # Alpha is a parameter that will be varied to generate different points on the frontier alpha = M.parameter() M.objective( "obj", @@ -55,22 +69,33 @@ def EfficientFrontier(n, mu, GT, x0, w, alphas): Expr.sub(Expr.dot(mu, x), Expr.mul(alpha, s)), ) - # Solve multiple instances by varying the parameter alpha + # Solve the optimization problem for each alpha value for a in alphas: + # Set the current alpha value alpha.setValue(a) - M._solve() + # Solve the optimization problem + M.solve() + # Record the solution point (alpha, expected return, variance) frontier.append((a, np.dot(mu, x.level()), s.level()[0])) return frontier if __name__ == "__main__": - n = 8 - w = 1.0 + # Define the portfolio problem parameters + n = 8 # Number of assets + w = 1.0 # Initial wealth + + # Expected returns for each asset mu = [0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379] + + # Initial holdings (all zero in this example) x0 = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] + + # Factor matrix GT such that Sigma = GT' * GT is the covariance matrix + # This is a lower triangular matrix (Cholesky factor of the covariance) GT = [ [0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638], [0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506], @@ -82,28 +107,36 @@ def EfficientFrontier(n, mu, GT, x0, w, alphas): [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202], ] - # Some predefined alphas are chosen + # Define a range of risk aversion parameters (alphas) to trace the efficient frontier + # Alpha = 0 corresponds to maximum return portfolio (risk-neutral) + # Higher alpha values give more weight to risk reduction alphas = [ - 0.0, - 0.01, - 0.1, + 0.0, # Risk-neutral (maximum return) + 0.01, # Very low risk aversion + 0.1, # Low risk aversion 0.25, 0.30, 0.35, 0.4, 0.45, - 0.5, + 0.5, # Moderate risk aversion 0.75, - 1.0, + 1.0, # High risk aversion 1.5, 2.0, 3.0, - 10.0, + 10.0, # Very high risk aversion ] + + # Compute the efficient frontier frontier = EfficientFrontier(n, mu, GT, x0, w, alphas) + + # Print the results in a formatted table print("\n-----------------------------------------------------------------------------------") print("Efficient frontier") print("-----------------------------------------------------------------------------------\n") print("%-12s %-12s %-12s" % ("alpha", "return", "risk (std. dev.)")) + + # Print each point on the frontier with its alpha, expected return, and standard deviation for i in frontier: print("{:<12.4f} {:<12.4e} {:<12.4e}".format(i[0], i[1], np.sqrt(i[2]))) diff --git a/experiments/init_algo.py b/experiments/init_algo.py index 10b32737..4b2fc1a0 100644 --- a/experiments/init_algo.py +++ b/experiments/init_algo.py @@ -1,17 +1,41 @@ +""" +Initial Algorithm Comparison Experiment + +This script compares two different implementations of the algorithm for finding +the first turning point in the Critical Line Algorithm (CLA) for portfolio optimization: +1. init_algo: The standard implementation +2. init_algo_lp: An implementation using linear programming + +Both algorithms compute the first turning point on the efficient frontier, +which is the portfolio with the highest expected return that satisfies the constraints. + +The experiment uses a large-scale problem with 10,000 assets, all having the same +expected return and the same bounds, to test the performance and behavior of both implementations. +""" + import numpy as np from loguru import logger from cvx.cla.first import init_algo, init_algo_lp if __name__ == "__main__": + # Define a large-scale portfolio problem with 10,000 assets n = 10000 + # All assets have the same expected return mean = np.ones(n) + # All assets have the same upper bound of 1.0 upper_bound = np.ones(n) - logger.info("Hello") + logger.info("Starting comparison of initial turning point algorithms") + # Compute the first turning point using the standard implementation tp = init_algo(mean=mean, lower_bounds=np.zeros_like(upper_bound), upper_bounds=upper_bound) + # Print the indices of free variables in the solution + print("Free variables from init_algo:") print(np.where(tp.free)[0]) + # Compute the first turning point using the linear programming implementation tp = init_algo_lp(mean=mean, lower_bounds=np.zeros_like(upper_bound), upper_bounds=upper_bound) + # Print the indices of free variables in the solution + print("Free variables from init_algo_lp:") print(np.where(tp.free)[0]) diff --git a/experiments/minvar.py b/experiments/minvar.py index 35401c82..a9ab4dfe 100644 --- a/experiments/minvar.py +++ b/experiments/minvar.py @@ -1,9 +1,41 @@ +""" +Minimum Variance Portfolio Optimization Experiment + +This script demonstrates different methods to solve the minimum variance portfolio optimization problem: +1. Analytical solution using Lagrange multipliers +2. Solution using Cholesky decomposition +3. Solution using convex optimization with CVXPY + +The minimum variance portfolio problem is formulated as: + minimize (1/2) * w^T * Sigma * w + subject to: + sum(w) = 1 (fully invested constraint) + +Where: + w: Portfolio weights + Sigma: Covariance matrix of asset returns +""" + import cvxpy as cp import numpy as np from loguru import logger def bilinear(mat, left=None, right=None): + """ + Compute the bilinear form: left^T * mat * right + + This function calculates a bilinear form with a matrix and two vectors. + If left or right are not provided, they default to vectors of ones. + + Args: + mat: A square matrix + left: Left vector (default: vector of ones) + right: Right vector (default: vector of ones) + + Returns: + The scalar result of the bilinear form + """ n, m = mat.shape assert n == m, "Matrix must be square" @@ -17,63 +49,88 @@ def bilinear(mat, left=None, right=None): if __name__ == "__main__": + # Set up a small test problem with 3 assets n = 3 + # Generate a random matrix A A = np.random.randn(n, n) + # Create a positive definite covariance matrix Sigma = A*A^T Sigma = A @ A.T + # Problem formulation: # We minimize the variance of the portfolio - # Var = min 1/2 * w'Sigma w - # subject to the constraint that the portfolio is fully invested - # and that all weights are non-negative. - # sum w == 1 - # and w >= 0 + # min (1/2) * w^T * Sigma * w + # subject to the constraint that the portfolio is fully invested: + # sum(w) = 1 - # We can _solve this problem using Lagrange multipliers + # Note: The non-negativity constraint (w >= 0) is not enforced in this example + # to allow for analytical solutions. - # -gamma*(sum w - 1) - # w - s^2 = 0 - # -theta_1*(w_1 - s_1^2) - # -theta_2*(w_2 - s_2^2) + # Method 1: Analytical solution using Lagrange multipliers + # The Lagrangian is: + # L(w, gamma) = (1/2) * w^T * Sigma * w - gamma * (sum(w) - 1) + # Taking derivatives and setting to zero: + # dL/dw = Sigma * w - gamma * 1 = 0 + # dL/dgamma = sum(w) - 1 = 0 - # For now let's drop the constraint of long-only + # From the first equation: w = gamma * Sigma^(-1) * 1 + # Substituting into the second: gamma * sum(Sigma^(-1) * 1) = 1 + # Therefore: gamma = 1 / sum(Sigma^(-1) * 1) - # from + # Calculate gamma (the Lagrange multiplier) gamma = 1 / bilinear(np.linalg.inv(Sigma), left=np.ones(n), right=np.ones(n)) + # Calculate the optimal weights w = gamma * np.linalg.solve(Sigma, np.ones(n)) - logger.info(f"Gamma: {gamma}") - logger.info(f"Weights: {w}") - logger.info(f"Sum of weights: {np.sum(w)}") - logger.info(f"Variance: {w.T @ Sigma @ w}") - - # values are in ascending order - # values, vectors = np.linalg.eigh(Sigma) - # logger.info(f"Min eigenvalue: {np.min(values)}") - - # vector = vectors[:,0] - # a = vector / np.sum(vector) - # logger.info(f"Eigenvalues of Sigma: {values}") - # logger.info(f"Scaled eigenvector: {a}") - # print(a.T @ Sigma @ a) - # print(np.sqrt(values)) - - # print((Sigma @ a)/a) - # MinVar without the non-negativity constraint - # is equivalent to the inverse of the covariance matrix + # Log the results + logger.info("Method 1: Analytical solution using Lagrange multipliers") + logger.info(f"Gamma (Lagrange multiplier): {gamma}") + logger.info(f"Optimal weights: {w}") + logger.info(f"Sum of weights: {np.sum(w)}") + logger.info(f"Portfolio variance: {w.T @ Sigma @ w}") + + # The following code is commented out as it explores an alternative approach + # using eigenvalue decomposition, which is not used in the final solution + # + # # values are in ascending order + # # values, vectors = np.linalg.eigh(Sigma) + # # logger.info(f"Min eigenvalue: {np.min(values)}") + # # vector = vectors[:,0] + # # a = vector / np.sum(vector) + # # logger.info(f"Eigenvalues of Sigma: {values}") + # # logger.info(f"Scaled eigenvector: {a}") + # # print(a.T @ Sigma @ a) + # # print(np.sqrt(values)) + # # print((Sigma @ a)/a) + + # Method 2: Solution using Cholesky decomposition + # The Cholesky decomposition gives Sigma = C*C^T + # We can solve the system more efficiently using this decomposition + print("\nMethod 2: Solution using Cholesky decomposition") + # Compute the Cholesky decomposition of Sigma C = np.linalg.cholesky(Sigma) + # Solve the system C*x = 1 (more efficient than solving Sigma*w = gamma*1) xxx = np.linalg.solve(C, np.ones(n)) + # Normalize to ensure sum(a) = 1 a = xxx / np.sum(xxx) - print(a) - print(a.T @ Sigma @ a) + print(f"Optimal weights: {a}") + print(f"Portfolio variance: {a.T @ Sigma @ a}") + # Method 3: Solution using convex optimization with CVXPY + print("\nMethod 3: Solution using convex optimization (CVXPY)") + # Define the variable representing portfolio weights x = cp.Variable(n) + # Define the objective function: minimize w^T * Sigma * w objective = cp.Minimize(cp.quad_form(x, Sigma)) + # Define the constraint: sum(w) = 1 parameters = [cp.sum(x) == 1] + # Create and solve the optimization problem prob = cp.Problem(objective, parameters) prob.solve() + # Get the optimal weights a = x.value - print(a.T @ Sigma @ a) + print(f"Optimal weights: {a}") + print(f"Portfolio variance: {a.T @ Sigma @ a}") diff --git a/experiments/unconstrained.py b/experiments/unconstrained.py index e10654a0..8d170b6b 100644 --- a/experiments/unconstrained.py +++ b/experiments/unconstrained.py @@ -1,34 +1,91 @@ +""" +Unconstrained Mean-Variance Portfolio Optimization Experiment + +This script explores the analytical solution to the unconstrained mean-variance portfolio +optimization problem for different values of the risk aversion parameter (lambda). + +The unconstrained problem is formulated as: + maximize lambda * (mu^T * w) - (1/2) * w^T * Sigma * w + +Where: + w: Portfolio weights (not constrained to sum to 1 or be non-negative) + mu: Expected returns for each asset + Sigma: Covariance matrix of asset returns + lambda: Risk aversion parameter (controls the trade-off between return and risk) + +Reference: + https://www.cs.ubc.ca/~schmidtm/Courses/Notes/linearQuadraticGradients.pdf +""" + import numpy as np from loguru import logger def f(lamb): + """ + Compute the optimal portfolio weights for a given risk aversion parameter (lambda). + + This function implements the analytical solution to the unconstrained mean-variance + portfolio optimization problem. It calculates the optimal weights and reports + various portfolio characteristics. + + The solution is derived by setting the gradient of the objective function to zero: + lambda * mu - Sigma * w = 0 + + Which gives: w = lambda * Sigma^(-1) * mu + + We then add a term to ensure the weights sum to 1: + w = lambda * Sigma^(-1) * mu + gamma * Sigma^(-1) * 1 + + Where gamma is chosen to ensure sum(w) = 1. + + Args: + lamb: Risk aversion parameter (lambda) + + Global variables used: + Sigma: Covariance matrix + mu: Expected returns + + Prints: + Lambda value, gamma value, optimal weights, sum of weights, and portfolio variance + """ + # Calculate the denominator for gamma: sum(Sigma^(-1) * 1) denom = np.sum(np.sum(np.linalg.inv(Sigma), axis=1)) + # Calculate the numerator for gamma: 1 - lambda * sum(Sigma^(-1) * mu) numerator = 1 - lamb * np.sum(np.linalg.inv(Sigma) @ mu) + # Calculate gamma to ensure the weights sum to 1 gamma = numerator / denom + # Calculate the optimal portfolio weights w = lamb * np.linalg.inv(Sigma) @ mu + gamma * np.sum(np.linalg.inv(Sigma), axis=1) + + # Log the results logger.info("********************************************************") logger.info(f"Lambda: {lamb}") logger.info(f"Gamma: {gamma}") logger.info(f"Weights: {w}") logger.info(f"Sum of weights: {np.sum(w)}") - logger.info(f"Variance: {w.T @ Sigma @ w}") + logger.info(f"Portfolio variance: {w.T @ Sigma @ w}") if __name__ == "__main__": - # https://www.cs.ubc.ca/~schmidtm/Courses/Notes/linearQuadraticGradients.pdf - + # Set up a small test problem with 3 assets n = 3 + # Generate a random matrix A A = np.random.randn(n, n) + # Create a positive definite covariance matrix Sigma = A*A^T Sigma = A @ A.T - # ones = np.ones(n) + # Generate random expected returns mu = np.random.randn(n) + # Test the function with different lambda values + # Lambda = 0: Minimum variance portfolio (no consideration for returns) f(lamb=+0.0) + # Lambda > 0: Increasing weight on expected returns f(lamb=+0.1) f(lamb=+0.2) + # Lambda < 0: Negative weight on expected returns (unusual in practice) f(lamb=-0.1) f(lamb=-0.2) From 5c274a9289b4574569e9a07b83136e0b90216f31 Mon Sep 17 00:00:00 2001 From: Thomas Schmelzer Date: Mon, 26 May 2025 11:51:32 +0400 Subject: [PATCH 11/12] remove sphinx --- book/docs/api.md | 2 +- book/sphinx/_static/custom.css | 1 - book/sphinx/_static/logo.jpeg | Bin 4668 -> 0 bytes book/sphinx/conf.py | 52 --------------------------------- book/sphinx/index.rst | 20 ------------- book/sphinx/license.rst | 4 --- 6 files changed, 1 insertion(+), 78 deletions(-) delete mode 100644 book/sphinx/_static/custom.css delete mode 100644 book/sphinx/_static/logo.jpeg delete mode 100644 book/sphinx/conf.py delete mode 100644 book/sphinx/index.rst delete mode 100644 book/sphinx/license.rst diff --git a/book/docs/api.md b/book/docs/api.md index c804d42f..b8cfa500 100644 --- a/book/docs/api.md +++ b/book/docs/api.md @@ -2,4 +2,4 @@ ## Sphinx -[API](https://www.cvxgrp.org/cvxcla/sphinx/) +[API](https://www.cvxgrp.org/cvxcla/pdoc/) diff --git a/book/sphinx/_static/custom.css b/book/sphinx/_static/custom.css deleted file mode 100644 index 449466a0..00000000 --- a/book/sphinx/_static/custom.css +++ /dev/null @@ -1 +0,0 @@ -.wy-nav-content { max-width: 100% } diff --git a/book/sphinx/_static/logo.jpeg b/book/sphinx/_static/logo.jpeg deleted file mode 100644 index f7a96c73fec244172c503e0029ea1d02d4cafcc0..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 4668 zcmds)cTm&Yw#R=EdNmLPsY;QK(nU%rhpy5)h=52Jks_iHMUfUjIMRh^=p{jV5l{q) z-~mKhq)0~~0tq#Sl*_sI&7C*%=G=Mr&im`FneYB%@4f!`thHv%S~M(e26zgvFflPR zF|sf-GqbX?uyH^*IoR1b&hYSZLqr6{L`4LJh0jVVNuL#0kPsG@(UeuVsH~=@CMK<= zdr3t{NmWgSj+K>_gPlWwlT$$DobWl7f7@v90Wb^j3HSt}69?$QbRaMtt&a`~0CbFW ze>dR2jE)|}z{teR!pg>e3ZSP0f#?}PjEoEnCqH9P-T($LBhNWy114S@FJ|#Dh|1&4 z*DMl-^*wyHqj*VG@4NA=Y^V7J&In4KmzI&0Q&ZQ_yrgy6=r>~%Q!{f5J9`I5CubK| zpPRn7{QLs~!y_W2?nU2^dGa*jSz=OhO4jc$vU76t@(Yk9rDf$6l~vUZjZMuht!?cc zAA0*f_G3N`41OIOpO~D&ew$ugT3%UQ`?0>UN!Z=nKR7%h{vy!`= z9(o1_5Cij{JaqK;P6ProFrHIp;xVvc_6p+_S9#0=G0c2j-@_`QYK!OdzB|fxT2gIM zits1W---TrK=J<((LaIy$wQk4I6!nK2?K!vC~!oQK|W&pzmPn)`#8Eb62U$5e$lJ* zZFB{r!7P&hhHkr!YrTi5`uHIZp~CrgSJ%YY?ui8rm^@_qDveB$)0e3oGO`12bkyej z{B6=kOEMkAFss*P3^nK|IO^^2o%_sG{J^X<^HIOcb6(8eO!UqRsdmlIbLh>bDu zuf%77UiG-I$fZ-!62L6H&B45@?yVWxJR~G~vG(0H#MjDAiNVRHnvBH@k{qz_?imw7 zW{SbbanI~>ay@8(ooYYyZ99GfL*APdw~Z|lfflljHT}{tudJd0InO^V(*RMiuZ?kM zWvy67q95hf7YKdCgen>PkU*}%4iAk(WzM2L*2qY-J2J$QJ`C<#;Ud1ZXD>1py9AmVddW)z z(%0TTX#a?MG1h8U;s<>+6ygxzJHOk&Cmk5@&bB-Ap5j)Zhj=7CALuiCUu=^Che7O|9643)sFx;Wy`=Pq-aUMUp2F(sjC{bX#|`m`@8dwTw8 zB1FizjZF2#&p&^cY&CLlS#~aDn`Z%$`JzT_9Ohb5rSsfhDf#2jH*m%Aa2N?hve&qv zhS$hcrcho_Z<~HMI1(ZVkkhoJ-6+;pstm1T_WA6>7Ya`2h-x9>o>N(*v2gO(A=zVX^nu9%QVcbsi)7m$B%Zvpd_>(I6b+71}+zbxCKGg1X%tm0FkAg7I5#L*o{i z9|hBZMsI>r1>2BLA0Fc4Gf#}pEG`iHc zIXACQS+_`Yik~&N+knfGPU$u8Xz)*xiV>l)fyZ0h5-vW$K5{0;;d)ZUki~h(T-n?T zkHKB;5yeIZ6QA^D`fgh_p< zPfT0N;EpB*X}e^}3xz6XF(sSjTg017`em6dz`eV2Eyr(6G}U+*V%LQ7a_mXqmtrxy zJL%VjjvcdumRNX?TAmu|F*{?)r4)f>Dx)o#i@-mlCSSzn_eYE3no%*KekG0*alGz0 z5%3|}c|5++Rk^ur#Hmh(*h~P~;I~%Ge@D*N@+%Za?EZ9;D_yj|2_9yJCd9nl!vuvY z_6_sMJbzoiUd?1)m%G6G(1ch}uD^HzefNE&nN#aRY6i-L>4mSf7FpQ<5({3Sm>fId zpXFBun(=He0Xt1M#7r>3aIyY3oyJSLZk7br6cwIt^x1~5l9{w54{({7vZzs$=Y5$b zuWcZ5mBPSfwn4(_1kqNXH>X;`D}7XIB6iYV&dwoJy@br=ZZCHYu{~Fyw9x?c*D3hGdKq?CKLt}imPFrx|mJ5P@W*$ zAQC(($E#pYC^!(hS`slrbTWDm4f4hBz$7wnv18}ALPAxjX-gq)b_B_=c+MvHJwu2W z|CDY}SFIoDg~tu|K$M?h8}1`yMeZc%9z~i8U}!*}Lue{=*RC0MeA4HTw%x^b zhNTjFIV$lZM1I*b`RDD#!>pP44_qRG%DhxY6FSn9>#K|Jz}V;tlT^F0 z*}VDHh}(i1A`XeDy9oX!k;_LtP6aRCn6$P$5S9J#X!eb5=@ElyaT^-CAT`@-H>uEY zg_F%Pz2`AzlY7I(Awh0j#NRagwYGYAIq}^R>OrqYfy-$5u}=8gWIu4t%SRe@f3TeS zEcT&APdIw+p$}553F2{WhW$=z|Bfl>3pG)1;!AX@egi=%Ijn5{y!VScy*nnoCEQ`2 z8b(U>_+E^(gsPjynHZ@)X%cv(UKE+l7D0e`sG-z}@lK}W2WwD1J@KK%(hT#_HHYz4 zq19af&~w^%qGw}C+?A-g&?V8_a-t{{Jac*Iu4@d2#Y!_RT*;hE6bTKKGLL+M-k zd}~o5PVcOsO0u-%-#A~^TLcv}HdJ6Ixx)cHZBzZ>_Ic^{G7fN4%}-M8}KI zf4SLuY>0CWOFT1w_yY5z0Det0VpAI>P|&FEU#CFu>rd0RC{k>aDH&g3K5EF3=gH8A zB^{^hHLtre)pl$@_Ni7-Wa&t_xr<#vn_f90O@_a=1>0pcczJs`U47#G^>!03`wvZJ zwW~i_`c2z#o@zu3DvX|NmZIHT?^T3SI;MZRCB4oigs-ct>7i;x-*MfX>>z`ewCh)f z^-rd|6g}Ix8Vs4KWA|5uw27NpSS;7bvUC!xK}Rsy`=NW_)fIRoINhBFNYQ}DPEfpj z@7uFo1df5vh(@;+7|ZI&kH~h0}T~2Xz(uBI2CP zh7Di09_?-+SzpF3&vlosP}L)+Cf;o3y4>bA_AyD3e?dr0y82YitLb-s74D)$=P9z) zudVB`a<(<a%`_l^2G9W8Q5x`mhdSl%^bzq(cKRKqo(7D{Uf-bs zY`70%`@o4)w-s>;BcWmS{k-D<*9*!!ms+1SO~+H^Qo-gTnHr z-~Y+%df@r=J9`_xJ5BdHve<({upJexKRZ03N6vzATi}{TIM!p-ifj=Mq1VzU2CkJ> z4P4Vk+7Q+dzLhx5!x+VPdAmAg;tALUli=Hzw#E=;u~v&0IHsem^q*X5rpu2DDC_5F z5Uqt(yrS=p#q*Q1i=fo*)syMe^`!e*sa47Mi)bocIT^Wj&DdBNZtNpdfZZKFGXI$R zgX9Zp0sTdHeuNu3U93L@Ws_BOYf_*f9lNyC&(G`8;_J!(a<$kd5${u32*|yPm*9sZRV(Qm*5qQphch z#qJSd#=3=1)cz=LWTl)Ph6K=_rAS^4Lkc(?1g-RqWj%O_30e;%d*M{&gm zQ==By0bfIUwtXDoa;4=hLc#%%AmKnh2vE%o*hmJbT@_9_BXDZa!~n7>uWA`_=`)N$ z7v0V`?qs1T@xrWTn93DJ0}gPF$dpM`z(ivqb~u~Gwj+Lax9-eCsdj=UywEw(CPh9d z4dHKU*A-RinJX;(=<-sReZ Date: Mon, 26 May 2025 12:31:04 +0400 Subject: [PATCH 12/12] README --- .pre-commit-config.yaml | 1 + README.md | 197 +++++++++++++++++++++++++++++++--------- 2 files changed, 156 insertions(+), 42 deletions(-) diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index 9d840408..0f390e49 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -19,6 +19,7 @@ repos: rev: v0.45.0 hooks: - id: markdownlint + args: ["--disable", "MD013"] - repo: https://github.com/asottile/pyupgrade rev: v3.20.0 diff --git a/README.md b/README.md index c363a602..93018a3f 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -# ๐Ÿ“ˆ [cvxcla](https://www.cvxgrp.org/cvxcla/book) +# ๐Ÿ“ˆ cvxcla - Critical Line Algorithm for Portfolio Optimization [![PyPI version](https://badge.fury.io/py/cvxcla.svg)](https://badge.fury.io/py/cvxcla) [![Apache 2.0 License](https://img.shields.io/badge/License-APACHEv2-brightgreen.svg)](https://github.com/cvxgrp/cvxcla/blob/master/LICENSE) @@ -8,65 +8,178 @@ [![Open in GitHub Codespaces](https://github.com/codespaces/badge.svg)](https://codespaces.new/cvxgrp/cvxcla) -## ๐Ÿ“Š Critical line algorithm +## ๐Ÿ“‹ Overview -The critical line algorithm is a method to compute the efficient frontier of a -portfolio optimization problem. +`cvxcla` is a Python package that implements the Critical Line Algorithm (CLA) +for portfolio optimization. +The CLA efficiently computes the entire efficient frontier for portfolio optimization +problems with linear constraints and bounds on the weights. -The algorithm has been introduced by Markowitz in -[The Optimization of Quadratic Functions Subject to Linear Constraints](https://www.rand.org/pubs/research_memoranda/RM1438.html) -and subsequently described in his book [Portfolio Selection](https://www.wiley.com/en-us/Portfolio+Selection%3A+Efficient+Diversification+of+Investments%2C+2nd+Edition-p-9781557861085). +The Critical Line Algorithm was introduced by Harry Markowitz +in [The Optimization of Quadratic Functions Subject to Linear Constraints](https://www.rand.org/pubs/research_memoranda/RM1438.html) +and further described in his book [Portfolio Selection](https://www.wiley.com/en-us/Portfolio+Selection%3A+Efficient+Diversification+of+Investments%2C+2nd+Edition-p-9781557861085). -The algorithm is based on the observation that the efficient frontier is a piecewise -linear function if expected return is plotted over expected variance. -The critical line algorithm computes the turning points, e.g. the corners -of the efficient frontier. +The algorithm is based on the observation that the efficient frontier +is a piecewise linear function when expected return is plotted against +expected variance. The CLA computes the turning points (corners) +of the efficient frontier, allowing for efficient representation of the entire frontier. -## ๐Ÿ“š Literature +## โœจ Features -We are using the following sources +- Efficient computation of the entire efficient frontier +- Support for linear constraints and bounds on portfolio weights +- Multiple implementations based on different approaches from the literature +- Visualization of the efficient frontier using Plotly +- Computation of the maximum Sharpe ratio portfolio +- Fully tested and documented codebase + +## ๐Ÿš€ Installation + +### Using pip + +```bash +pip install cvxcla +``` + +### Development Setup + +To set up a development environment: + +1. Clone the repository: + + ```bash + git clone https://github.com/cvxgrp/cvxcla.git + cd cvxcla + ``` + +2. Create a virtual environment and install dependencies: + + ```bash + make install + ``` + +This will: + +- Install the uv package manager +- Create a Python 3.12 virtual environment +- Install all dependencies from pyproject.toml + +## ๐Ÿ”ง Usage + +Here's a simple example of how to use `cvxcla` to compute the efficient frontier: + +```python +import numpy as np +from cvx.cla.markowitz.cla import CLA + +# Define your portfolio problem +n = 10 # Number of assets +mean = np.random.randn(n) # Expected returns +cov = np.random.randn(n, n) +covariance = cov @ cov.T # Covariance matrix +lower_bounds = np.zeros(n) # No short selling +upper_bounds = np.ones(n) # No leverage + +# Create a CLA instance +cla = CLA( + mean=mean, + covariance=covariance, + lower_bounds=lower_bounds, + upper_bounds=upper_bounds, + A=np.ones((1, n)), # Fully invested constraint + b=np.ones(1) +) + +# Access the efficient frontier +frontier = cla.frontier + +# Plot the efficient frontier +fig = frontier.plot(volatility=True) +fig.show() + +# Get the maximum Sharpe ratio portfolio +max_sharpe_ratio, max_sharpe_weights = frontier.max_sharpe +print(f"Maximum Sharpe ratio: {max_sharpe_ratio}") +print(f"Weights for maximum Sharpe ratio portfolio: {max_sharpe_weights}") +``` + +## ๐Ÿ“š Literature and Implementations + +The package includes implementations based on several key papers: ### ๐Ÿ“ Niedermayer and Niedermayer -They suggested a method to avoid the expensive inversion of the covariance matrix. -[Applying Markowitz's critical line algorithm](https://www.researchgate.net/publication/226987510_Applying_Markowitz%27s_Critical_Line_Algorithm) -It turns out that implementing their method in Python is not significantly faster -than the explicit inversion of the covariance matrix relying on LAPACK via `numpy.linalg.inv`. +They suggested a method to avoid the expensive inversion +of the covariance matrix in [Applying Markowitz's critical line algorithm](https://www.researchgate.net/publication/226987510_Applying_Markowitz%27s_Critical_Line_Algorithm). +Our testing shows that in Python, this approach is not significantly +faster than explicit matrix inversion using LAPACK via `numpy.linalg.inv`. ### ๐Ÿ“ Bailey and Lopez de Prado -We have initially started with their code published in -[An Open-Source Implementation of the Critical-Line Algorithm for Portfolio Optimization](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2197616). -We have updated their original code and covered it in tests. We have made a few -noteworthy changes: +We initially started with their code published +in [An Open-Source Implementation of the Critical-Line Algorithm for Portfolio Optimization](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2197616). +We've made several improvements: -* Use a boolean numpy array to indicate whether a weight is free or blocked. -* Rewrote the computation of the first turning point. -* Isolated the computation of $\lambda$ and the update of weights to make them testable. -* Use modern and immutable dataclasses throughout. +- Using boolean numpy arrays to indicate whether a weight is free or blocked +- Rewriting the computation of the first turning point +- Isolating the computation of ฮป and weight updates to make them testable +- Using modern and immutable dataclasses throughout -The code is not part of the published package though. -It is only used for testing purposes. We recommend it for educational purposes only. +This implementation is included for testing and educational purposes only. ### ๐Ÿ“ Markowitz et al -In [Avoiding the Downside: A Practical Review of the Critical -Line Algorithm for Mean-Semivariance Portfolio Optimizatio](https://www.hudsonbaycapital.com/documents/FG/hudsonbay/research/599440_paper.pdf) -Markowitz and a team of researchers from Hudson Bay Capital Management and Constantia -Capital provide a step-by-step tutorial on how to implement the critical line algorithm. +In +[Avoiding the Downside: A Practical Review of the Critical Line Algorithm for Mean-Semivariance Portfolio Optimization](https://www.hudsonbaycapital.com/documents/FG/hudsonbay/research/599440_paper.pdf), +Markowitz and researchers from Hudson Bay Capital Management and Constantia Capital +a step-by-step tutorial. + +We address a problem they overlooked: after finding the first starting point, +all variables might be blocked. We enforce that one variable +labeled as free (even if it sits on a boundary) to avoid a singular matrix. + +Rather than using their sparse matrix construction, we bisect the +weights into free and blocked parts and use a linear solver for the free part only. + +## ๐Ÿงช Testing + +Run the test suite with: + +```bash +make test +``` + +## ๐Ÿงน Code Quality + +Format and lint the code with: + +```bash +make fmt +``` + +## ๐Ÿ“– Documentation + +- [Online Documentation](https://www.cvxgrp.org/cvxcla/book) +- [API Reference](https://www.cvxgrp.org/cvxcla/pdoc/) + +## ๐Ÿ‘ฅ Contributing + +Contributions are welcome! Please feel free to submit a Pull Request. -We address a problem they oversaw: After finding the first starting point -all variables might be blocked. We need to enforce that one variable is labeled -as free even it sits on a boundary otherwise the matrix needed is singular. +1. Fork the repository +2. Create your feature branch (`git checkout -b feature/amazing-feature`) +3. Run the tests to make sure everything works (`make test`) +4. Format your code (`make fmt`) +5. Commit your changes (`git commit -m 'Add some amazing feature'`) +6. Push to the branch (`git push origin feature/amazing-feature`) +7. Open a Pull Request -Rather than using their involved construction of the sparse matrix -to estimate the weights we bisect the weights into a free and a blocked part. -We then use a linear solver to compute the weights only for the free part. +## ๐Ÿ“„ License -We alter some of their Python code. Our experiments to combine it with Niedermayer's -ideas to accelerate the computation of the matrix inverses did not yet justify -the additional complexity. +This project is licensed under the Apache License 2.0 - see the [LICENSE](LICENSE) +file for details. -## ๐Ÿ” previous work +## ๐Ÿ” Related Projects -In the [repo](https://github.com/phschiele/PyCLA) by Philipp Schiele. +- [PyCLA](https://github.com/phschiele/PyCLA) by Philipp Schiele - A +previous implementation of the Critical Line Algorithm in Python.